Knowledge in a Nutshell: Astrophysics

Chapter 20 Cosmogenesis

In the previous chapter we discussed the Inflationary Era, which occurred as the Grand Unified Theory (GUT) Era came to an end. The Inflationary Era ended when the transition to the True Vacuum finished, but the way in which this happened has huge consequences for the Standard Model, and the way our universe looks today.

Theoretical modelling suggests that the transition to the True Vacuum occurred as the Higgs bosons gained mass, but GUT theories also suggest that other very massive particles called leptoquark bosons existed as well. These supermassive particles (1014 GeV) were spawned as the enormous vacuum energy of the Higgs field produced pairs of these massive particles, which would decay to the familiar Standard Model particles at a later time. The removal of vacuum energy by pair production of these supermassive particles may be the event that gradually caused inflation to come to a ‘graceful’ end, but when these supermassive particles annihilated, they caused a reheating of the universe to nearly the GUT energy once again… but not quite.

Today we find that we live in a matter-dominated universe with little or no antimatter to be found. The CMBR photons also outnumber the baryons (protons) by nearly one billion to one. This fact cannot be explained by any known process in the Standard Model, so cosmologically the origin of this asymmetry must have happened before the end of the Electroweak Era. One possibility being investigated is that it happened during the reheating of the universe after Inflation. At this time, there were supermassive bosons and leptoquarks present, and in some models for GUT there seem to be decay processes that favour more baryons than antibaryons. The detailed calculations are very model-dependent and as yet there is no experimental guidance as to which models for GUT are favoured.

The GUT Era ended with Inflation at about 10-36 seconds (s) ABB. However, the beginning of the GUT Era takes us to an even earlier time in cosmic history that may well be the final moment that can be discerned, where at last we come face-to-face with the actual origin of the universe itself.

The Planck Era

To describe this era we have to take a last step in physics by unifying the GUT force with gravity. For decades, the road to unifying gravity with the Standard Model has been fraught with difficulties. Chief among these is that the language of the gravitational force, represented by Einstein’s theory of general relativity, is largely incompatible with the mathematics of quantum field theory upon which the Standard Model is based. One of the major difficulties is that the Standard Model and its extensions in string theory and supersymmetry theory are dependent on the four-dimensional spacetime of general relativity pre-existing. All the equations and formulations of quantum mechanics and the states of particles and fields use spacetime as a background framework and are therefore called background-dependent theories. General relativity, in addition to not being a quantum theory of gravity, is also manifestly relativistic. This means that space and time and spacetime itself are features derived from the relationships between bodies and do not pre-exist as some framework upon which gravity operates, which means that general relativity is background-independent.

A key feature of combining general relativity with quantum mechanics is that the gravitational field will be quantized. What this means is that the gravitational field of the universe, which we call spacetime, is composed of packets of geometry much like the electromagnetic field is composed of the packets of energy we call photons. To make general relativity a quantum theory of gravity we have to find a new way to describe gravity as the interactions among quanta of gravity. It is generally recognized from what is called ‘quantum gravity theory’ that this will happen at physical scales given by the Planck Units of mass, energy, time and space originally proposed as ‘natural units’ for physics in 1899 by Max Planck. These units can be formed by using the Newtonian constant of gravity (G), the speed of light (c), and Planck’s constant (h), in the appropriate combinations to create the appropriate physical units as follows:

When the appropriate values are used for these constants you get

Planck length Lp=1.6×10-33 cm

Planck mass mp=2.2×10-5 g

Planck time tp =5.4×10-44 s

Planck temp. Tp=1.4×1032 K

Planck energy Ep = mp c2 = 1.3×1019 GeV (or 2.0×1016 ergs)

Compare these units to the proposed GUT Era scales of 1015 GeV and 10-36 s just before the Inflationary Era begins and it is pretty clear that by the GUT Era at 10-36 seconds ABB we are very close to the scale at which the gravitational field itself displays quantum properties. The GUT Era is considered to exist between the Inflation Era at 10-36 s and about 10-43 s ABB, with the Planck Era occurring for times earlier than 10-43 s, if time itself is a meaningful concept.

