SURVEYING THE SKY

In chapter 12, I described how galaxy-redshift surveys revealed a visible universe marked by an incredible weblike structure of clusters of galaxies organized in filaments separated by almost empty voids. Since 2000 there have been dozens of new surveys that have greatly enhanced the database.¹

The most extensive, the Sloan Digital Sky Survey (SDSS), uses the 2.5-meter-wide-angle optical telescope at the Apache Point Observatory in New Mexico. Starting in 2000 and still gathering data, SDSS has collected observations of five hundred million objects, including the spectra for five hundred thousand new objects for which light left seven billion years ago.

Of special cosmological significance, included in the SDSS survey is a baryon oscillation spectrographic survey (BOSS) that maps the spatial distribution of highly redshifted luminous red galaxies and quasars in order to obtain the acoustic signal of the baryons (atomic matter) in the early universe.² Just as the sound waves produced by primordial fluctuations have left an imprint on the CMB, they also left an imprint on the distribution of early galaxies. While these fluctuations produced inhomogeneities in the dark matter as well as in atomic matter, the dark matter offers no resistance to the gravitational collapse of high-density regions while the atomic matter has radiation pressure that opposes gravity. The two opposing forces result in an oscillation that affects the distribution of galaxies.

Using data for 46,748 luminous red galaxies in the redshift range 0.16 to 0.47, in 2005 a team led by Daniel Eisenstein of the Harvard-Smithsonian Center for Astrophysics reported a slight excess of galaxies separated by five hundred million light-years, matching the shape and location of the expected imprint of the acoustic oscillation at the time of recombination as predicted by the standard cosmological model.3

HEARING THE BANG

In the previous chapter, we closed out our review of the final decade of the second millennium of the Common Era by showing the angular spectra from COBE along with those from sixteen ground-based or balloon CMB experiments having better angular resolution but less statistical precision that followed shortly after (see figure 13.5). They provided the first indication of the expected fundamental acoustic peak that was inaccessible to COBE. The first year of the new decade would witness the strong confirmation of that peak and the observations of two more peaks by two spectacular high-altitude balloon flights and two more magnificent space telescopes.

The balloon experiments BOOMERANG (Balloon Observations of Millimetric Extragalactic Radiation and Geophysics) and MAXIMA (Millimeter Anisotropy Experiment Imaging Array) were each the product of large international collaborations. BOOMERANG flew over the South Pole in 1998 and 2003 at altitudes over forty-two thousand meters. MAXIMA made flights at forty thousand meters over Palestine, Texas, in 1998 and 1999. Their combined results, shown in figure 14.1, were published on a joint paper in 2001.4 These confirm not only the fundamental peak at ℓ = 220 but also the smaller secondary peaks at ℓ = 500 and 750.

Figure 14.1. CMB angular spectra from BOOMERANG and MAXIMA. Reprinted figure with permission from Andrew H. Jaffe, P. A. R. Ade, A. Balbi, J. J. Bock, J. R. Bond, J. Borrill, A. Boscaleri, et al., “Cosmology from MAXIMA-1, BOOMERANG, and COBE DMR Cosmic Microwave Background Observations,” Physical Review Letters 86, no. 16 (2001): 3475–79. © 2001 by the American Physical Society.

The data were fit to two models, the better fit having 70 percent dark energy and 20 percent cold dark matter and 10 percent baryons with the total density of the universe equal to the critical density within 4 percent.

But there's nothing like space (including the cost). On December 30, 2001, the NASA Microwave Anisotropy Probe spacecraft was launched from Cape Canaveral. It would later be renamed the Wilkinson Microwave Anisotropy Probe (WMAP) in honor of the microwave-astronomy pioneer David Wilkinson, who died in 2002.

WMAP gathered data for nine years and published its final results in 2013.5

Figure 14.2 shows the angular power spectrum from the first seven years of data.⁶ The secondary acoustic peaks are evident. The curve is a fit to these data alone for a six-parameter model that will be described shortly.⁷

Just like light from the sun is polarized, so are microwaves. Polarization results, also shown, were also published by WMAP and other experiments.

