2 The origins of our universe

Laws, testability and observability in cosmology

Michela Massimi and John Peacock

Introduction: cosmology — from a branch of metaphysics to scientific discipline

Over the past few years, philosophers of science have paid increasing attention to cosmology. This renewed philosophical attention to cosmology comes in the aftermath of the experimental confirmation of an accelerating expansion of the universe (via observations of Type la supernovae, for which the 2011 Nobel Prize was awarded). It comes also at a time when cosmology is witnessing a wealth of new data coming from large spectroscopic and photometric galaxy surveys, designed to give an answer to pressing questions about the existence of dark matter and dark energy.

For a very long time, cosmology was regarded as somehow having a special status compared with other sciences, closer to philosophy than to mathematical physics. Although the study of the cosmos was well known to ancient civilizations (from the Babylonians to ancient Greeks and the Maya, among others), the term 'cosmology' is much more recent (dating back to the seventeenth or eighteenth century). And even then, the term was often used interchangeably with 'cosmogony', as a generic term for any theory about the origin of the universe. Such cosmogonies were often of philosophical-religious flavour, and involved speculations that eluded the mathematical rigour and experimental tests typical of the new sciences emerging with the scientific revolution.

Consider Newton's Mathematical Principles of Natural Philosophy (1st edn, 1687). This extraordinary book laid the foundations of modern physics, by providing testable laws of nature that could explain a variety of observed phenomena (from free fall to planetary motions). Yet Newton's mathematical physics did not explain what set planets in motion at the origins of the universe. Explaining the origins of our universe, how planets and stars formed, how they evolved, and what set them in motion, was beyond the scope of Newton's Principia. And the task was often taken up by philosophers in the context of either a discussion of Newton's natural philosophy (e.g. Maupertuis in his 1732 Discours sur les differentes figures des astres), or in the context of metaphysics. For example, the German philosopher Alexander Baumgarten (1714-62) in his 1739 book Metaphysics, Part 2 (§§351—2) dedicated to Cosmology, distinguished between empirical cosmology as the 'science based upon experience that is nearest to hand', and rational cosmology 'based upon the concept of the world'. He concluded that since cosmology contained the first principles of psychology, physics, theology, teleology, and practical philosophy, cosmology should belong to metaphysics. A similar classification of cosmology can also be found in another influential German philosopher of the time, Christian Wolff (1679-1754) in his Cosmologia generalis. Why was cosmology regarded as a branch of metaphysics? And why did it take so long for cosmology to become a science in its own right? An easy answer to both questions comes to the fore. One may be tempted to reply that cosmology could not have risen to the status of a proper science until sufficient technological advances made available the right kind of data. Yet, this answer - simple and natural as it is - is not sufficient to answer these questions. A more comprehensive answer to these questions has to address the relation between cosmology and metaphysics in the eighteenth century, first; and, second, the specific problems and challenges that cosmology faces as a science. Let us discuss each of these two points in turn.

That cosmology was for so long regarded as a branch of metaphysics should not come as a surprise. While Newton in the Principia offered rigorous mathematical demonstrations of phenomena and refused to indulge in speculative hypotheses about the causes of those phenomena, the job of speculating about the causes of phenomena (and, the very first causes of the world) was left to theologians and metaphysicians. Thus, cosmology, in works such as those of Baumgarten or Wolff, became a rational exercise in examining the concept of the 'world" or 'universe' as a multitude of finite beings; the nature of their interconnections; the contingency and necessity of the parts and the whole and so forth. In the aftermath of Principia, across the Continent (in Germany in particular) there was a widespread feeling that Newton's mathematical method was insufficient to shed light on key questions about the origins of the universe. This widespread feeling, and the necessity of supplementing Newton's mathematical demonstrations with metaphysical foundations, found its most influential expression in the work of the German philosopher Immanuel Kant (1724-1804). One of the first attempts at a modern metaphysical explanation of the origin of the universe, according to Newtonian principles, can be found in Kant's 1755 Universal Natural History and Theory of the Heavens, whose subtitle reads Essay on the constitution and the mechanical origins of the whole universe according to Newtonian principles. In this text, Kant hypothesized that the universe at its origin was not a vast empty space (as Newtonian physics suggested), but was instead filled with a 'fine matter', on which two fundamental, Newtonian forces acted. Attraction was a force capable of lumping the fine matter into what became the bodies of planets and stars; repulsion was a force balancing attraction and causing fine matter to whirl in vortices that would become the nucleation sites for planets and stars. While both attraction and repulsion can be found in Newton as fundamental forces of nature, both in the Principia and in the Optics, Kant's original take on Newton consisted in using these two forces to offer an explanation of the presumed mechanism at play in the constitution of the universe. Kant's explanation in terms of a counterbalance between attraction and repulsion of Tine matter' diffused across space, provided metaphysical foundations for Newton's physics, foundations that at the time were regarded as essential for answering open cosmological questions. In so doing, Kant also laid the foundations of what became later known as the Kant-Laplace nebular hypothesis, one of the very first attempts at a scientific explanation of the origins of the universe from an original nebula of gases (see Brush 1996). Here we see exemplified a first important interaction between philosophy and the sciences. Kant's 1755 cosmogony shows how philosophy (in this case, metaphysics) played a heuristic role in the development of some important scientific ideas.

Yet Kant himself remained sceptical about the possibility of developing cosmology as a science, because the metaphysical idea of a universe having a beginning in time and space seemed fraught with contradictions (what Kant called antinomies of reason in his mature work). To Kant's eyes, metaphysics did not give a clear answer to the big questions about the origins and evolution of the universe. Thus, at the end of the eighteenth century the prospects of further developing cosmology as a branch of metaphysics looked dim, and the path to cosmology as a science seemed still very long. Why did it take so long for cosmology to become a science in its own right? It was not just that the eighteenth-century metaphysical foundations of cosmology proved fraught with contradictions. Three main problems stood in the way of developing cosmology as a science in its own right. We review each of them briefly here.

