Inflationary origin

Print edition : May 02, 2014

Figure 1: The dark sector lab, located about a kilometre from the South Pole, houses the BICEP2 telescope (left) and the South Pole Telescope (right). Photo: STEFFEN RICHTER, HARVARD UNIVERSITY

Figure 2: History of the universe with inflation: The bottom part of this illustration shows the scale of the universe versus time. The density waves appear as temperature and "E-mode" polarisation. The gravitational waves leave a characteristic signature in the CMB polarisation: the "B-modes". Both density and gravitational waves come from quantum fluctuations, which have been magnified by inflation to be present at the time when the CMB photons were emitted.

Figure 4: polarisation can be decomposed into E- and B-modes. The former are radial or tangential with no preferred handedness. B-modes do have handedness. This peculiar pattern can be produced only by gravitational waves, not by density fluctuations.

Figure 5: Gravitational waves from inflation generate a distinctive twisting pattern in the polarisation of the CMB, known as a "curl" or B-mode pattern. For the density fluctuations that generate most of the polarisation of the CMB, this part of the primordial pattern is zero. The figure shows the B-mode pattern observed with the BICEPS2 telescope, with the line segments showing the polarisation from different spots in the sky. The red and blue shading shows the degree of clockwise and anti-clockwise twisting of this B-mode pattern.

The sun rises behind the CMB telescopes at the National Science Foundation's South Pole station. Photo: Steffen Richter, Harvard University

The first detection of primordial gravitational waves could provide observational evidence of how the universe evolved.

MARCH 17, 2014, is certain to go down as a red letter day in the history of astronomy. On this day, a research team led by the Harvard-Smithsonian Centre for Astrophysics (CfA) in the United States announced to the world the first detection of “primordial gravitational waves”, ripples in the fabric of space-time produced during the birth throes of the universe, in the first fleeting fractions of a second after the Big Bang 13.8 billion years ago, which brought matter and light into existence in the form of an expanding extremely hot ball of dense plasma consisting of electrons, protons, neutrons and photons.

These “first tremors of the Big Bang” have been detected by BICEP2, or Background Imaging of Cosmic Extragalactic Polarisation, with the 2 indicating the second phase of the international collaboration experiment on the basis of observational data collected between January 2010 and December 2012 with a highly sensitive radio telescope mounted at the South Pole (figure 1). Encouraged by the performance of BICEP1, which operated between January 2006 and December 2008, the instrument was made much more sensitive using advanced technology sensors at the focal plane while reusing the same telescope and mount. The telescope itself was a simple, small-aperture (26 cm) all-cold refractor housed entirely in a liquid helium cryostat. While BICEP1 observed at radio frequencies of 100 GHz and 150 GHz, BICEP2 observed only at 150 GHz.

Gravitational waves (GWs) are a consequence of the equations of Einstein’s theory of general relativity. Any gravitational disturbance, such as moving masses, perturbs the space-time, generating waves akin to a boat moving across a lake or a stone thrown into water. But gravitational waves are extremely subtle; only cataclysmic cosmic events involving massive celestial objects such as black holes or neutron stars or supernova explosions are expected to produce ripples that are strong enough to travel for even millions of years and be detectable today on the earth.

To date only one indirect evidence of GWs has been found, one involving a binary pulsar—two pulsars (radiating neutron stars) orbiting around a common centre of mass—which was found to be losing energy in accordance with Einstein’s theory. This discovery was made in 1974 by Russel Hulse and Joseph Taylor, for which they received the Nobel Prize in 1993. Although highly sensitive (second generation) GW detectors are currently operational for a direct detection, the technology is yet to achieve the threshold of sensitivity required to increase the probability of detection. Many third-generation GW detectors are being built or being planned around the world (including one in India), but it will be a few years before they come up with some result.

Although the present detection, too, is only indirect evidence, the experiment has made the first direct “imaging” of primordial GWs across the primordial sky. This is like taking a snapshot of the high-water mark left by a receding sea tide. What BICEP2 has found are the distinct imprints of these primordial GWs on the cosmic microwave background (CMB) radiation, which is the all-pervading faint and cold remnant afterglow of the Big Bang. The BICEP2 instrument was designed specifically to detect this imprint by observing the CMB at large (degree level) angular scales (1-5°) in a specific patch in the sky.

