**William Nelson, PennState**

**Title:**Inhomogeneous loop quantum cosmology

PDF of the talk (500k)

Audio [.wav 32MB], Audio [.aif 3MB].

William Nelson's talk is a follow-up of the work presented by Iván Agulló a few months ago in this seminar series about their common work in collaboration with Abhay Ashtekar. Iván's talk was reviewed in this blog by Edward Wilson-Ewing, so the reader is referred to that entry for completeness. Even if substantial material will overlap with that post, here I will try to focus on other aspects of this research.

Due to the finiteness of the speed of light, when we look at a distant point, like a star, we are looking to the state of that point in the past. For our regular daily distances this fact hardly affects anything, but if we consider larger distances, the effect is noticeable even for our slow-motion human senses. For instance, the sun is 8 light-minutes away from us, so if it suddenly were switched off we would be able to do a fair number of things in the mean time until we find ourselves in the complete darkness. For cosmological distances this fact can be really amazing: we can see far back in the past! But, how far away? Can we really see the instant of the creation?

The light rays, that were emitted during the initial moments of the universe and that arrive to the Earth nowadays, form our particle horizon, which defines the border of our observable universe. As a side remark, note that the complete universe could be larger (even infinite) than the observable one, but not necessarily. We could be living in a universe with compact topology (like the surface of a balloon) and the light emitted from a distant galaxy would reach us from different directions. For instance, one directly and other once after traveling around the whole universe. Thus, what we consider different galaxies would be copies of the same galaxy in different stages of its evolution. In fact, we could even see the solar system in a previous epoch!

Since the universe has existed for a finite amount of time (around 14 billions of years), the first guess would be that the particle horizon is at that distance: 14 billions of light years. But this is not true mainly for two different reasons. On the one hand, our universe is expanding, so the sources of the light rays that were emitted during the initial moments of the universe are further away, around 46 billions of light-years away. On the other hand, at the beginning of the universe, the temperature was so high that atoms or even neutrons or protons could not be formed in a stable way. The state of the matter was a plasma of free elementary particles, in which the photons interacted very easily. The mean free path of a photon was extremely short since it was almost immediately absorbed by some particle. In consequence, the universe was opaque to light, so none of the photons emitted at that epoch could make its way to us. The universe became transparent around 380000 years after the Big Bang, in the so-called recombination epoch (when the hydrogen atoms started to form),

and the photons emitted at that time form what is known as the Cosmic Microwave Background (CMB) radiation. This is the closest event to the Big Bang that we can nowadays measure with our telescopes. In principle, depending on the technology, in the future we might be able to detect also the neutrino and gravitational-wave backgrounds. These were released before the CMB photons since both neutrinos and gravitational waves could travel through the mentioned plasma without much interaction. The CMB has been explored making use of very sophisticated satellites, like the WMAP, and we know that it is highly homogeneous. It has an almost perfect black body spectrum that is peaked on a microwave frequency corresponding to a temperature of 2.7 K. The tiny inhomogeneities that we observe in the CMB are understood as the seeds of the large structures of our current universe.

Furthermore, the CMB is one of the few places where one could look for quantum gravity effects since the conditions of the universe during its initial moments were very extreme. The temperature was very high so that the energies of interaction between particles were much larger than we could achieve with any accelerator. But we have seen that the CMB photons we observe were emitted quite after the Big Bang, around 380.000 years later. Cosmologically this time is insignificant. (If we make an analogy and think that the universe is a middle-age 50 years old person, this would correspond to 12 hours.) Nevertheless, by that time the universe had already cooled down and the curvature was low enough so that, in principle, Einstein's classical equations of general relativity should be a very good approximation to describe its evolution at this stage. Therefore, why do we think it might be possible to observe quantum gravity effects at the CMB? At this point, the inflationary scenario enters the game. According to the standard cosmological model, around 10^(-36) seconds after the Big Bang, the universe underwent an inflationary phase which produced an enormous increase of its size. In a very short instant of time (a few 10^(-32) seconds) the volume was multiplied by a factor 10^78. Think for a while on the incredible size of that number: a regular bedroom would be expanded to the size of the observable universe!

This inflationary mechanism was introduced by Alan Guth in the 1980s in order to address several conceptual issues about the early universe like, for instance, why our universe (and in particular the CMB) is so homogeneous. Note that the CMB is composed by points that are very far apart and, in a model without inflation, could not have had any kind of interaction or information exchange during the whole history of the universe. On the contrary, according to the inflationary theory, all these points were close together at some time in the past, which would have allowed them to reach this thermal equilibrium. Furthermore, inflation has had a tremendous success and it has proved to be much more useful than originally expected. Within this framework, the observational values of the small inhomogeneities of the CMB are reproduced with high accuracy. Let us see in more detail how this result is achieved.