1 Laws of nature

Scientific theories allow scientists to make inferences based on laws of nature. For example, given Newton's law of gravity, scientists can make inferences about planetary motions no less than the free fall of an apple, or the times of the tides. Philosophers of science have long been investigating what a law of nature is, and the allegedly universal validity and necessity of the laws. A specific problem arises in cosmology when we try to use our current laws of nature to make inferences about the origins of our universe. How can we be sure that the same laws of nature we know and love today, apply also to the origins of the universe? Did not our laws presumably come into existence with the existence of our universe? How can we extrapolate from the present physics and its laws to the physics of the early universe?

2 Uniqueness

The other problem with cosmology is the uniqueness of its object of investigation: our universe (for a discussion of this point, see Smeenk 2013, §4). If cosmology has to have the status of an experimental science, it should be possible to run experiments to test hypotheses. But running an experiment typically involves being able to repeat the test more than once, and on several different samples. For example, to test the law of free fall, Galileo had to perform the same experiment with balls rolling down planes of different lengths and inclinations. Or, when in the nineteenth century, the physicists Fizeau, Foucault and Maxwell performed tests to establish the value of the velocity of light in empty space, they repeated the same experiment with a beam of light going through spinning mirrors across a variety of media (water, air). If repeating tests on multiple samples of the same kind (e.g. Galileo's inclined planes) and/or in different circumstances (e.g. in air or water) is key to testing a scientific theory, then again the prospects for cosmology as a science may look prima facie unpromising. We have only one universe to observe and experiment upon - ours. In the words of a prominent physicist (Ellis 2014, p. 6): 'Cosmology is the unique case where there is no similar entity with which we can compare the object of study, because by definition the Universe is all that there is*. So, if testability so conceived is a distinctive feature of experimental science, cosmology seems to face a problem.

3 Unobservability

A third problem with cosmology, somehow related to the first one, concerns the extent to which we can extrapolate information from our current vantage point (our planet Earth) to the universe as a whole. The problem does not affect just theoretical inferences based on laws of nature, which might break down or not be valid at the origins of our universe. It affects also the amount of information and data we can access from our vantage point, considering the speed-of-light limit, which constrains how far back into the history of our universe we can 'observe', so to speak. There are bound to be vast regions of our universe that will remain unobservable from the vantage point of an observer on Earth.

The unobservability of scientific entities has been at the centre of a lively debate in philosophy of science over the past 30 years between defenders of so-called scientific realism, who claim that our beliefs in the existence of unobservable entities (be they electrons, quarks, DNA, bacteria or other) is justified, and defenders of a variety of scientific anti-realism (for details about this debate, see Massimi 2013). Let us be clear on this point. The unobservability affecting cosmology has nothing to do with its objects being not-observable-to-our-naked-eyes (as in the realism-anti-realism debate), although cosmologists often resort to computer techniques to produce visualizations of cosmological entities. Nor does unobservability affect scientists" ability to make theoretical inferences about the universe. Progress can be made by starting with educated guesses, such as the cosmological principle, that the universe is homogeneous and isotropic, i.e. it is the same in all spatial positions and directions, no matter from which vantage point it may be observed. Initially, we only know that conditions are isotropic from the vantage point of the Milky Way, so it is a significant leap to assert that this property must hold for all observers. To make such an argument, it is necessary to add the Copernican principle: that our place in the universe should not be special. Although this sounds like common sense, it is clearly a critical extra step. But having made this assumption, we gain the framework of a simple uniform universe to act as a model for the interpretation of data. Better still, with sufficient data, the initial guess can be tested: we now possess three-dimensional surveys of the positions of around 1 million galaxies, from which it is possible to verify that the density of galaxies is indeed highly uniform on sufficiently large scales i.e. the cosmological principle has moved from being an educated guess to something that is supported empirically.

This need for cosmology to proceed in such an initially ill-founded manner highlights a specific problem about unobservability in cosmology: our vantage point as observers in the universe constrains all the information we can access to the events in the so-called past light cone, i.e. parts of space that have been able to send information to us. This horizon problem comes in two forms with different degrees of severity. At the most basic level, objects more than about a distance ct away (where c is the speed of light) cannot be seen before a time /; this in itself is not a huge objection in principle, since it might be presumed that our horizon will grow and any object will eventually be seen, however distant. But in an accelerating universe, there exists an event horizon: points sufficiently far apart can never contact each other.

Despite these three distinctive methodological problems, cosmology has come a long way from the time of the Kant-Laplace nebular hypothesis, and has established itself as a scientific discipline in its own right within just over a century. The path that led cosmology from a branch of metaphysics to a proper science has not been without difficulties and lively philosophical discussions. Still in 1950, W. H. McCrea complained that cosmology was a 'highly unsatisfactory subject, and in 1954, G. J. Whitrow (1954, p. 272) lamented that 'many physicists find it [i.e. cosmology] so baffling compared to other branches of physics that they pay as little attention to current cosmological theories as to the original theory of Thales'. In the next section, we briefly review some of the milestones in the history of theoretical and observational cosmology of the last century. We return to the issues of laws, uniqueness and unobservability at the end of the chapter, where we draw some philosophical conclusions about what philosophers can learn from the practice of cosmology.

