Observational signatures of loop quantum cosmology?

by Edward Wilson-Ewing, Penn State

• Ivan Agullo, March 29th 2011. Observational signatures of loop quantum cosmology? PDF of the slides, and audio in either .wav (40MB) or .aif format (4MB).

In the very early universe the temperature was so high that electrons and protons would not combine to form hydrogen atoms but rather formed a plasma that made it impossible for photons to travel significant distances as they would continuously interact with the electrons and protons.  However, as the early universe expanded, it cooled and, 380 000 years after the Big Bang, the temperature became low enough for hydrogen atoms to form in a process called recombination.  At this point in time, it became possible for photons to travel freely, as the electrons and protons had combined to become electrically neutral atoms.  It is possible today to observe the photons from that era that are still travelling through the universe: these photons form what is called the cosmic microwave background (CMB).  By observing the CMB, we are in fact looking at a photograph of what the universe looked like only 380 000 years after the Big Bang!  Needless to say, the detection of the CMB was an extremely important discovery and the study of it has taught us a great deal about the early universe.

The existence of the CMB was first predicted in 1948 by George Gamow, Ralph Adler and Robert Herman, when they estimated its temperature to be approximately 5 degrees Kelvin.  Despite this prediction, the CMB was not detected until Arno Penzias and Robert Wilson made their Nobel Prize-winning discovery in 1964.  Ever since then, there have been many efforts to create better radio telescopes, both Earth- and satellite-based, that would provide more precise data and therefore more information about the early universe.  In the early 1990s the COBE (COsmic Background Explorer) satellite's measurements of the small anisotropies in the CMB were considered so important that two of COBE's principal investigators, George Smoot and John Mather, were awarded the 2006 Nobel Prize.  The state-of-the-art data today comes from the WMAP (Wilkinson Microwave Anisotropy Probe) satellite and there is already another satellite that has been taking data since 2009.  This satellite, called Planck, has a higher sensitivity and better angular resolution than WMAP ,and its improved map of the CMB is expected to have been completed by the end of 2012.

The CMB is an almost perfect black body and its temperature has been measured to be 2.7 degrees Kelvin.  As one can see in the figure below, the black body curve of the CMB is perfect: all of the data points lie right on the best fit curve.  It is possible to measure the CMB's temperature in every direction and it has been found that it is the same in every direction (what is called isotropic) up to one part in 100 000.

Even though the anisotropies are very small, they have been measured quite precisely by the WMAP satellite, and one can study how the variations in temperature are correlated by their angular separation in the sky.  This gives the power spectrum of the CMB, where once again theory and experiment agree quite nicely:

In order to obtain a theoretical prediction about what the power spectrum should look like, it is important to understand how the universe behaved before recombination occurred.  This is where inflation, an important part of the standard cosmological model, comes in.  The inflationary epoch occurs very soon after the universe leaves the Planck regime (where quantum gravity effects may be important), and during this period the universe's volume increases by a factor of approximately e^(210) in the very short time of about 10^(-33) seconds (for more information about inflation, see the previous blog post).  Inflation was first suggested as a mechanism that could explain why (among other things) the CMB is so isotropic: one effect of the universe's rapid expansion during inflation is that the entire visible universe today occupied a small volume before the beginning of inflation and had had time to enter into causal contact and thermalize.  This pre-inflation thermalization can explain why, when we look at the universe today, the temperature of the cosmic microwave background is the same in all directions.  But this is not all: using inflation, it is also possible to predict the form of the power spectrum.  This was done well before it was measured sufficiently precisely by WMAP and, as one can see in the graph above, the observations match the prediction very well!  Thus, even though inflation was introduced to explain why the CMB's temperature is so isotropic, it also explains the observed power spectrum.  It is especially this second success that has ensured that inflation is part of the standard cosmological model today.

However, there remain some issues that have not been resolved in inflation.  For example, at the beginning of inflation, it is assumed that the quantum fields are in a particular state called the Bunch-Davies vacuum.  It is then possible to evolve this initial state in order to determine the state of the quantum fields at the end of inflation and hence determine what the power spectrum should look like.  Even though the predicted power spectrum agrees extremely well with the observed one, it is not entirely clear why the quantum fields should be in the Bunch-Davies vacuum at the onset of inflation.  In order to explain this, we must try to understand what happened before inflation started and this requires a theory of quantum gravity.

Loop quantum cosmology is one particular quantum gravity theory which is applied to the study of our universe.  There have been many interesting results in the field over the last few years: (i) it has been shown in many models that the initial big bang singularity is replaced by a “bounce” where the universe contracts to a minimal volume and then begins to expand again; (ii) it has also been shown that quantum gravity effects only become important when the space-time curvature reaches the Planck regime, therefore classical general relativity is an excellent approximation when the curvature is less than the Planck scale; (iii) the dynamics of the universe around the bounce point are such that inflation occurs naturally once the space-time curvature leaves the Planck regime.

The goal of the project presented in the ILQGS talk is to use loop quantum cosmology in order to determine whether or not the quantum fields should be in the Bunch-Davies vacuum at the onset of inflation.  More specifically, the idea is to choose carefully the initial conditions at the bounce point of the universe (rather than at the beginning of inflation) and then study how the state of the fields evolves as the universe expands in order to determine their state at the beginning of inflation.  Now one can ask: Does this change the state of the quantum fields at the onset of inflation?  And if so, are there any observational consequences?  These are the questions addressed in this presentation.