Gravitational waves from the Big Bang
6 Feb, 2007 10:56 am
Gravitational waves are copiously produced during the violent process of reheating the Universe after cosmic inflation, i.e. at the Big Bang. Such a background could be observed in the near future thanks to gravitational wave observatories like LIGO (already underway), LISA or the proposed Big Bang Observer. The amplitude and shape of the gravitational wave spectrum contains information about that poorly known era of the Universe when the huge energy density that was driving inflation gets violently converted into relativistic matter and radiation. The discovery of such a background would open a new window into the very early Universe, which could be as rich in information as the present Cosmic Microwave Background, except that it would correspond to a minute fraction of a second after the Big Bang itself, and not 380,000 years later.
In a recent paper, just accepted for publication in Physical Review Letters , we predict a new cosmological background which comes from this violent period, when large amounts of matter were moving around and colliding at close to the speed of light, creating a significant fraction of energy density in the form of gravitational waves (GW). Gravitational waves are ripples in space-time that travel at the speed of light. Their emission by relativistic bodies like inspiralling black hole binaries and violent astrophysical phenomena like supernova explosions is a robust prediction of general relativity. The change in the orbital period of a binary pulsar known as PSR 1913+16 was used by Hulse and Taylor to obtain indirect evidence of their existence . Just like black holes inspiralling together or bubbles colliding at a cosmic phase transition can create a large amount of gravitational waves, the violent process of reheating also produces a huge GW background.
The phenomenon of reheating after inflation occurs through three subsequent phases: first a quick growth driven by the exponential growth of the energy density of the fields interacting with the inflaton; then particle and GW production due to the collisions of bubble-like structures formed in the distribution of the energy density of these fields; and finally a period of turbulence, i.e. the stirring up of the fluid, before thermalization. We predict that this is a relic cosmic background because it comes from all directions (just like the microwave background) and because we cannot disentangle the individual sources (the bubble collisions and the turbulent flows) that generated them. The production of this GW background is particularly robust in Hybrid Inflation, i.e. in a concrete model of inflation in which the inflaton field driving the expansion is coupled to a symmetry breaking (Higgs) field that triggers the end of inflation. The advantage of this model is that it allows for inflation to occur at low scales without affecting the amplitude of temperature fluctuations in the cosmic microwave background (CMB). In a Physical Review Letter published five years ago, together with Andrei Linde, Lev Kofman and others , we discovered that reheating in hybrid models must have occurred in a very violent way.
Let's analyze the specific signatures of this new cosmological background. It is well known that the cosmic microwave background has a black body spectrum of frequencies that exactly matches a uniform temperature of 2.75 K across the sky . It is a black body spectrum because the photons were in equilibrium with the plasma when they decoupled. When the gravitational wave background was generated at reheating, the plasma was very far from thermal equilibrium, the inflaton energy density was violently converted into radiation and matter, but had not yet thermalized. Nevertheless, the GW background also has a spectrum of frequencies, and its shape (the amplitude it has for a given frequency) contains exquisite information about the process of reheating (comparatively, the blackbody spectrum has information only about one quantity, its temperature). In fact, since the gravitational interaction is so weak, the GW produced at reheating are immediately decoupled from the plasma, so they will have travelled unimpeded since. If we find this background we will be looking at the Universe when it was just a minute fraction of a second after the Big Bang, and not 380,000 years, like with the CMB. Moreover, those waves that were produced in the first stage of quick growth after inflation will have decoupled earlier than those at bubble collisons and later will decouple those coming from the stage of turbulence.
These three periods have specific signatures, and a future detailed measurement of the spectrum might allow us to disentangle them, with the subsequent welth of knowledge about one of the most obscure (until now) epochs of the Early Universe, the period of reheating after inflation, i.e. the "Big Bang". Of course, the GW spectrum will be redshifted. All energy redshifts in an expanding universe, and these waves redshift as photons of the CMB do. The original spectrum would have frequencies (and therefore energies) 24 orders of magnitude larger than today. The expansion of the universe since reheating has redshifted those frequencies to a range that could be probed in the near future by GW observatories like LIGO, LISA or BBO. Note however that this cosmological background is in fact very close to noise: if it weren't for its spectral features it would be impossible to disentangle from the ordinary instrumental noise. It is thanks to the extreme ability of experimental researchers working in GW detectors that these types of background can be measured in the future.