The expanding universe: a very brief history of observational and theoretical cosmology

The history of cosmology shows a striking interplay of empirical discovery integrated into a theoretically motivated framework. The pace of this progress has been astonishingly rapid: a century ago, our general knowledge about the important features of the universe barely differed from that of the stone age, whereas today there is a sense that observational study of the universe is converging. This may seem paradoxical: how can our knowledge of a (probably infinite) universe be complete? The answer is that we inhabit an evolving universe, which we study using signals that propagate at the speed of light. This latter fact is convenient in that it leads to the cliche that 'telescopes are time machines' - we see distant parts of the universe as they were in the deep past. But at early enough times, rather little had happened; in particular the galaxies that host the stars and planets important for life had yet to form. In some areas of the sky, we have thus been able to use instruments like the Hubble Space Telescope to look back to a time before the galaxies existed so we know that no more than about 100 billion galaxies exist to be imaged even if we could study the whole sky with unlimited sensitivity. Within a decade, it is possible that a significant fraction of this task will have been accomplished. But it is not necessary to go so far, as we already know that the universe is highly uniform on large scales, so progress in understanding the history of the expanding universe is possible by studying only part of it. The fraction that has been observed in detail is now large enough that future observations will only shrink statistical errors that are already rather small in most cases.

The discovery of the expanding universe makes an interesting piece of history. As is often the case in science, cosmology has its 'creation myth' in the form of a simplified story that is seriously at variance with the actual events. It is thus 'well known' that the expansion of the universe was discovered by Edwin Hubble in 1929, when he demonstrated that galaxies displayed a redshift (displacement of spectral features to longer wavelengths) that increased linearly with distance. Assuming for the present that the redshift can be interpreted as a Doppler shift indicating a radial velocity, v, this result can be written as Hubble's law relating the velocity to distance, D: v = HD (the issue of how to interpret the redshift is discussed in detail below). The constant of proportionality is the Hubble constant; this is now known to be about 70 km s^-1 Mpc^-1 (1 Mpc is 3 x 10²² m, which is also the typical distance between galaxies). The reciprocal of H has the unit of time, with a value of about 14 billion years; as we will see, this tells us that the expansion of the universe has been taking place for about such a period. This can be made plausible by considering the simplest model for Hubble"s law: a single explosion. Explode a grenade at a point at time t = 0 and debris will fly off at various speeds, reaching distances D = v t. Thus, we get Hubble's law with H = 1/t. This is a dangerous analogy with the true Big Bang, which was absolutely not a single explosion that filled previously empty space; nevertheless, it gives some insight into what Hubble's law might mean.

Perhaps the biggest problem with this tale is that the universal redshift, indicating expansion, was actually discovered by V. M. Slipher, at the Lowell Observatory in Arizona. For nearly a decade, starting in 1912, this virtuoso experimentalist was the only astronomer capable of making these observations, and the recent centenary of his revolutionary discovery received surprisingly little notice (although see Way and Hunter 2013). By 1917, Slipher had measured radial velocities for 25 galaxies, which were positive in twenty-one cases (four nearby galaxies actually approach the Milky Way). Thus the tendency for the system of galaxies to expand on average was already empirically demonstrated at this time. Establishing that the expansion is uniform (i.e. Hubble's law) is much harder - and we now know that Hubble's 1929 sample is far too shallow to prove such a relation convincingly.

But in the meantime, theorists had not been standing idle. Einstein wrote down his relativistic gravitational field equations in 1915, improving on Newton's law of gravity, which had survived unchanged for over two centuries. However, Einstein realized that his new equations did not solve a challenge that had puzzled Newton: what happens to an infinite uniform distribution of matter? Both Einstein and Newton thought that it was obvious that the matter should stay in place, based on the apparently unchanging nature of the heavens. But Einstein realized that this was only possible if there was some means of countering the gravitational force that would otherwise tend to pull the matter together. He therefore changed his field equations in 1917 specifically in order to permit a static cosmological solution - ironically unaware that Sliphers work had just rendered this unnecessary. Einstein's adjustment was to introduce the cosmological constant, A, which he viewed as representing the curvature of spacetime even in the absence of matter. Today, it is more common to view this as an energy density associated with the vacuum, so that all of space is in effect filled with a substance that cannot be removed (for which the modern name is dark energy - see next chapter). In any case, the gravitational effect of this term (discussed in more detail in the next chapter) opposes the attraction of normal matter, allowing the desired static universe. But almost immediately the situation became more complicated. In 1917, de Sitter showed that Einstein's field equations could be solved by a model that was completely empty apart from the cosmological constant - i.e. a model with no matter whatsoever, just dark energy. This was the first model of an expanding universe, although this was unclear at the time. The whole principle of general relativity was to write equations of physics that were valid for all observers, independently of the coordinates used. But this means that the same solution can be written in various different ways, some of which were easier to interpret than others. Thus de Sitter viewed his solution as static, but with a tendency for the rate of ticking of clocks to depend on position. This phenomenon was already familiar in the form of gravitational time dilation (clocks deep in gravitational potential wells run slow), so it is understandable that the de Sitter effect was viewed in the same way. It took a little while before it was proved (by Weyl, in 1923) that the prediction was of a redshifting of spectral lines that increased linearly with distance (i.e. Hubble's law). Now, experimental scientists love a theoretical prediction, as they can't lose by testing it; so it is unsurprising that a number of astronomers set out to search for the de Sitter effect as a tendency for redshift to increase with distance. And at least three of them had found such evidence prior to Hubble's 1929 paper. There is no doubt that Hubble was influenced by the de Sitter-Weyl prediction: he cites earlier searches, and concludes ' ... the velocity-distance relation may represent the de Sitter effect ... \ So this is far from being a pure observational discovery, unlike SIipliers pioneering efforts.