Now, it is important not to expect that the sound spectrum plotted here will resemble exactly that of a musical instrument. Indeed, if the frequencies and intensities are shifted to ranges audible to the human ear, they are indistinguishable from noise. Watch, and listen to, the Great Courses lectures 15 and 16 by Mark Whittle for a delightful demonstration and his attempts to disentangle the various harmonics to make the “music of the spheres” more musical.⁸ Also, see his webpage “Cosmic Acoustics.”⁹

A number of “distortions” are present in the expanding ball of photons and other particles whose vibrations are producing the sound. These fill in the gaps and reduce some of the power in the higher harmonics in the angular spectrum. But what is wonderful is that these distortions provide us with information about the nature of that medium that we would not have from the pure spectrum alone.

A program that simulates the big bang called CMBFAST, written by Uros Seljak and Matias Zaldarriaga, is widely used to fit the CMB anisotropies and polarizations to various models.¹⁰ Let us look at this model, which continues to describe all the data remarkably well although more sophisticated models will probe deeper as the data get better.

Figure 14.2. The WMAP seven-year temperature and temperature-polarization power spectra. The curves are fits to the data with the six-parameter ΛCDM model described in the text. Image from N. Jarosik et al., “Seven-Year Wilkinson Microwave Anisotrophy Probe (WMAP) Observations: Sky Maps, Systemic Errors, and Basic Results,” Astrophysical Journal Supplement Series 192, no. 2 (2011): 14. © AAS. Reproduced with permission.

ΛCDM

As the increasingly precise measurements of the CMB angular power spectra and polarizations, along with other remarkable astronomical observations such as the accelerated expansion and the web of galaxies, were being produced by large collaborations of observational astronomers and astrophysicists, theoretical physicists and cosmologists were developing models to describe the data in terms of basic physics.

A comparatively simple model that was applied to the 2005 WMAP data is called the six-parameter ΛCDM model. It assumes a universe composed of baryonic (atomic) matter, cold dark matter (CDM), and dark energy (Λ) resulting from the cosmological constant. The model parameters are:

• Ω_b: the density of baryonic matter relative to the critical density
• Ω_c: the density of cold dark matter relative to the critical density
• Ω_Λ: the density of dark energy relative to the critical density
• n: the spectral index characterizing the original fluctuation power spectrum (see chapter 11)
• A: the amplitude of the original fluctuation
• τ: the reionization optical depth

Reionization has not been previously mentioned. To describe it I need to elaborate on the evolution of the universe from decoupling to the formation of the first stars, which is an important part of the story.

THE FIRST STARS

Just after photon decoupling at 380,000 years, the universe was a ball of thermal atomic gas, mostly hydrogen and helium along with the now-noninteracting photon gas, all at the same temperature of 3,000 K. This temperature corresponds to a peak wavelength of about one micron, which is in the near-infrared region of the blackbody thermal spectrum. However, since the spectrum is broad, there is still plenty of visible light and the sky is bright orange.

As the ball of gas expanded, both components cooled accordingly, their spectra peaking at longer and longer wavelengths and the sky became increasingly redder until at about six million years the universe emitted little visible light. The period that followed, called the “Dark Age,” lasted a few hundred million years until the first stars were formed and finally there once again was visible light.

Also expanding was the dark matter, which began to clump as it cooled, causing the much less massive atomic matter to clump along with it. Because of its weak interaction with other matter, dark-matter clumping did not result in any dissipation of energy. The atoms, on the other hand, collided with one another more frequently and so dissipated energy, cooling more rapidly than they would have from the expansion alone. This made it even easier for the atoms’ own gravity and that of the dark matter to compress the atomic matter even further so that hot, dense cores formed inside a cooler surrounding medium. These cores eventually reached a high-enough temperature and pressure to ignite nuclear fusion so that the first stars could form.

Now these were not much like the stars in our current universe. The earliest stars were some hundred times more massive than today's stars and, furthermore, almost entirely composed of just hydrogen and helium. As a result, they burned at very high temperatures and emitted ultraviolet radiation that ionized the surrounding medium. This is called “reionization.”

The first galaxies that formed as these stars clumped were quasars and other active galaxies with supermassive black holes at the center that emitted intense radiation, also contributing to reionization.