Gravity waves from point sources like inspiralling black holes, or exploding supernovae, have a very distinct spectral shape, typically very sharp around a given frequency (related to the actual size of the system), while the GW background from reheating will have a relatively broad spectrum, ranging several decades in frequency. The actual characteristic wavelength of such a background can vary from around 1 Hertz to 1 GHz, depending on the scale of inflation. What is interesting is that for the first time we have predicted a GW background from reheating that could be within reach of future GW observatories, not only within their frequency range but also within their proposed sensitivity. In particular, the future Big Bang Observer (BBO), proposed for searching for the gravitational waves produced during inflation, may in fact measure the waves produced at the end of inflation, i.e. at the "Big Bang", which would more appropriately justify its name, BBO. As I mentioned above, since the waves were produced when the plasma was very far from equilibrium, we cannot speak of a temperature of these waves: the spectrum is very far from a blackbody spectrum, it is more like a turbulent spectrum with a sharp cutoff at high frequencies.
The idea of searching for gravitational waves from inflation is not new. Gravity waves produced during inflation are supposed to leave a trace in the polarization anisotropies of the microwave background. This inflationary background is crucial because its amplitude determines the energy scale of inflation, still unknown, and because inflation makes a very specific prediction for a relation between this amplitude and the spectral tilt. If such a consistency relation is found valid, it would definitely imply that something like inflation must have taken place. However, if the scale of inflation is too low (one or two orders of magnitude below the present bounds), then we will never be able to measure this predicted background, nor test the consistency relation. In particular, in a hybrid model like the one we used in our work, such a background would be unobservable.
However, the background we are discussing here arises not during inflation but at the end of inflation, during the violent conversion of the inflaton energy into matter and radiation, which was predicted by Linde, Kofman and Starobinsky  a few years ago to proceed explosively in a process known as ``preheating'' (because it occurred before reheating and thermalization). Soon afterwards, Tkachev and Khlebnikov  proposed that such a process could produce a background of gravitational waves with typical frequencies in the GHz range, which would never be seen by present or future detectors. However, immediately afterwards, in a paper published in the Proceedings of the 1998 Moriond Conference , we predicted that in the case of a hybrid model, where the scale of inflation could be as low as 100 GeV, the generated GW background would fall precisely on the frequency range of future GW observatories.
It took us almost 10 years to develop the numerical code that would finally convince the community that such a background is indeed produced for hybrid models in the range of frequencies predicted. What we have in fact realized is that the mechanism of GW production at preheating is much more complex than we imagined. Not only do we have the exponential growth of modes during the first stages, but also the production of bubble-like structures (peaks in a Gaussian random field associated with the quantum fluctuations of the Higgs) of high density contrast that expand at speeds close to the speed of light and eventually collide, liberating huge amounts of gravitational waves, as well as an intermediate (and rather long) process of turbulent flows that contribute further to the predicted background, until the universe finally thermalizes and the spectrum redshifts unchanged until the present. There are other GW backgrounds of astrophysical origin, like galactic white dwarf binaries, which could give a similar signal. However, they peak at a frequency which is also lower than this background, as we discuss in the letter, and has a different spectral signature, so it is in principle distinguishable. Of course, a more detailed analysis of both backgrounds is needed in specific models before giving a robust conclusion.
I think the most important result of our work is the possibility to have access, thanks to a new messenger (gravitational waves), to the widely unknown process of reheating after inflation, generated a minute fraction of a second after the Big Bang. In fact, we would be looking at the process that generated the Big Bang itself. Such an epoch cannot be reached by electromagnetic waves (as much as we cannot see the interior of a cloud) nor neutrinos, while it is easily probed by gravitational waves. It contains crucial information about the generation of the matter-antimatter asymmetry, the possible production of topological defects like cosmic strings, primordial magnetic fields, and possibly even superheavy dark matter. If, in the future, GW observatories are precise enough to disentangle the three main stages of preheating, we would have at our disposal tools (comparable to those provided by the observed anisotropies of the microwave background) for extracting information about the nature and couplings of the inflaton to all the rest of the matter in the Universe. We cannot dismiss this opportunity for looking back in time to the very beginning of our Universe.
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