From an interpretative point of view, what is fascinating is that Hubble did not say 'the universe is expanding', and indeed it took some while for this to become clear. The general solution of Einstein's equations for matter plus cosmological constant was given in a pair of papers by the Soviet cosmologist Friedmann in 1922 and 1924. The second paper was especially notable for introducing the idea of an infinite open universe of negative spatial curvature. The idea of spatial curvature is already radical, but it can just about be grasped intuitively by considering the surface of a sphere as an example of a curved surface embedded in a three-dimensional space. By analogy, we might imagine that 3D space itself could share a similar property: unbounded, but finite, so that you return to your starting point if you attempt to travel along a straight line in a single direction. Such a model would be termed a closed universe, and Einstein thought it was very likely that the real universe should be closed in this way. But the mathematics of such curvature admits another possibility: negative curvature. This is actually impossible to visualize in the same way: the surface of a sphere has uniform positive curvature, but no surface of uniform negative curvature exists. The best that can be done is to think locally. Without spatial curvature, the angles of a triangle add up to 180 degrees, but a triangle drawn on a sphere will have angles summing to more than 180 degrees; the sign of negative curvature is that the sum would be less than 180 degrees. A saddle has a point of negative curvature where the rider sits. Realizing that the universe might have such a property - curved but still infinite - was a huge leap forward. But although Friedmann did say explicitly that his solutions were non-stationary, and that the curvature of space depended on time, a clear and direct statement that the universe was expanding, with galaxies moving apart from each other, was not given until Lemaître's 1927 work, and not really widely appreciated until this appeared in English translation in 193].

But how certain are we that this modern way of looking at things is the correct, or indeed the only, way of interpreting the data? Empirically, answering this question is not so straightforward: we measure redshifted radiation here today, but we have no direct means of measuring the properties of the radiation as it was emitted, or of studying what happens to it en route. We know from terrestrial experiments that the frequency of radiation can be shifted either by the Doppler effect of motion, or gravitationally, so it is natural to assume that the cosmological effect is some combination of these effects. It is easy to show that gravitational time dilation should scale quadratically with distance, so that the Doppler effect should be the dominant process at small separations. It is striking that Slipher had the confidence to assert this interpretation in his first (1913) paper on galaxy spectroscopy ' ... we have at the present no other interpretation for it. Hence we may conclude that the Andromeda Nebula is approaching the solar system ...'. Although the velocity of Andromeda seems very small today (300 km s^-1), it was very large for the day, and its Doppler origin might have been queried.

Indeed, it is a reasonable concern that there might be physical mechanisms for frequency shifts that are only detectable on cosmological scales. A well-known example is Zwicky's 1929 tired light hypothesis: that photons lose energy as they travel over large distances through some unspecified dissipative effect. This can be tested in a number of ways, most simply using the fact that the Doppler shift is a form of time dilation: receding clocks appear to run more slowly. Atomic clocks are one example, leading to the shift of spectral lines, but the time dilation would also apply to macroscopic objects. A perfect example for this application is provided by Type la supernovae; these exploding stars are very nearly standard objects, both in their energy output and in the history of their emission, which rises to a peak about two weeks after explosion, and then declines over a similar period. These have been seen at large enough distances that the redshifting stretches wavelengths by over a factor of 3 - and indeed these distant supernovae appear to evolve more slowly by just this factor.

A more subtle alternative interpretation of redshifting is given by the concept of expanding space, which is a frequent source of confusion. The expansion of an ideal symmetric universe is uniform, so that the separations of all pairs of particles increase by a common factor over a given period of time. If the volume of the universe is finite, then the total volume of space undoubtedly increases with time - as can be seen intuitively in the common analogy of galaxies as dots painted on the surface of an inflating balloon. Moreover, the redshift factor turns out to be exactly proportional to the expansion factor: if we receive light from a galaxy where the wavelength of a spectral feature is twice the laboratory value, we know that this light was emitted when the universe was half its present size. This suggests a picture where the galaxies are not really moving, but the space between them is 'swelling up', stretching light as it does so; this explanation is to be found in innumerable introductory textbooks and semipopular articles. So what causes redshift? Is it the Doppler effect or expanding space? Or, are they equivalent descriptions of the same thing? At the level of a uniform universe, the expanding-space viewpoint may be more attractive, since it can deal simply with very large redshift factors, which require one to worry about relativistic corrections in a Doppler interpretation. But expanding space as a general concept is problematic, and can easily lead the unwary to incorrect conclusions. For example, does the expansion of space apply in the solar system? Is the Earth trying to move away from the sun? What prevents it from doing so?

The answer is that the expansion of space cannot be detected locally. The problem is that our physical intuition is influenced by imperfect analogies like the inflated balloon, where the rubber surface has friction. If you stood on a rubber sheet, you would notice if it stretched, since friction at your shoes would pull your feet apart - but what about a perfectly frictionless surface, such as an ice rink? There, the expanding surface would slide under your feet in an undetectable way. Similarly, there is no additional frictional force in three dimensions that corresponds to the expansion of the universe trying to pull things apart, even though it is unfortunately commonly believed to be the case. The issue here is related to the concept of the ether, which was the hypothetical medium whose oscillations constituted light waves. Prior to special relativity, there seemed to be a paradox: the speed of light should apparently depend on the motion of the observer relative to the ether, but no such effect had been detected. Einstein did not disprove the existence of the ether, but he explained why motions relative to it could not be detected. But a physical concept that cannot be detected is not of much practical use. A similar view should be taken of expanding space: it adds nothing to the simple view of the expanding universe as consisting locally of galaxy motions in a spacetime that is extremely close to that of special relativity.