And so, the previously dark, electrically neutral universe now once again contained charged particles. While their density was much lower than it was prior to decoupling, it was sufficient to cause space to lose some of the transparency it gained when the universe became neutral. The fog produced by reionization served to reduce the intensity of the CMB that we eventually would observe on Earth. This is parameterized in ΛCDM by the reionization depth parameter τ, which measures the thickness of the fog. From this, the time at which reionization occurred was estimated to be about four hundred million years after the big bang.

THE PLANCK SATELLITE

On May 14, 2009, the European Space Agency Planck satellite was launched from the Guiana Space Centre in French Guiana. It started taking data in February 2010 and published its initial results in March 2013. The CMB angular power spectrum is shown in figure 14.3.¹¹

The media played up the fact that several of the numbers were different from the previous consensus, notably a somewhat-greater age of the universe. However there were no statistically significant disagreements for these numbers.

Much has been made of a so-called tension between the Planck results and those of the Hubble Space Telescope and other instruments that study galaxies that formed long after the CMB was emitted at decoupling. In particular, the model described above that fits the Planck data predicts a mass for galactic clusters that is about 80 percent of that measured from an all-sky survey of clusters.¹² We will discuss this further in a moment.

Figure 14.3. Angular power spectrum from Planck satellite published in 2013. Here we see the full harmonic structure determined with spectacular precision. Note that we have seven significant bumps. Table 14.1 lists a selection of parameters determined from fitting both the Planck and WMAP data along with other observations that I need not detail. The six-parameter ΛCDM described above fits the data well, although extended models containing more adjustable parameters have been tested. Image from Planck Collaboration, P. A. R. Ade, et al., “Planck 2013 Results. I. Overview of Products and Scientific Results,” arXiv preprint arXiv:1303.5062 (2013).

The media often highlights reports of new theories that do away with the expansion of the universe, the big bang, or inflation. Pay no attention until one of those theories is able to reproduce the observations in figures 10.4 and 14.3 as accurately and parsimoniously as the inflationary big-bang model described here. And, as we will shortly see, recent observations have made inflation almost as certain as the big bang itself.

t0	Age of the universe in billions of years	13.798 ± 0.037
H0	Hubble's constant in km/sec/Mpc	67.80 ± 0.77
Ωb	Baryon density as a fraction of critical density	0.04816 ± 0.00052
Ωc	Density of cold dark matter as a fraction of critical density	0.2582 ± 0.0037
ΩΛ	Density of dark energy as a fraction of critical density	0.692 ± 0.010
n	Spectral index of primordial fluctuations	0.9608 ± 0.0054
τ	Reionization optical depth	0.092 ± 0.013
Ωk	Energy density of spatial curvature, 95% confidence level	–0.0005 ± 0.0066
Σmv	Sum of masses of neutrinos in eV, 95% confidence level	< 0.230
Neff	Effective number of neutrinos, 95% confidence level	3.30 ± 0.53
YP	Fraction of baryon mass in helium, 95% confidence level	0.267 ± 0.039
w	Dark energy equation of state factor, 95% confidence level	–1.13 ± 0.24

Table 14.1. Parameters determined by a fit to 2013 data from Planck, WMAP, and other experiments. Please note that these are just the best numbers as of the date of this publication and are sure to be modified as time goes on and the data improve.

The spectral index of primordial fluctuations is now slightly less than 1 with high statistical significance, confirming the expectation from inflation. Thus inflation has passed yet another falsifiable test. Of particular note is that the dark-energy equation-of-state factor is still consistent with w = –1, continuing to support the hypothesis that the cosmological constant is the source of dark energy. However the 21 percent error is still large, and some form of quintessence remains a possibility. Indeed, if the dark energy is quintessence with w very close to –1, it will be very difficult to distinguish any differences from a cosmological constant and to determine its exact nature.

Theoretical cosmologists continue to propose other models, one or more of which may turn out superior to what I have described. However, at this writing none is anyway near replacing ΛCDM.13

The Planck team has compared its data with a number of different models for the potential energy function that gave rise to inflation.¹⁴ While several are ruled out, others remain viable. In particular, Linde's chaotic model, which I have been using as a specific example since it is the most natural and simple, is still in the running and even somewhat supported by the most recent results on primordial gravitational waves, which will be discussed shortly.

