Inflation and observational constraints on loop quantum cosmology

by Ivan Agulló, Penn State

• Gianluca Calcagni, Inflationary observables and observational constraints on loop quantum cosmology January 18th 2011. PDF of the slides, and audio in either .wav (40MB) or .aif format (4MB).

Cosmology has achieved a remarkable progress in the recent years. The proliferation of meticulous observations of the Universe in the last two decades has produced a significant advance in our understanding of its large scale structure and of its different stages of evolution. The precision attained in the observations already made, and in the observations expected in the near future, is such that the Cosmos itself constitutes a promising "laboratory" to obtain information about fundamental physics. The obvious drawback is that, unlike what happens in common  laboratories on earth, such as the famous Large Hadron Collider at CERN, our Universe has to be observed as it is, and we are not allowed to select and modify the parameters of the "experiment". The seminar given by Gianluca Calcagni, based on results obtained in collaboration with M. Bojowald and S. Tsujikawa, shows an analysis of the effects that certain aspects of quantum gravity, in the context of Loop Quantum Cosmology, could produce on observations of the present Universe.

One of the important pieces of the current understanding of the Universe is the mechanism of inflation. The concept of inflation generically makes reference to the enormous increase of some quantity in a short period of time. It is a concept that is surely familiar to everyone, because we all have experienced an epoch when, for instance, house prices have experienced an alarming growth in a brief period. In the case of cosmological inflation the quantity increasing with time is the size of the Universe. Inflation considers that there was a period in the early Universe in which its volume increased by a factor of arround 10⁷⁸ (a 1 followed by 78 zeros!) in a period of time of about 10^-36 seconds. There is no doubt that, fortunately, this inflationary process is more violent than anything that we experience in our everyday life. The inflationary mechanism  in cosmology was introduced by Alan Guth in 1981, and was formulated in its modern version by A. Linde, A. Abrecht, P. Steinhard a year later. Guth realized that a huge expansion would make the Universe look almost flat and highly homogeneous for its inhabitants, without requiring it had been like that since its origin. This is consistent with observations of our Universe, which looks like highly homogeneous on large scales; and we know, by observing the cosmic microwave background (CMB), was even more homogeneous in the past. The CMB constitutes a "photograph" of the Universe when it was 380000 years old (a teenager compared with its current age of about 14000000000 years) and shows that the inhomogeneities existing at that time consisted of tiny variations (of 1 part in 100000) of its temperature. These small fluctuations are the origin of the inhomogeneities that we observe today in form of galaxies cluster, galaxies, stars, etc.

However, a few years after the proposal of inflation, several researchers (Mukhanov, Hawking, Guth, Pi, Starobinsky, Bardeen, Steinhardt and Turner) realized that inflation may provide something more valuable than a way of understanding the homogeneity and flatness of the observable Universe. Inflation provides a natural mechanism for generating the small inhomogeneities we observe in the CMB through one of the most attractive ideas in contemporary physics. A violent expansion of the Universe is able to amplify quantum vacuum fluctuations (that exist as a consequece of the Heisenberg’s uncertainty principle), and spontaneously produce tiny density fluctuations. In that way, General Relativity, via the exponential expansion of the Universe, and Quantum Mechanics, via the uncertainty principle, appear together (but not scrambled) in the game to generate a spectrum of primordial cosmic inhomogeneities out from the vacuum. This spectrum constitutes the "seed" that, by the effect of gravity, will later evolve into the temperature fluctuations of the CMB and then into the structures that we observe today in our Universe, from galaxy clusters to ourselves. The statistical properties of the temperature distribution of the CMB, analyzed in great detail by the WMAP satellite in the last decade, confirm that this picture of the genesis of our Universe is compatible with observations. Although there is not enough data to confirm the existence of an inflationary phase in the early stages of the Universe, inflation is one of the best candidates in the landscape of contemporary physics to explain the origin of the cosmic structures.

The mechanism of inflation opens a window of interesting possibilities for both theoretical and experimental physicists. The increase of the size of the Universe during inflation is such that the radius of an atom would expand to reach a distance that light would take a year to travel. This means that, if there was a period of inflation in the past, by observing the details of small temperature fluctuations in the CMB, we are actually getting information about physical processes that took place at extremely small distances or, equivalently, at very large energies. In particular, inflation predicts that the origin of the CMB temperature variations are generated from quantum vacuum fluctuations when the energy density of the Universe was about 10^-11 times the Planck density (the Planck density corresponds to 5·10¹¹³ Jules per cubic meter). The energy density that the Large Hadron Collider at CERN is going to reach is around 10^-60 times the Planck density, that is 49 orders of magnitude smaller! In this sense, the observation of our own Universe is a promising way to reveal information about physical theories that only become apparent at very high energies, as it is the case of quantum gravity. This fact has motivated experts in quantum gravity to focus their research on the predictions of potential observable signatures of their theories in cosmology, as shown in this seminar by Gianluca Calcagni.

Gianluca Calcagni shows in this seminar an analysis of the effects that certain aspects of quantum gravity, from the perspective Loop Quantum Cosmology (LQC), could produce on the generation of primordial fluctuations during inflation. Generally, LQC introduces two types of corrections to the equations describing the evolution of cosmic inhomogeneities; the so-called holonomy corrections and inverse volume corrections. This seminar focuses on the latter type, leaving the former for future work. Gianluca shows that it is possible to obtain the equations describing cosmic inhomogeneities during the inflationary epoch including inverse volume effects in LQC consistently (in the case that these corrections are small). With these equations it is possible then to recalculate the properties of the temperature distribution of the CMB including such LQC corrections. Generically, the effects that quantum aspects of gravity introduce into the classical equations are relevant when the scale of energy density is close to the Planck scale, and quickly disappear at lower scales. One would expect, therefore, that at the energy density at which inflation occurs, which is eleven orders of magnitude below the Planck scale, the effects of quantum gravity would be suppressed by a factor of 10^-11. The authors of this work argue that, surprisingly, this is not the case, and inverse volume corrections may be larger. In summary, the conclusions of this seminar suggests that even though the effects that quantum aspects of gravity have on the CMB are small, cosmological observations can put upper bounds on the magnitude of the corrections coming from quantum gravity that may be closer to theoretical expectation than what one would expect.

Although there is still a lot of work to do, the observation of our Universe via the cosmic microwave background and the distribution of galaxies is shown as a promising way to obtain information about physical processes where the relationship of Quantum Mechanics and General Relativity plays a major role. In this sense, it may be the Universe itself which give us a helping hand toward the understanding of the fundamental laws of physics.