Even once the basic nature of expansion at a given instant has been clearly grasped, however, the expanding universe has more puzzles in store once we think about its evolution. Running a video of the expansion backwards inevitably tells us that at earlier times the universe was denser and hotter. A little more thought along these lines shows that the energy density of the early universe was actually dominated by radiation, rather than ordinary matter. As things are compressed, conserving particles causes the density to rise: when the universe was half its present size, the volume was 2³ = 8 times smaller, so the number density of all particles was 8 times greater, including photons. But because of redshifting, each photon was twice as energetic in the past: so the energy density in radiation was 16 times greater. Continuing this process, and using E = mc². we can therefore see that the mass density of the universe will be dominated by the radiation if we go back far enough. And according to Einstein's relativistic theory of gravity, a radiation-dominated universe cannot expand forever: at a finite time in the past, the extrapolation of the expansion reaches a singularity, where the density becomes infinite.

This was recognized early on as a major problem, since, as we mentioned at the beginning of this chapter, the laws of physics cannot follow nature's behaviour to times before the singularity, on pain of a huge inductive leap. Fred Hoyle proposed instead the steady-state universe, in which matter was continually created so as to allow eternal expansion (i.e. the density was not larger in the past). In 1949, Hoyle criticized the simple radiation-dominated model as having an unexplained start as 'a big bang' - but there is now abundant evidence that the universe did pass through a hot and dense early phase, and the Big Bang is a commonly used term for this period.

Figure 2.1 An all-sky image ol the cosmic microwave background, from the European Space Agency's Planck satellite. The emission at wavelengths around one millimetre has been carefully cleaned of contributions from our own Milky Way, to show the relic radiation that has been travelling since the universe was smaller than at present by a factor 1,100. The intensity displays small fluctuations of around 1 part in 100,000: these are the seeds of subsequent structure formation, and a window into the earliest times. According to the theory of inflationary cosmology, we are staring at amplified quantum fluctuations, generated when the entire visible universe was of subnuclear dimensions. (Copyright photo: European Space Agency)

The most direct evidence for a hot early phase is the cosmic microwave background (CMB, see Figure 2.1). This was discovered serendipitously in 1965, although its existence was predicted. It is inevitable that the universe must contain a last scattering surface, at the point where the temperature drops to a few thousand degrees and matter changes from an ionized plasma into neutral atoms. Thereafter, radiation can propagate freely, so that we should see the entire sky blazing like the surface of the sun - except cooled by the fact that the last scattering surface lies at high redshift. In practice, the observed radiation corresponds to a present-day temperature of 2.725 degrees (Kelvin), for which black-body emission peaks near a wavelength of 1 milli-metre; this originates when the universe was about 1,100 times smaller than today. This is the furthest back in time we can ever see (about 400,000 years after the Big Bang singularity) using electromagnetic radiation, and it shows us the universe in a relatively simple state, prior to the formation of complex structures such as galaxies. The CMB is thus a treasure trove of information about the nature of the universe, and how it reached its present form.

In particular, the CMB radiation is found to contain small fluctuations with direction on the sky, of around 1 part in 100,000. These represent small fluctuations in the density of matter at early times, which are expected to grow under their own gravitational attraction into larger fluctuations today: the galaxies themselves, together with their large-scale clustering into super-clusters, which make up patterns of extent over 100 million light years. The existence of galaxy clustering has been known since the 1930s, and it was used to predict the necessity for small fluctuations in the CMB radiation, which were finally detected by NASA's COBE satellite in 1992. Observing the build-up of structure in the universe has been a great triumph, but it introduces another puzzle with the Big Bang: the way that gravitational instability works implies that the fluctuations in the curvature of spacetime remain constant at early times, so that the spacetime could not have been perfectly uniform near the time of the Big Bang. So not only did the entire expanding universe appear from nowhere, but it already carried within it the seeds of the future structure. All these strange initial conditions cry out for a direct explanation, which arose in the 1980s in the form of inflationary cosmology, discussed in Chapter 4.

But despite the puzzles associated with the Big Bang singularity, we can be confident that the Big Bang model does describe the universe for a large portion of its expansion. This conclusion does not require us to see directly beyond the last-scattering era, since there are indirect relics of earlier and hotter phases. The most well-understood of these relics is in the form of the light chemical elements. Via spectroscopy, we know that all stars are mostly composed of hydrogen, followed by helium (about 25 per cent of their mass), and trace amounts of all other elements. Although nuclear reactions in stars do generate helium, the lack of any hydrogen-only stars shows that the helium must have predated the first stars - i.e. it was formed by nuclear reactions at early times. The theory of primordial nucleosynthesis follows these reactions, and shows that the observed helium fraction is inevitable. This is a great triumph, giving an indirect view of conditions in the universe back to temperatures of around 10¹⁰ degrees (Kelvin) and times of 1 second.

Cosmology and scientific methodology: a primer

As we have seen, cosmology has successfully established itself as a science in its own right, in just over a century. As often in science, the success story of cosmology is entangled with theoretical predictions (from Hubble's law, to de Sitter's model, among others) no less than experimental discoveries (from the CMB to the supernova la). What can philosophers learn from the history of cosmology? How does a branch of metaphysics become ultimately a scientific theory? In what follows, we go back to the three problems we identified at the beginning of this chapter (i.e. laws of nature, uniqueness, and unobservability) and place them within the wider context of philosophical and methodological discussions.