No telescope based on electromagnetic signals can peer back into those very early moments because the scattering of zillions of photons by electrons inside the hot, dense plasma ensured that no light could escape from it for the first 380,000 years after the Big Bang and reach us today. During this period, this plasma was opaque, like a thick fog. The universe later expanded and cooled down to about 3,000 kelvin (0 °Celsius corresponds to 273 K), causing protons and electrons to combine and form hydrogen atoms (the “recombination” epoch). In the absence of free electrons, photons could now decouple from matter and stream free through the universe. These decoupled photons, now greatly cooled down to microwave energies (corresponding to an average temperature of 2.7 K) because of the expansion of the universe in the intervening billions of years, fill the universe and constitute the CMB radiation, which we can detect and study in detail. Over the years, satellites COBE, WMAP and Planck have mapped the CMB across the entire sky with increasing accuracy and spatial resolution (figures 2 and 3).

It was thus realised that only observation of primordial GWs could provide observational evidence for the manner in which the infant universe evolved, revealing the high-energy processes that currently remain opaque to even the highest energy particle accelerators and would be so for many years into the future. But direct detection of GWs resulting from the dynamics of the early universe would be well beyond the reach of any GW detector for the foreseeable future because just like the CMB radiation the free-streaming primordial GWs, too, would have been stretched by the expansion of the universe to enormous wavelengths, making it practically undetectable.

But physicists reasoned that these primordial GWs would have interacted with the photons of the early universe in a specific way just before they decoupled from matter, and the imprint of this on the CMB, albeit small, should be detectable. The interaction, as it turns out, affects the polarisation characteristics of the CMB radiation in a very distinct manner, which should be detectable with very sensitive polarisation-measuring instruments. (Light is said to be polarised when the vibrations are confined to one plane along the direction of propagation.) The BICEP telescope, which is basically a CMB-measuring instrument, was, in fact, designed with the sole objective of detecting the specific polarisation signatures of the primordial GWs on the CMB.

Inflation theory

One of the concepts that now form a part of the widely accepted Standard Cosmological Model is that of a primordial high-energy process called inflation. According to the inflation theory, which was postulated by Alan Guth in 1979 and was later refined by Andre Linde and Paul Steinhardt in 1981-82, the universe underwent a sudden and exponential burst in the early fractions of a second, between 10 -35 and 10 -32 of a second, after the Big Bang. During that extremely brief period, quicker than the blink of an eye, it doubled in size about 100 trillion trillion times. That is, it expanded by a factor of 2 20.

This hypothesis has remained untested so far even though the idea solves in one stroke a host of theoretical and observational problems associated with the non-inflation theory. However, what caused this sudden explosive expansion and its abrupt end, and at what energy scale this actually occurred, remain unexplained and unknown. One popular idea, based on field theory, is that, just as the Higgs field generated all the mass in the universe, quantum fluctuations of an “inflation” field caused inflation by exerting extreme negative (repulsive) pressure on the slowly expanding infant universe, resulting in extreme expansion. The idea of inflation has also gained ground as the large structure implied in the WMAP and Planck observations is believed to conform to the predictions of models of inflation.

Of course, this violent and chaotic expansion would have resulted in the production of strong GWs which would have affected the subsequent evolution of this inflated universe. BICEP2 was, in fact, designed specifically to look for the effects of GWs arising from an inflationary scenario. This it did by measuring CMB polarisation at larger degree-level angular scales because the polarisation effects of primordial GWs are expected to peak at these scales, and not at lower angular scales, according to the inflation theory. The specific results of the experiment have led to the BICEP2 research team as well as large sections of the cosmological community to claim them to be proof of inflation. While the argument, given the specific details of the finding, may be persuasive, it is still premature to claim it as proof of inflation.

Gravitational wave imprint

How do primordial GWs leave an imprint of the polarisation of CMB radiation? As GWs travel they squeeze and stretch space in perpendicular directions and act on matter or radiation through this stretching and squeezing of space. For radiation, this implies a corresponding stretching or squeezing of its wavelength in orthogonal directions, resulting in a variation in its power spectrum in perpendicular directions, which is called “quadrupole anisotropy”.