After exhausting its supply of liquid helium used as a coolant, the Planck Observatory shut down on October 23, 2013.

GRAVITATIONAL WAVES

One of the predictions of general relativity is the existence of gravitational waves. Just as an electromagnetic wave is produced by an oscillating charge and causes another charge at a distance to oscillate, a gravitational wave is produced by an oscillating mass and causes another mass at a distance to oscillate. But the gravitational effect is much smaller.

For years, attempts have been made to directly observe the oscillations of mass caused by gravitational waves. The most recent is the Laser Interferometer Gravitational Wave Observatory (LIGO). It is located at two sites 3,002 kilometers apart in Hanford, Washington, and Livingston, Louisiana, enabling source location by triangulation. Each observatory is composed of an L-shaped, high-vacuum pipe five kilometers on each side with a laser beam bouncing back and forth between mirrors at the ends of each pipe. A gravitational wave would be detected when it produces a slight change in the length of one beam relative to the other, resulting in an interference between the two laser beams, similar to a Michelson Interferometer. Since 2002, the results have been negative. Currently the observatories are being upgraded.

Once again, the cosmic background radiation provides another avenue of approach to a fundamental phenomenon. Not only has it, at this writing, presented the first significant evidence for gravitational waves, it has also provided the strongest confirmatory evidence yet for inflation.

Recall our discussion of B-Mode polarization in the section on gravitational lensing in chapter 11. B-Mode polarization cannot be produced by normal scalar inflaton field perturbations. However, its detection in the CMB power spectrum in the multipole range 30 < ℓ < 150 is an almost-sure sign that fluctuations in the tensor gravitational field in the early universe have been greatly amplified by inflation. In their book Endless Universe: Beyond the Big Bang, Paul Steinhardt and Neil Turok called the detection of B-Mode polarization the “sixth milestone test of the inflationary scenario.”¹⁵ In 2001, Steinhardt, Turok, and two other coauthors proposed an alternative to inflationary cosmology called the Ekpyrotic universe in which the universe is produced by colliding “branes.”¹⁶ Branes are two-dimensional objects that occur in M-theory (see chapter 11). Ekpyrotic comes from the Greek ekpyrosis () which was used by the Stoics to mean “conversion into fire.”

The discovery of significant B-Mode polarization in the CMB with the expected power spectrum, peaking at ℓ ~ 80, was announced with great fanfare on March 17, 2014, by another South Pole experiment called BICEP2 (Background Imaging of Cosmic Extragalactic Polarization).¹⁷ The null hypothesis was ruled out at a statistical significance level of at least one part in 3.5 million. The data, shown in figure 14.5, fit the ΛCDM model with a tensor/scalar ratio of 0.20 ± 0.06. Cosmologists have urged caution, awaiting independent replication and the complete ruling out of all other possible sources of the effect. But if that occurs, we will have witnessed a discovery ranking among the most important in scientific history.

Figure 14.4. BICEP2 results for the B-mode polarization power spectrum compared to previous lower limits from a variety of observations. The circles are the data points at different multipoles ℓ, with error bars indicated. The dashed curve labeled r = 0.2 is the prediction of the ΛCDM model for a tensor/scalar ratio of 0.2. The solid curve is the expectation from gravitational lensing. Image from P. A. R. Ade et al., “Detection of B-Mode Polarization at Degree Angular Scales by BICEP2,” Physical Review Letters 112, no. 24 (2014): 241101.

Note that the lensing effect, observed earlier by others, has a very small contribution at the lower multipoles.

