Duration of inflation and conditions at the bounce as a prediction of effective isotropic loop quantum cosmolog

Loop quantum cosmology with a scalar field is known to be closely linked with an inflationary phase. In this article, we study probabilistic predictions for the duration of slow-roll inflation, by assuming a minimalist massive scalar field as the main content of the universe. The phase of the field in its "prebounce" oscillatory state is taken as a natural random parameter. We find that the probability for a given number of inflationary e-folds is quite sharply peaked around 145, which is consistent with the most favored minimum values. In this precise sense, a satisfactory inflation is therefore a clear prediction of loop gravity. In addition, we derive an original and stringent upper limit on the Barbero-Immirzi parameter. The general picture of inflation, superinflation, deflation, and superdeflation is also much clarified in the framework of bouncing cosmologies.Comment: 7 pages, 7 figure

Modified Friedmann equation and survey of solutions in effective Bianchi-I loop quantum cosmology

In this article, we study the equations driving the dynamics of a Bianchi-I universe described by holonomy corrected effective loop quantum cosmology. We derive the LQC-modified generalized Friedmann equation, which is used as a guide to find different types of solutions. It turns out that, in this framework, most solutions never reach the classical behavior.Comment: 11 pages, 11 figure

Anomaly-free perturbations with inverse-volume and holonomy corrections in Loop Quantum Cosmology

This article addresses the issue of the closure of the algebra of constraints for generic (cosmological) perturbations when taking into account simultaneously the two main corrections of effective loop quantum cosmology, namely the holonomy and the inverse-volume terms. Previous works on either the holonomy or the inverse volume case are reviewed and generalized. In the inverse-volume case, we point out new possibilities. An anomaly-free solution including both corrections is found for perturbations, and the corresponding equations of motion are derived.Comment: previous mistake corrected leading to new result

Primordial tensor power spectrum in holonomy corrected Omega-LQC

The holonomy correction is one of the main terms arising when implementing loop quantum gravity ideas at an effective level in cosmology. The recent construction of an anomaly free algebra has shown that the formalism used, up to now, to derive the primordial spectrum of fluctuations was not correct. This article aims at computing the tensor spectrum in a fully consistent way within this deformed and closed algebra.Comment: 5 pages, 6 figures, accepted by Phys. Rev.

Silent initial conditions for cosmological perturbations with a change of space-time signature

Recent calculations in loop quantum cosmology suggest that a transition from a Lorentzian to an Euclidean space-time might take place in the very early Universe. The transition point leads to a state of silence, characterized by a vanishing speed of light. This behavior can be interpreted as a decoupling of different space points, similar to the one characterizing the BKL phase. In this study, we address the issue of imposing initial conditions for the cosmological perturbations at the transition point between the Lorentzian and Euclidean phases. Motivated by the decoupling of space points, initial conditions characterized by a lack of correlations are investigated. We show that the "white noise" gains some support from analysis of the vacuum state in the deep Euclidean regime. Furthermore, the possibility of imposing the silent initial conditions at the trans-Planckian surface, characterized by a vanishing speed for the propagation of modes with wavelengths of the order of the Planck length, is studied. Such initial conditions might result from a loop-deformations of the Poincar\'e algebra. The conversion of the silent initial power spectrum to a scale-invariant one is also examined.Comment: 24 pages, 9 figures. Revised version accepted for publication in IJMP

Primordial scalar power spectrum from the Euclidean Big Bounce

In effective models of loop quantum cosmology, the holonomy corrections are associated with deformations of space-time symmetries. The most evident manifestation of the deformations is the emergence of an Euclidean phase accompanying the non-singular bouncing dynamics of the scale factor. In this article, we compute the power spectrum of scalar perturbations generated in this model, with a massive scalar field as the matter content. Instantaneous and adiabatic vacuum-type initial conditions for scalar perturbations are imposed in the contracting phase. The evolution through the Euclidean region is calculated based on the extrapolation of the time direction pointed by the vectors normal to the Cauchy hypersurface in the Lorentzian domains. The obtained power spectrum is characterized by a suppression in the IR regime and oscillations in the intermediate energy range. Furthermore, the speculative extension of the analysis in the UV reveals a specific rise of the power.Comment: 13 pages, 4 figure

Multi-photon emission in QED with strong background fields

In recent and upcoming years new lasers are being constructed withever higher intensity. These lasers open up the possibility of probingthe high intensity regime of particle physics, which will lead to etherconrming our current models in this regime or the discovery of beyondstandard model physics. However most previous theoretical results in thisarea are based old assumptions about the intensity and shape of the laserpulse that are no longer valid. In this thesis we calculate the tree-levelprobabilities for multi photon emission from an electron propagating inan arbitrary plane wave electromagnetic eld. We show that the classicallimit of our result agrees with the purely classical description of the sameevent. We calculate the soft emission correction to non-linear Comptonscattering. We conclude that our results are infrared divergent and arguethat this will be solved by including loop contributions to the process. Ourresults provide an important component for the theoretical predictions forthe outcome of scattering experiments in high intensity background eld.This thesis will add to the understanding of high intensity QED