Laws of nature, perfect cosmological principle and cosmological natural selection

The first methodological problem that we mentioned at the beginning of this chapter was the difficulty in extrapolating the validity of our current laws of nature to the early universe, with the ensuing 'inductive leap' involved in such an extrapolation. The problem was acutely felt already in the 1950s, when, for example, Munitz (1954, p. 42) wrote 'any attempt to apply the generalisations won on the basis of terrestrial experience to vaster regions of space and time and ultimately to the structure of the universe as a whole, requires some justification for extrapolating such generalisations. Here reliance is made on an argument originally due to Mach ...' Curiously enough, the aforementioned Machian argument about the illegitimacy of extrapolating from the current laws to those that might have applied at the origin of our universe, was at the time used by Bondi and other defenders of the steady-state universe to support the perfect cosmological principle, which 'postulates that the universe is homogeneous and stationary in its large-scale appearance as well as in its physical laws' (ibid., p. 43). Only by assuming this perfect cosmological principle, as the latest incarnation of what philosophers of science call the principle of the uniformity of nature, namely that nature is indeed uniform and pretty much the same from any place at any time, could the pressing problem of laws of nature be bypassed. Not surprisingly, however, this line of argument suffers from exactly the same problem of induction that affects the principle of the uniformity of nature: the perfect cosmological principle is itself a universal generalization in need of justification. More to the point, the steady-state universe, within which the perfect cosmological principle was originally formulated, has long been disproved by experimental evidence for an evolving universe from the CMB. Yet this does not mean the end of philosophical reflections on the role of the laws in cosmology. Let us only briefly mention two of the current options.

The first option, discussed by Smeenk (2013, p. 627), is to offer a philosophically more nuanced account of what it is to be a 'law of the universe". And a closer inspection can soon reveal that cosmological laws are as testable as Newton's laws, even in the early universe, in so far as they give us 'more refined descriptions of some aspect of the universe's history', no matter if we have only one universe and it is given to us once and for all.

The second option, so-called cosmological natural selection developed by the physicist Lee Smolin (2013, p. 123) is that Tor cosmology to progress, physics must abandon the idea that laws are timeless and eternal and embrace instead the idea that they evolve in real time'. Once this key step is taken, the problem of explaining why and how the universe came to be governed by our current laws (rather than other possible, different ones) evaporates, and no suspicious inductive leap is required to answer the original question. On Smolin's account, our laws of nature have evolved with us, and our universe. The first of two bonuses of this account, in Smolins own description, is that a cosmology with evolving laws does not need to rely on the anthropic principle (see Chapter 4) to explain why we live in a universe that seems hospitable to forms of life like ours. As in biology life is always evolving and never reaches a final ideal state, similarly our universe is evolving, and so are the laws of nature. The second bonus is that 'the hypothesis of cosmological natural selection makes several genuine predictions, which are falsifiable by currently doable observations' (Smolin 2013, p. 126), e.g. that the biggest neutron stars cannot be heavier than a certain limit. The Popperian flavour of Smolins hypothesis brings us to our second methodological point, namely the role of Popper's falsification in discussions about the scientific status of cosmology.

Uniqueness and Popper’s methodological criterion of falsification

Recall the uniqueness of our universe and the specific problem it poses to the testability of cosmology. Key to our ordinary ideas of what it is like to be a scientific theory is the ability to pass severe tests, tests which are typically run across multiple samples, and by tweaking the circumstances of the phenomenon we want to investigate. But cosmology has only one object to test and experiment upon, our universe, unique and unrepeatable as it is, and no other objects to compare our universe with. How could cosmology become a scientific discipline, despite the uniqueness of its object of study?

Karl Popper's criterion of falsification seems to offer a solution to the problem. As we saw in Chapter 1, Popper believed that the method of science consisted in a deductive method, whereby given a hypothesis or conjecture with risky novel predictions, scientists can go about and search for the one single piece of negative evidence that can potentially falsify the hypothesis. Theories that have passed severe tests and have not been falsified, are said to be 'corroborated'. If falsification is indeed the method of science, the uniqueness of our universe does not pose an insurmountable obstacle for cosmology and its scientific status. All that is needed from cosmology is one single risky prediction, which may be tested and proved wrong (what Popper called a potential falsifier).

Thus, on a Popperian approach, the uniqueness of the universe does not really constitute a problem for the scientific status of cosmology, because cosmological theories can indeed make risky and testable predictions (say, the hypothesis of the Big Bang, which implied the existence of CMB, as the last remnant of a hot early phase of the universe, with CMB being experimentally detected in 1965).

Here there is an interesting story to be told, with a surprising twist, about cosmology and Popper's method of falsification (for details about Popper's personal views on cosmology, and some of these debates, see Kragh 2013). In the 1950s, the cosmologist Bondi appealed precisely to the 'uniqueness" of our universe to defend the steady-state universe (namely, the hypothesis of a 'continuous creation' of matter in the universe to explain its expansion). Because there is only one universe, there must have been only one primitive 'substance' of the world emerging, disappearing, and being created again over time during the history of the universe. Funnily enough, Bondi also adamantly defended Popper's method of falsification in cosmology. In an interesting exchange with Whitrow that took place in the British Journal for the Philosophy of Science in 1953 (Whitrow and Bondi 1953, pp. 277-8), Bondi asserted that 'the most characteristic feature of any science is that it confines its attention to the establishment of connections between existing results of experiments and observation, and the forecasting of new ones. The chief claim that can be made for any scientific theory is that it fits the facts, and forecasts (or has forecast correctly) the results of new experiments; the chief method of disproof of any theory is that it disagrees with the facts'. Bondi's adherence to Popper's falsificationism was noted by Whitrow, who in his reply qualified falsificationism 'as a method employed in that thoroughgoing pursuit of general unanimity which, in my view, characterizes scientific work' (ibid., p. 280). Whitrow's remarks pointed the finger to the necessity of supplementing falsification with an important sociological, so to speak, aspect of scientific research (i.e. scientific results being unanimously endorsed by a community), to which we'll come back in the next chapter. The interesting final twist of the story is that Bondi's steady-state universe was itself disproved (via the discovery of the CMB in 1965) by the same Popperian method he had hailed. The second, even more ironical twist of the story is that Popper joined these methodological discussions about the scientific status of cosmology, and became (unsurprisingly perhaps) a public supporter of the steady-state universe till the 1980s, when the scientific community had already long dismissed the view (see Kragh 2013 for details).