The detection of this form of CMB polarization rules out most models that attempt to address the flatness, horizon, and homogeneity problems in cosmology without inflation, including the Ekpyrotic universe—as Steinhardt has admitted.18

SEARCHING FOR DARK MATTER

In chapter 11, I mentioned the phenomenon of gravitational lensing in which a large mass such as a cluster of galaxies can bend the light from a source so that multiple images of the same source are seen. Gravitational lensing has been used to great effect in confirming the existence of dark matter and mapping out its distribution, and we can expect a lot more examples in the future.¹⁹

Multiple images are produced when the mass of the lens is very high. This is called strong lensing. When the lens mass is lower we have weak lensing in which we do not get multiple images but simply a distortion of the image of the source. It can be stretched or magnified, or both. While a single galaxy can be elongated in shape, when a set of elongated galaxies line up in some way, we have a good sign that some invisible mass is acting as a distorting lens. From the amount of distortion and the distribution of the distorted galaxies, the mass of the lens and its distribution can be estimated. When this is done, there is clear evidence for dark matter.²⁰

However, gravitational lensing does not tell us what the dark-matter particles may be. As of this writing, for two decades some thirty or so experiments have been conducted or are in current operation to detect and identify dark matter.²¹ Recent results are tantalizing but not yet confirmed.

Basically two techniques are employed: direct searches that attempt to detect the passage of dark-matter particles through detectors, and indirect searches in which one looks for the secondary particles produced when dark-matter particles annihilate with one another. Until now, both techniques have been largely directed toward WIMPS, weakly interacting massive particles, and, in particular, the neutralinos predicted to exist from supersymmetry, with a few direct searches specially designed to detect axions. However, with the failure so far to see SUSY particles at the LHC, a lot of attention is now being given to sterile neutrinos as a possible alternative, as mentioned in chapter 13.

Most direct searches are deep underground to reduce backgrounds from cosmic rays, while indirect searches are done with high-altitude balloons or spacecraft. On October 30, 2013, the first results were reported from what is called “the world's most sensitive dark matter detector,” LUX (Large Underground Xenon experiment) in Lead, South Dakota.22 It failed to confirm earlier reports of signal “hints” from several less-sensitive experiments, pretty much ruling out WIMPs in the mass range 5–20 GeV.

Hints of dark-matter signals have also been reported from several indirect searches. Again the emphasis is on WIMPs, especially those suggested by supersymmetry.

Neutralinos are expected to be their own antiparticles, so they should annihilate into high-energy gamma rays, electron-positron pairs, or proton-antiproton pairs. The three experiments I will describe are indirect experiments that look for the products of neutralino annihilation.

PAMELA (Payload for Antimatter Exploration and Light-nuclei Astrophysics) is an experiment assembled by a collaboration from Russia, Italy, Germany, and Sweden. It is mounted on the Russian satellite Resure-DK1 that was launched on a Soyuz rocket on June 15, 2006. It is still operating. In August 2008, the collaboration announced that it had detected an excess of positrons in cosmic rays above 10 GeV.²³

In November 2008, the high-altitude balloon experiment ATIC (Advanced Thin Ionization Calorimeter) launched from Antarctica, reported an excess of electrons in the energy range 300–800 GeV, although it could not distinguish positrons from electrons.

The Fermi Gamma-Ray Space Telescope is a collaborative effort of NASA and agencies in France, Germany, Italy, Japan, and Sweden. It was launched on a Delta rocket from Cape Canaveral on June 11, 2006. In 2009, the collaboration reported an excess of positrons that agreed with the PAMELA results.²⁴ More significant, in February 2014, PAMELA reported “a compelling case for annihilating dark matter” with the observation of an excess of 1–3 GeV gamma rays from a region around ten degrees from the center of the Milky Way. The signal is well fit by a 31–40 GeV dark-matter particle.25 This may be the best indication yet for neutralino dark matter. Dark-matter masses around a few TeV implied by previous reports are higher than expected.²⁶

Another major project to search for dark matter is the NASA Alpha Magnetic Spectrometer (AMS-02) onboard the International Space Station. The principle investigator of this large multinational collaboration is Nobel laureate physicist Samuel Ting of the Massachusetts Institute of Technology. AMS-02 was deployed by the space shuttle Endeavor on May 19, 2011.

Figure 14.5. The positron fraction measured by AMS-02. The data are fit to a model that parameterizes the position and electron fluxes as the sum of individual diffuse power law spectra and the contribution of a single source. Reprinted figure with permission from M. Aguilar et al., “First Result from the Alpha Magnetic Spectrometer on the International Space Station: Precision Measurement of the Positron Fraction in Primary Cosmic Rays of 0.5–350 GeV,” Physical Review Letters 110, no. 14 (2013). © 2013 by the American Physical Society.