During the GUT Era, there are effectively two forces that can be distinguished: gravity and the GUT (strong + electroweak) force. We do not know what kinds of particles were present, nor do we know just how much of the CBR was in existence. These details depend on the exact nature of the theory describing GUT unification, which is one of the areas being investigated in quantum gravity theory.

John Wheeler in the 1960s proposed that the gravitational field becomes a quantum field at the Planck scale in which its geometry is a superposition of possible geometries, and that the topology or shape of spacetime fluctuates wildly among many possible forms. This can be described as a foaming landscape where quantum black holes form and evaporate and wormhole-like connections and bridges turn spacetime into a dynamic Swiss cheese.

This conception for quantum gravity-scale physics is incomplete because it derives directly from general relativity and does not have a place for the Standard Model. There seems to be no way to go from this description to the idea of fermions and bosons as geometric features of this landscape.

Another approach is via superstring theory in which elementary particles are represented as one-dimensional ‘strings’ that vibrate in up to 11 dimensions, of which four are normal three-dimensional space and time. A tremendous effort has been expended in working out the details of string theory since it was proposed by Michael Green and John Schwartz in 1980, but this has generally led to no solid predictions that can be experimentally tested. It has also opened up the mathematical possibility that there are a multitude of self-consistent string theories that are possible but no way to discern why our particular ‘solution’ was selected for our universe. Instead there is a complex landscape of string theories for which some means of selecting ours has to be invoked. The currently favoured way to do this is via the Anthropic Cosmological Principle in which our own existence provides the missing constraint to uniquely specify the parameters of the string theory. A tremendous amount of theoretical effort has gone into investigating superstring theory and in applying it to the only physical setting where it can be reasonably tested: the origin of the universe itself. The theory requires spacetime to have as many as 11 dimensions within which our universe exists. Some investigators such as Lisa Randall at Harvard University have investigated the properties of such a spacetime in which our universe exists as a 4-D ‘brane’ separated by other similar ‘Braneworlds’ via the additional dimensions of the Bulk. All of the Standard Model particles and fields are trapped within our 4-D brane. The Randall-Sundrom model describes the dynamics of such systems and explains how gravity is a weak force because most of its strength extends across the additional dimensions of the Bulk. Cosmogenesis could also have occurred as these 4-D Braneworlds collide.

An important note, however, is that string theory already requires a background spacetime in which its string particles operate, so gravity in the guise of the 4-D spacetime is merely a background. As we noted before, that makes string theory background-dependent and not technically consistent with the background-independent ‘relativity’ of general relativity.

Lisa Randall won first place in the 1980 Westinghouse Science Talent Search at the age of 18, and at Harvard University in 1987 earned her PhD in theoretical particle physics under Howard Georgi. She became the first tenured woman in the Princeton physics department and the first tenured female theoretical physicist at Harvard University. She is a prolific writer and popularizer of string theory, and her theoretical work involves baryogenesis, inflation, grand unification theory and general relativity.

Finally, the theory of loop quantum gravity (LQG) appears to solve the relativity problem by being completely background-independent from the start. The work by Lee Smolin and Carlo Rovelli has shown that, by borrowing some of the earlier ideas developed by Roger Penrose in the 1960s, you can create objects called spin networks. The vertices of these networks are quantized volumes of space, and the links between them are relationships that determine how much area is associated with each quantum of volume. In essence, space has dissolved into a collection of elementary points, and the geometric properties come from the relativistic relationships between these points. When spin networks are linked together to represent how one set of networks changes into another set, a new four-dimensional object called a ‘spin foam’ is created. At this level, four-dimensional spacetime has been fully quantized into discrete spin foams. The scale at which this happens is the Planck scale, and it leads to an interesting problem of epistemology; the study of knowledge and how we acquire it.