In the usual inflationary models, at the early universe the existence of a scalar particle (called the inflaton) is considered. The inflaton is assumed to have a very large but flat potential. During the inflationary epoch it slowly loses potential energy (or, as it is usually referred, it slowly rolls down its potential), and produces the exponential expansion of the universe. At the end of this process the inflaton's potential energy is still quite large. Since nowadays we do not observe the presence of such a particle, it is argued that after inflation, during the so-called reheating process, all this potential energy is converted into "regular" (Standard Model) particles. Even though this process is not yet well understood.

It is also usually assumed that at the onset of inflation the quantum fluctuations of the inflaton (and of the different quantities that describe the geometry of the universe) were in a vacuum state. This quantum vacuum is not a static and simple object, as one might think a priori. On the contrary, it is a very dynamical and complex entity. Due to the Heisenberg uncertainty principle, the laws of physics (like the conservation of energy) are allowed to be violated during short instants of time. This is well-known in regular quantum field theory and it happens essentially because the nature does not allow to perform any observation during such a short time. Therefore, in the quantum vacuum there is a constant creation of virtual particles that, under regular conditions, are annihilated before they can be observed. Nevertheless, the expansion of the universe turns this virtual particles into real entities. Intuitively one can think that a virtual particle and its corresponding antiparticle are created but, before they can interact again to disappear, the inflationary expansion of the universe tears them so apart that the interaction is not possible anymore. This initial tiny quantum fluctuations, amplified through the process of inflation, produces then the CMB inhomogeneities we observe. Thus, the inflation is a kind of magnifying glass that allows us to have experimental access to processes that happened at extremely short scales and hence large energies, where quantum gravity effects might be significant.

On the other hand, loop quantum cosmology (LQC) is a quantum theory of gravity that describes the evolution of our universe under the usual assumptions of homogeneity and isotropy. The predictions of LQC coincide with those of general relativity for small curvature regions. That includes the whole history of the universe except for the initial moments. According to general relativity the beginning of the universe happened at the Big Bang, which is quite a misleading name. The Big Bang has nothing to do with an explosion, it is an abrupt event where the whole space-time continuous came to existence. Technically, this point is called a singularity, where different objects describing the curvature of the spacetime diverge. Thus general relativity can not be applied there and, as it is often asserted, the theory contains the seeds of its own destruction. LQC smooths out this singularity by considering quantum gravity effects and the Big Bang is replaced by a quantum bounce (the so-called Big Bounce). According to the new paradigm, the universe existed already before the Big Bounce as a classical collapsing universe. When the energy density became too large, it entered this highly quantum region, where the quantum gravity effects come with the correct sign so that gravity happens to be repulsive. This caused the universe to bounce and the expansion we currently observe began. The aim of Will´s talk is to study the inflationary scenario in the context of LQC and obtain its predictions for the CMB inhomogeneities. In fact, Abhay Ashtekar and David Sloan already showed that inflation is natural in LQC. This means that itis not necessary to choose very particular initial conditions in order to get an inflationary phase. But there are still several questions to be addressed, in particular whether there might be any observable effects due to pre-inflationary evolution of the universe.

As we have already mentioned, in the usual cosmological models, the initial state is taken as the so-called Bunch-Davies vacuum at the onset of inflation. This time might be quite arbitrary. The natural point to choose initial conditions would be the Big Bang but this is not feasible since it is a singular point and the equations of motions are no longer valid. In any case, the extended view has been that, even if there were some particles present at the onset of inflation, the huge expansion of the universe would dilute them and thus the final profile of the CMB would not be affected. Nevertheless, recently Iván Agulló and Leonard Parker showed that the presence of such initial particles does matter for the final result since it causes the so-called stimulated emission of quanta: initial particles produce more particles, which themselves produce more particles and so on. In fact, this is the same process on which the nowadays widely used laser devices are based. Contrary to the usual models based on general relativity, LQC offers a special point where suitable initial conditions can be chosen: the Big Bounce. Thus, in this research, the corresponding vacuum state is chosen at that time. The preliminary results presented in the talk seem quite promising. The simplest initial state is consistent with the observational data but, at the same time, it slightly differs from the CMB spectrum obtained within the previous models. These results have been obtained under certain technical approximations so, the next step of the research will be to understand if this deviation is really physical. If so, this could provide a direct observational test for LQC that would teach us invaluable lessons about the deep quantum regime of the early universe.