Observability, indeterminism, and induction

As mentioned at the beginning of this chapter, the third distinctive problem posed by cosmology is the restricted access to what we can observe about our universe. According to the general relativity notion of the past light cone, the observable universe is defined as 'the past-light cone of Earth-now, and all physical events within it, even microscopic (and so humanly unobservable) ones' (Butterfield 2014, p. 58). This restricted access to the observability of the universe poses specific problems about the kind of warranted theoretical inferences cosmologists can make about the universe as a whole. The main problem is a form of indeterminism about spacetime. There might be observationally indistinguishable spacetimes (i.e. different models of spacetime, which are nonetheless compatible with the same observable past light cone of events), so that 'locally' an observer looking at the past light cone of their events, will not be able to tell in which spacetime they live. This is a mathematical result originally brought to the general attention by philosophers of physics (Glymour 1977; Malament 1977; Manchak 2009; for a recent discussion see Butterfield 2014). As John Norton (2011) nicely illustrates the problem, we are like ants on an infinite, fiat (Euclidean) sheet of paper, who can survey only about a 10,000-square-foot patch, and hence are not able to tell whether the spacetime they inhabit is indeed infinitely flat, or curved like a cylinder with a circumference of 1 mile. This shows what Norton calls also 'the opacity of cosmic inductions', namely the 'absence of warranting facts for inductions in the spacetime case" (Norton 2011, p. 173). Given our past light cone, we might inductively infer to very different, and yet observationally indistinguishable spacetime models, and no facts can make the inference to one of these models more legitimate or warranted than to another model. Norton reports how the considerations usually adduced to bypass this problem seem to appeal to abstract metaphysics and even to Leibniz's principle of plenitude and concludes as follows: 'One cannot help but be struck by how tenuous the grounding has become. We are now to secure our inductions in abstract metaphysics. The principle of plenitude itself is sufficiently implausible that we need to prop it up with anthropomorphic metaphors. We are to imagine a personified Nature in the act of creating spacetime. ... [and] supposedly loath to halt with a cubic mile-year of spacetime still uncreated'.

Chapter summary

For centuries cosmology was regarded as a branch of metaphysics rather than a science. The Kant-Laplace nebular hypothesis at the end of the eighteenth century was one of the first attempts at a scientific explanation of the origins of the universe.

Cosmology faces three distinct methodological problems as a science: whether our current laws apply to the early universe; the uniqueness of its object of study; and the unobservability of large portions of the universe.

Progress in the subject has then depended on the large-scale uniformity of the universe. Initially in the form of a guess, this cosmological principle has since been verified over large patches of the currently visible universe.

Observationally, much of the probing of the distant universe rests on Hubble s law, where the spectroscopic redshift is linearly proportional to distance. The main foundation for this was the pioneering spectroscopy of V. M. Slipher over the decade from 1913.

Theory played a large part in establishing cosmology. Einstein introduced the idea of a cosmological constant (equivalent to the modern idea of dark energy) in 1917, in order to permit a non-expanding universe, but de Sitter immediately found the first expanding solution, with a prediction of Hubble"s law.

Initially, and until the late 1920s, the non-static nature of the de Sitter model was not appreciated, although this did not prevent astronomers (including Hubble) searching for and finding the 'de Sitter effect'. Since then, we have viewed cosmological models as describing expanding spacetimes, although the idea of expanding space can lead to misconceptions, since it is not detectable locally.

Generalization of expanding models to cases containing matter and radiation by Friedman in 1922 and 1924 showed that the origin of the expansion lay in a singularity at a finite time in the past - the Big Bang. With the discovery of the CMB (cosmic microwave background) in 1965, this hot origin for the universe became the accepted picture.

The main constituents of the universe are dark matter and dark energy. The former is a form of matter that can clump, but which does not support sound waves; the latter is effectively an energy density associated with empty space, which causes a tendency for the expansion of the universe to accelerate.

The early universe should be hot, and dominated by the density of relativistic particles. This leads to the prediction of the CMB, when the universe cooled sufficiently to become neutral.

The radiation-dominated universe must emerge from a singularity in the Big Bang, only a finite time in the past. It is impossible to ask what came before such a time, and yet the universe at this point must be set up in a special uniform state. It should also contain small fluctuations in the curvature of spacetime in order to seed the future formation of galaxies and other astronomical structures.

Two possible ways of overcoming the problem with laws in cosmology are either by revising our philosophical intuitions about the testability of the laws, or by assuming that the laws evolve and change over time with our universe.

Despite there being only one object to study, the universe, cosmology seems amenable to Popper's method of falsification, whereby evidence coming from the CMB eventually falsified the hypothesis of the steady-state universe.

The restriction of observability to the past light cone of events means that there might well be many observationally indistinguishable spacetimes and any inductive inference from available data to the exact nature of the spacetime we live in is inevitably unwarranted.

Study questions

Why was cosmology regarded as a branch of metaphysics in the eighteenth century?

What was Kant's contribution to the history of cosmology?

What is the problem with laws in cosmology?