When an electromagnetic wave is incident on a free electron, the scattered wave is polarised perpendicular to the incidence direction. If the incident radiation were isotropic or had only a right-left variation, the scattered radiation would have no net polarisation. However, if there are variations in the incident radiation from perpendicular directions (quadrupole anisotropy), a net linear polarisation will result.

Now imagine the scenario in the primordial universe. The turbulent disturbances soon after the Big Bang would have resulted in mass and density fluctuations in the primordial matter as well as in the production of GWs. The density fluctuations provided the initial seed for the creation of galaxies and clusters of galaxies in the large-scale structure of the universe today, and the small temperature variations in the CMB sky are a measure of that initial seeding that occurred when the universe was less than 380,000 years old. In inflationary scenarios, quantum fluctuations in the inflation field became density fluctuations in the CMB, and, at much later times, in galaxy distributions.

As the infant universe expanded and, about 380,000 years later, atoms formed and light decoupled from matter, the escaping CMB photons would have also got polarised (on account of quadrupole anisotropy in the photon field) as they got scattered from the rapidly dwindling number of free electrons at the time of recombination. But quadrupole anisotropy can result not only from primordial GWs, as discussed above, but also from density fluctuations in the primordial matter. But the ways in which the two perturb the primordial photon field are different. Density fluctuations cause “scalar perturbations” and the GWs lead to “tensor perturbations”. The orientations of the CMB polarisation they cause, which can be measured, are also correspondingly different.

A map of CMB polarisation in the sky will, therefore, display two modes of orientations: the E-mode and the B-mode. While the former (figure 4) are either radial or tangential, the latter have a twist, or swirly, pattern (“curl”) in the polarisation maps. The detection of B-mode polarisation in the CMB sky would imply a definitive proof of primordial GWs. The B-mode polarisation map would constitute an “‘image”’ of the primordial GWs. It is this B-mode polarisation imprint on the CMB that BICEP2 has seen and measured in a small region of the sky at angular scales of a few degrees (figure 5).

The CMB polarisation itself is a small effect (the polarised intensity of the CMB is less than a millionth of its total brightness) because the number of free electrons available at the time of decoupling is small, but the tensor-to-scalar ratio (called r) gives a measure of the strength of the perturbations arising from the primordial GW background. This is obtained by measuring the amount of E-mode and B-mode polarisation in the polarisation map of the CMB sky.

The r value measured by BICEP2 is about 0.2, which is larger than the limit of 0.11 obtained by Planck researchers on the basis of the temperature measurements in the CMB sky.

It must, however, be pointed out that the r value reported from Planck and other previous experiments are not from B-mode polarisation. Instead, they come from CMB temperature measurements. Also, they are at much smaller angular scales. But there is a disagreement here that needs to be resolved, and the planned detailed polarisation measurements by Planck should be able to do this. But the BICEP2 researchers at the March 17 press conference said that certain fine-tuning could be made to an extension of what is known as the lambda-cold dark matter (lambda-CDM) model—what currently forms an essential component of the Standard Cosmological Model—so that the two results could agree.

“But these tweaks would be tremendously ugly,” said Neil Turok, a cosmologist and director of the Perimeter Institute in Canada. “In fact, I believe that if both Planck and the new results agree, then together they would give substantial evidence against inflation,” he said.

Significantly, the measured angular spectra of polarisation, and the cross-correlations among the different modes, also peak at higher angular scales (at about 2°) with high significance precisely as required by inflationary models. “We have extensively studied possible contamination from instrumental effects and feel confident that we can limit them to much smaller than the observed signal. Inflationary GWs appear to be by far the most likely explanation for the signal that we see,” says the BICEP2 team.

Last year, another telescope in the same South Pole region as BICEP2 and, in a sense a competitor to BICEP2, called the South Pole telescope (SPT), was the first to report the observation of B-mode polarisation in the CMB. However, the signal was over much smaller angular scales of less than 1° and was attributed to the curvature of the space due to galaxies in the foreground through which the CMB radiation reached the telescope.