Phénoménologie de la cosmologie quantique à boucles

Loop quantum gravity (LQG) is an attempt to solve the problem of quantum gravity. Loop quantum cosmology (LQC) is an attempt to apply LQG to early cosmology. The purpose of LQC is to connect LQG with observations. It is very hard to observe any quantum gravity effects because enormous energy density is most likely required. This is exactly why the early Universe is chosen as a stage to search for quantum gravity phenomena.The central result of LQC is that the big bang singularity is replaced by a big bounce. However this is not something that is possible to observe today. For this reason, we have investigated how cosmic perturbations are affected by LQC. We have used the so called deformed algebra approach, and have calculated the resulting spectrums for both scalar and tensor perturbations.The spectrums that we have found are not compatible with observation. However this can not bee taken as very strong evidence against LQG since there are too many assumptions on the way. Rather this is a result for this specific interpretation of LQC.We have also studied the background dynamics (the homogenous part of the equations) of LQC. Since slow-roll inflation is essential in explaining many features of the universe, including the CMB, we want to know if slow-roll inflation is compatible with LQC. We have found that, indeed, it is. If a square potential inflation field is added to the theory, the bounce will lift the potential energy enough to provide around 145 e-folds of slow-roll inflation. However, when anisotropies are taken into account, the amount of inflation decreases, and can even disappear completely if there is too much shear at the time of the bounce.We have derived the modified Friedman equation for anisotropic LQC. This has allowed us to study anisotropic LQC not just numerically, but also analytically, which has given us a much more comprehensive understanding of the situation than what was known before.Finally, we have studied some geometric aspects of de Sitter space, which has resulted in two very different considerations. Firstly we found that we can, for a general theory of modified cosmology and under some quite conservative assumptions, derive the dynamics for a spatially curved universe, given the dynamics of a spatially flat one. This is relevant in theories such as LQC, where it is easier to find the flat solution than the curved one. Secondly, we propose a possible mechanism for the origin and rebirth of the Universe.Boucle gravité quantique (LQG) est une tentative pour résoudre le problème de la gravité quantique. Boucle cosmologie quantique (LQC) est une tentative d'appliquer LQG à la cosmologie précoce. Le but de LQC est de se connecter LQG avec des observations. Il est très difficile d'observer les effets de la gravité quantique parce que la densité d'énergie énorme est très probablement nécessaire. Ceci est exactement pourquoi l'Univers est choisi comme une étape pour rechercher des phénomènes de gravité quantique.Le résultat central de LQC est que la grande singularité bang est remplacé par un gros rebond. Toutefois, ce ne sont pas quelque chose qui est possible d'observer aujourd'hui. Pour cette raison, nous avons étudié la façon dont les perturbations cosmiques sont affectées par LQC. Nous avons utilisé l'approche dite d'algèbre déformée, et nous avons calculé les spectres obtenus pour les deux perturbations scalaires et tenseurs. Les spectres que nous avons trouvé ne sont pas compatibles avec l'observation. Cependant cela ne peut abeille considérée comme très forte preuve contre LQG car il y a trop d'hypothèses sur le chemin. Plutôt cela est le résultat de cette interprétation spécifique de LQC.Nous avons également étudié la dynamique de fond (la partie homogène des équations) de LQC. Depuis lent-roll inflation est essentielle pour expliquer de nombreuses caractéristiques de l'univers, y compris le CMB, nous voulons savoir si lent-roll inflation est compatible avec LQC. Nous avons constaté que, en effet, il est. Si un champ d'inflation potentiel carré est ajouté à la théorie, le rebond va lever l'énergie potentielle suffisante pour fournir environ 145 e-plis de lent-roll inflation. Toutefois, lorsque anisotropies sont pris en compte, le montant de l'inflation diminue, et peut même disparaître complètement s'il y a trop de cisaillement au moment du rebond.Nous avons dérivé l'équation Friedman modifié pour anisotrope LQC. Cela nous a permis d'étudier anisotrope LQC pas seulement numériquement, mais aussi analytiquement, qui nous a donné une compréhension beaucoup plus complète de la situation que ce qui était connu auparavant.Enfin, nous avons étudié certains aspects géométriques de l'espace de Sitter, qui a donné lieu à deux considérations très différentes. Tout d'abord nous avons constaté que nous pouvons, pour une théorie générale de la cosmologie modifiée et sous certaines hypothèses assez conservatrices, tirer la dynamique d'un univers spatialement incurvée, étant donné la dynamique d'un un espace plat. Cela est pertinent dans les théories telles que LQC, où il est plus facile de trouver la solution plate que celle incurvée. Deuxièmement, nous proposons un mécanisme possible pour l'origine et la renaissance de l'Univers