Why does the uniqueness of our universe pose a problem for cosmology as a science?

Can you clarify the exact nature of the problem of unobservability in cosmology?

Explain the meaning of 'telescopes are time machines'.

Why do we expect that the density of the universe will be dominated by radiation at sufficiently early times?

Radiation from sufficiently great distances originates from plasma at temperatures of over 1,000 degrees. Why then is it dark at night?

Does the history of cosmology show that Popper's falsificationism is the right scientific method?

Can you explain what Norton means by 'the opacity of cosmic inductions'?

Introductory further reading

Beisbart, C. and Jung, T. (2006) 'Privileged, typical or not even that? Our place in the world according to the Copernican and cosmological principles', Journal for General Philosophy of Science 40: 225-56.

Brush, S. G. (1996) A History of Modern Planetary Physics: Nebulous Earth, Cambridge: Cambridge University Press. (A good introduction to the history of the Kant-Laplace nebular hypothesis up to the early twentieth century.)

Ellis, G. E R. (2014) 'On the philosophy of cosmology', Studies in History and Philosophy of Modern Physics 46: 5-23.

Guth, A. H. (1998) The Inflationary Universe: The Quest for a New Theory of Cosmic Origins, London: Vintage. (This is a very good introduction to inflationary cosmology, written by one of the creators of the theory.)

Kragh, H. (2013) "'The most philosophically important of all the sciences": Karl Popper and physical cosmology', Perspectives on Science 21: 325-57.

Liddle, A. R. (2003) An Introduction to Modern Cosmology, Maiden, MA: Wiley-Blackwell. (An introductory undergraduate text for non-specialists.)

Massimi, M. (2013) 'Are scientific theories true?', in M. Chrisman and D. Pritchard (eds ) Philosophy for Everyone, London: Routledge.

Munitz, M. K. (1954) 'Creation and the "new" cosmology', British Journal for the Philosophy of Science 5: 32-46.

Norton, J. (2011) 'Observationally indistinguishable spacetimes: a challenge for any inductivist', in G. J. Morgan (ed.) Philosophy of Science Matters: The Philosophy of Peter Achinstein, Oxford: Oxford University Press, pp. 164-76. (An excellent paper that explains the physics and the philosophy behind indistinguishable spacetimes in a very clear and accessible way.)

Sklar, L. (1974) Space, Time, and Spacetime, Berkeley: University of California Press. (An excellent introduction to a variety of philosophical aspects concerning theories of space and time.)

Smolin, L. (2013) Time Reborn, London: Penguin Books.

Whitrow, G. J. (1954) 'The age of the universe', British Journal for the Philosophy of Science 5: 215-25.

Whitrow, G. J. and Bondi, H. (1953) 'Is physical cosmology a science?', British Journal for the Philosophy of Science 4: 271-83.

Advanced further reading

Butterneld, J. (2014) 'On under-de termination in cosmology', Studies in History and Philosophy of Modern Physics 46: 57-69. (An excellent introduction to the problem of observationally indistinguishable spacetimes by a world-leading philosopher of physics.)

Glymour, C. (1977) 'Indistinguishable spacetimes and the fundamental group', in J. Earman, C. Glymour and J. Stachel (eds) Foundations of Spacetime Theories, Minnesota Studies in Philosophy of Science 8, Minneapolis: University of Minnesota Press, pp. 50-60.

Malament, D. (1977) 'Observationally indistinguishable spacetimes', in J. Earman, C. Glymour and X Stachel (eds) Foundations of Spacetime Theories, Minnesota Studies in Philosophy of Science 8, Minneapolis: University of Minnesota Press, 61-80.

Manchak, J. (2009) 'Can we know the global structure of spacetime?', Studies in History and Philosophy of Modem Physics 40: 53-56.

Peacock, J. A. (1999) Cosmological Physics, Cambridge: Cambridge University Press. (This is a comprehensive postgraduate text covering most areas of modern cosmology. )

Smeenk, C. (2013) 'Philosophy of cosmology', in R. Batterman (ed.) The Oxford Handbook of Philosophy of Physics, Oxford University Press, pp. 607-52. (This is an excellent introductory chapter to some of the main philosophical trends by a leading expert in the field.)

Way, M. and Hunter, D. (eds) (2013) Origins of the Expanding Universe: 1912-1932, Astronomical Society of the Pacific Conference Series, vol. 471, San Francisco: Astronomical Society of the Pacific. (A meeting held in September 2012 to mark the Centenary of Slipher's first measurement of the radial velocity of M31.)

Internet resources

John Templeton Foundation (n.d.) Philosophy of Cosmology, Oxford University [website] www.philosophy-of-cosmology.ox.ac.uk (accessed 26 May 2014) (This is the official website of the Templeton-funded project on philosophy of cosmology, based at Oxford and Cambridge University. It provides useful links to key concepts and podcasts of events and lectures.)

John Templeton Foundation (n.d.) Rutgers Templeton Project in Philosophy of Cosmology, Rutgers School of Arts and Sciences, Rutgers University [website] http://philocosmology.rutgers.edu (accessed 26 May 2014) (This is the equivalent counterpart of the Templeton-funded project at Rutgers University. It contains a very helpful blog too.)

Peacock, J. A. (2013) 'MPhys advanced cosmology', University of Edinburgh [online lecture notes], www.roe.ac.uk/japwww/teaching/

Wright, N. (n.d.) Cosniological Tutorial, UCLA Division of Astronomy and Astrophysics [website], www.astro.ucla.edu/~wright/cosmolog.htm (accessed 9 June 2014) (A wide-ranging overview of many issues in cosmology. Simplified for a general audience, but far from simplistic. )