In a paper published in 2013, Ting and collaborators presented the results shown in figure 14.5, showing a dramatic increase in the fraction of positrons from 10 GeV to 250 GeV based on 6.8 × 10⁶ positron and electron events.27 The positron fraction shows no fine structure, and no significant variations with time or preferred direction were observed, as expected if their source was dark matter. The result is consistent with the results from PAMELA but not the most recent Fermi result mentioned previously.

Note that the peak seems to be flattening out at high energy. If with more data the peak turns over, this would be strong evidence for the annihilation of a particle with mass of several hundred GeV. However, the result is still preliminary and we will have to wait and see. In any case, the authors note, the features of their data imply the existence of a new phenomenon of some type.

RECENT HINTS OF STERILE NEUTRINO DARK MATTER

In chapter 13 I mentioned the possibility that dark matter is composed of sterile neutrinos. These are three species of neutrinos that interact very weakly with the rest of matter, even more weakly than the three familiar neutrinos species, ν_e, ν_μ, and ν_τ. They are expected to exist with a minimal extension of the standard model. The original form of the model assumed but did not require massless neutrinos and has been modified to allow for neutrino mass since its discovery in 1998.²⁸

While this book was in production, two independent groups looking at satellite observations from superimposed clusters of galaxies reported a signal of 3.5 keV slightly above background.²⁹ It is conjectured that these results for the decay of 7 keV sterile neutrino into two photons, although this remains far from being a confirmed discovery. Galactic clusters are particularly concentrated centers of dark matter, and this mass is sufficient to constitute dark matter. These neutrinos would be “cold” by decoupling time.

Since a sterile neutrino is likely to be accompanied by two others, sterile neutrinos in the mass range of a few eV might also solve the empirical tension mentioned earlier that exists between the predictions of the model used to fit the CMB data and telescopic observations of galactic clusters.30 At decoupling, these neutrinos would still be “hot,” in which case they would not clump so readily. Since they would still be a component of dark matter, this would result in lower cluster formation when galaxies later formed.

HIGHEST-ENERGY NEUTRINOS EVER

In the last chapter I mentioned that I worked for many years on a project called DUMAND, which sought to place a large neutrino detector on the bottom of the ocean near the Big Island of Hawaii to look for very high-energy neutrinos from extraterrestrial sources. A number of other experiments of the same nature have also been underway at other locations such as Lake Baikal in Siberia and the Mediterranean Sea.³¹ DUMAND was eventually terminated because it was deemed too difficult and expensive to work in the deep ocean. A more hospitable environment than the ocean off Hawaii was found by a different team of scientists headquartered at the University of Wisconsin—the South Pole.

Once again, the technique involves detecting the Cherenkov light from the charged particles produced when very high-energy neutrinos collide with nuclei in a transparent medium, in this case Antarctic ice. In the 1990s, the AMANDA project (Antarctic Muon and Neutrino Detector Array) deployed strings of photomultiplier tubes deep in the ice at the Amundsen-Scott South Pole Station. Starting in 2005, it was expanded to encompass a cubic kilometer at a depth between 1,450 meters and 2,450 meters and renamed IceCube. Construction was completed in December 2010. IceCube is by far the most sensitive of any of the existing experiments.

On November 21, 2013, the IceCube collaboration announced that it had detected twenty-eight neutrinos above 30 TeV, two of which had energies exceeding 1 PeV (10¹⁵ eV).32 If future data enables it to pinpoint sources, IceCube will have finally opened up the nu window on the universe. While this book was in production, a third PeV neutrino was announced.

Astrophysicist Floyd Stecker of the Goddard Space Flight Center, with whom I have worked in the past, has shown that the PeV neutrinos are consistent with a prediction he and three collaborators made in 1991 that ultra-high-energy neutrinos could be produced in the cores of active galaxies.³³

A WORD OF CAUTION

As in the previous section, several of the new results I describe in this chapter (also in chapter 11) were inserted into the manuscript after it had already been submitted to the publisher. Some of the references still exist only in preprint form. Obviously, particle physics and cosmology are very rapidly developing areas of study, so nothing here should be taken as final. I can only present a snapshot of the situation as it existed when this book was published.