In quantum mechanics, if you want to study the state of a system you have to use photons whose sizes match the scale of the state being investigated. But photon sizes, called wavelengths (see page 11), depend on the energy of the photon; the smaller the wavelength of light the higher the energy of the photon required. If quantum gravity follows this same basic quantum relationship between size and resolution we encounter a severe problem. To probe the quantum gravity scale at 10-33 cm we need to use photons with energies equal to 1019 GeV. But these photons carry enough mass to become quantum black holes, which will evaporate after 10-43 seconds. This means that the Planck scale is a hard limit to the smallest scales we can ever probe to verify the accuracy of a theory of spacetime and gravity. If you wanted to ‘see’ what events look like at these scales, the light messenger would immediately turn into a quantum black hole and bury the information you seek.

Another feature of quantum gravity theory is that it does not provide an explanation for one of the deepest mysteries in physics: Why does time exist? As quantum gravity theory probes the deep structure of spacetime, it does not provide a clear explanation for why our four-dimensional spacetime isn’t just a pure four-dimensional space in which the concept of ordered change does not exist. For example, your family photo album is a collection of two-dimensional photographs ordered in a three-dimensional format through the pages of the album, but this object is static. Although the photographs imply slices through a time-ordered sequence, the album remains a fixed space-like object. Each vertex in your family tree is a three-dimensional person. The lines you draw between these vertices express the information that one of these vertices is closer to one than another, but this ‘closeness’ is not closeness in space, but related to closeness in time.

Special and general relativity are based on the idea of four-dimensional spacetime, but this spacetime ‘object’ is eternal. Within it you can follow the entire history of a particle from birth to death as a complete worldline and see it from the ‘all-at-once’ perspective. This is called the Block Universe, and essentially eliminates time as an important concept. But nevertheless, we experience time, and moreover the present moment, as being very real. This leads to the conundrum that time is literally annihilated in the Block Universe perspective of Einstein’s relativity, but is a vital ingredient to how we experience the world. This has been expressed by physicists as the problem of Now in the universe.

An intriguing explanation for time has been proposed by George Ellis. Experiments at the quantum level suggest that the Block Universe perspective of relativity is not correct. Although the past can be reconstructed from essentially classical physics and records of stored information (such as photographs), the future is closely determined by probabilities and principles found in quantum mechanics. According to Ellis, the ‘present’ is when the quantum mechanical probabilities of the future become ‘crystallized’ into the certainty of the past. This crystallization process seems to involve a variety of subtle processes such as quantum entanglement and observer participation operating at the foundation of the observable world. As for the origin of the universe itself, according to Stephen Hawking, a quantum mechanical tunnelling process may have occurred at the Big Bang. In its initial state, which could have been similar to the space-like attributes of the spin networks in LQG, cosmic spacetime may have been in a four-dimensional, pure space state. The spin foam we discussed previously may have been a purely four-dimensional space-like object. But then through a tunnelling event, one of the space-like dimensions tunnelled into a time-like dimension and, quite literally, time began. From then on one might suppose that the quantum entanglement process created events and sub-systems called ‘clocks’ from which state changes would be interpreted as on-going, time-like changes between states. Taking Hawking’s idea one step further, the tunnelling event may have been irregular so that some regions of the pre-existing four-dimensional space may have remained unaffected while other ‘bubbles’ of the true spacetime may have formed with a time-direction.

So the Big Bang event during, or shortly after, the end of the Planck Era was the origin of three-dimensional space and of time itself, by some process that is currently not understood. We can surmise that the intense quantum fluctuations of spacetime (gravity) gave rise to the physics of the GUT Era by literally creating matter and energy out of ‘empty’ spacetime, but the details are currently not known.

Key Points

• Understanding the physics of the origin of the universe requires a deep understanding of gravity as a quantum phenomenon, which is described by Quantum Gravity Theory.

• The scale at which quantum effects in gravity and spacetime take place is characterized by the Planck Units of mass, time, energy and size.

• Two quantum gravity theories, string theory and loop quantum gravity, are incompatible because string theory depends on a pre-existing four-dimensional spacetime while loop quantum gravity does not.

• The origin of the dimension of time, and the physical definition of the moment called Now, remain deeply mysterious issues at the forefront of physics and cosmology.

• The Big Bang was the origin of space, time and matter represented by events taking place near ‘Time-Zero’ or at 10-43 seconds during the Planck Era.