Consistency and observational consequences of loop quantum cosmology

Boucle gravité quantique (LQG) est une tentative pour résoudre le problème de la gravité quantique. Boucle cosmologie quantique (LQC) est une tentative d'appliquer LQG à la cosmologie précoce. Le but de LQC est de se connecter LQG avec des observations. Il est très difficile d'observer les effets de la gravité quantique parce que la densité d'énergie énorme est très probablement nécessaire. Ceci est exactement pourquoi l'Univers est choisi comme une étape pour rechercher des phénomènes de gravité quantique.Le résultat central de LQC est que la grande singularité bang est remplacé par un gros rebond. Toutefois, ce ne sont pas quelque chose qui est possible d'observer aujourd'hui. Pour cette raison, nous avons étudié la façon dont les perturbations cosmiques sont affectées par LQC. Nous avons utilisé l'approche dite d'algèbre déformée, et nous avons calculé les spectres obtenus pour les deux perturbations scalaires et tenseurs. Les spectres que nous avons trouvé ne sont pas compatibles avec l'observation. Cependant cela ne peut abeille considérée comme très forte preuve contre LQG car il y a trop d'hypothèses sur le chemin. Plutôt cela est le résultat de cette interprétation spécifique de LQC.Nous avons également étudié la dynamique de fond (la partie homogène des équations) de LQC. Depuis lent-roll inflation est essentielle pour expliquer de nombreuses caractéristiques de l'univers, y compris le CMB, nous voulons savoir si lent-roll inflation est compatible avec LQC. Nous avons constaté que, en effet, il est. Si un champ d'inflation potentiel carré est ajouté à la théorie, le rebond va lever l'énergie potentielle suffisante pour fournir environ 145 e-plis de lent-roll inflation. Toutefois, lorsque anisotropies sont pris en compte, le montant de l'inflation diminue, et peut même disparaître complètement s'il y a trop de cisaillement au moment du rebond.Nous avons dérivé l'équation Friedman modifié pour anisotrope LQC. Cela nous a permis d'étudier anisotrope LQC pas seulement numériquement, mais aussi analytiquement, qui nous a donné une compréhension beaucoup plus complète de la situation que ce qui était connu auparavant.Enfin, nous avons étudié certains aspects géométriques de l'espace de Sitter, qui a donné lieu à deux considérations très différentes. Tout d'abord nous avons constaté que nous pouvons, pour une théorie générale de la cosmologie modifiée et sous certaines hypothèses assez conservatrices, tirer la dynamique d'un univers spatialement incurvée, étant donné la dynamique d'un un espace plat. Cela est pertinent dans les théories telles que LQC, où il est plus facile de trouver la solution plate que celle incurvée. Deuxièmement, nous proposons un mécanisme possible pour l'origine et la renaissance de l'Univers.Loop quantum gravity (LQG) is an attempt to solve the problem of quantum gravity. Loop quantum cosmology (LQC) is an attempt to apply LQG to early cosmology. The purpose of LQC is to connect LQG with observations. It is very hard to observe any quantum gravity effects because enormous energy density is most likely required. This is exactly why the early Universe is chosen as a stage to search for quantum gravity phenomena.The central result of LQC is that the big bang singularity is replaced by a big bounce. However this is not something that is possible to observe today. For this reason, we have investigated how cosmic perturbations are affected by LQC. We have used the so called deformed algebra approach, and have calculated the resulting spectrums for both scalar and tensor perturbations.The spectrums that we have found are not compatible with observation. However this can not bee taken as very strong evidence against LQG since there are too many assumptions on the way. Rather this is a result for this specific interpretation of LQC.We have also studied the background dynamics (the homogenous part of the equations) of LQC. Since slow-roll inflation is essential in explaining many features of the universe, including the CMB, we want to know if slow-roll inflation is compatible with LQC. We have found that, indeed, it is. If a square potential inflation field is added to the theory, the bounce will lift the potential energy enough to provide around 145 e-folds of slow-roll inflation. However, when anisotropies are taken into account, the amount of inflation decreases, and can even disappear completely if there is too much shear at the time of the bounce.We have derived the modified Friedman equation for anisotropic LQC. This has allowed us to study anisotropic LQC not just numerically, but also analytically, which has given us a much more comprehensive understanding of the situation than what was known before.Finally, we have studied some geometric aspects of de Sitter space, which has resulted in two very different considerations. Firstly we found that we can, for a general theory of modified cosmology and under some quite conservative assumptions, derive the dynamics for a spatially curved universe, given the dynamics of a spatially flat one. This is relevant in theories such as LQC, where it is easier to find the flat solution than the curved one. Secondly, we propose a possible mechanism for the origin and rebirth of the Universe

LQC on curved FLRW space time

International audienceThis study uses very simple symmetry and consistency consid erations to put constraints on pos- sible Friedmann equations for modified gravity models in cur ved spaces. As an example, it is applied to loop quantum cosmology