The BICEP2 data, according to the researchers, also strongly disfavour contamination by galactic emission or polarised dust in the interstellar space. “The best current models of polarised galactic emission in our observing region show it to be much fainter than the signal we see. Also, there is little evidence for correlation between our B-mode maps and the predicted pattern from the galaxy. Finally, within our own data, the spectrum of the B-modes found by comparing different frequencies is consistent with CMB and disfavours galactic contamination,” the researchers say.

As was discussed, polarisation requires scattering. This requirement limits the epochs during which polarisation can be generated to (1) during the process of recombination when the universe was 380,000 years old and (2) much later when electrons are liberated from hydrogen, but then scatterings would be rare as the universe would be very dilute then. The characteristic angular scales at which polarisation signals peak in inflationary models are about 2° and 50° respectively. BICEP2 has found only the former. The latter require, as the BICEP paper points out, the coverage of nearly the entire sky, which may not be feasible for quite some time. But an observation at that scale would clinch the issue for inflation.

But, even in some inflationary scenarios, such a high r value was not quite expected. The observation implies a highly energetic domain in which the primordial GW process (inflationary or not) occurred. This r value, according to the BICEP2 team, corresponds to an energy of about 10 16 GeV (giga or billion electronvolt). The energy scale is an indication of how fast the universe expanded during inflation. Also, the precise time at which inflation occurred can be inferred from this energy value, and it turns out to be 10 -37 seconds, two orders of magnitude earlier than what most inflationary models assume. Compare this with the highest total energy of 14 TeV (tera or trillion electronvolt) that the colliding protons at the Large Hadron Collider (LHC) are expected to attain by the year end. It is a factor of a trillion more and it is beyond any man-made machine even in the foreseeable future.

Assuming inflation is true, the data, in particular the energy scale at which it is supposed to have happened, will result in the “spring cleaning” of inflation models, as one article put it, throwing out whole classes of them. According to Andre Linde, nearly 90 per cent of the models, in particular, models that use the idea of a particle called axion driving the inflation. And so would perhaps be ideas of cyclical universes.

Linde’s own pet theory of a multiverse—chaotic inflation leading to several parallel universes being created—can, however, survive with some fine-tuning, he believes. But, at a theoretical level, at this energy a Grand Unification of the strong-nuclear, the weak-nuclear and the electro-weak forces of interaction is expected to occur when all the forces become equal and unify into a single unified force. It is naturally appealing for the proponents of inflation generally to argue, on the basis of the BICEP2 results, that inflation indeed occurred at that energy scale.

However, to re-emphasise, the observation of B-mode polarisation per se is not sufficient proof of inflation. Inflation is still a theory that needs to be proven conclusively by further experimental observations. There could be a host of other gravitational processes in the early universe soon after the Big Bang, independent of inflation, which could have produced GWs and tensor perturbations on the CMB. Also, BICEP2 has focussed only on a small part of the sky. It would only be conjecture that it is across the sky in general. As of now, it is only clear evidence of primordial GWs.

Specifically, as L.M. Krauss and company (who otherwise believe in inflation) have argued, another possibility is that of phase transition in the early universe—change from one state of matter to another, like solid to liquid—which can produce a stochastic GW background with an inflation-like power spectrum. This signal, according to Krauss, can be enhanced so that even phase transitions below the scale of inflation could produce a comparable signal. Neil Turok, too, is sceptical. “I will quote Carl Sagan and say ‘extraordinary claims require extraordinary evidence’, and they don’t have extraordinary evidence yet,” Turok told the journal Physics World. The BICEP team is itself planning a still -improved experiment called BICEP3 that should clear up a lot of the lingering doubts.

Despite all the caveats, given the present scenario with regard to observation of GW signals, the BICEP2 discovery is remarkable and indeed heroic. It is a testimony to the team’s ingenuity in harnessing advanced technologies to make the most sensitive CMB polarisation measurements possible today. In terms of the significance of the present discovery —irrespective of whether it is an indication of inflation or not—it must rank alongside the discovery of the Higgs boson in recent times.

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