Cosmology without time: What to do with a possible signature change from quantum gravitational origin?

Within some approaches to loop quantum cosmology, the existence of an Euclidean phase at high density has been suggested. In this article, we try to explain clearly what are the observable consequences of this possible disappearance of time. Depending on whether it is a real fundamental effect or just an instability in the equation of motion, we show that very different conclusions should be drawn. We finally mention some possible consequences of this phenomenon in the black hole sector.Comment: Invited contribution for CQ

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.

Observational Exclusion of a Consistent Quantum Cosmology Scenario

It is often argued that inflation erases all the information about what took place before it started. Quantum gravity, relevant in the Planck era, seems therefore mostly impossible to probe with cosmological observations. In general, only very ad hoc scenarios or hyper fine-tuned initial conditions can lead to observationally testable theories. Here we consider a well-defined and well motivated candidate quantum cosmology model that predicts inflation. Using the most recent observational constraints on the cosmic microwave background B modes, we show that the model is excluded for all its parameter space, without any tuning. Some important consequences are drawn for the deformed algebra approach to loop quantum cosmology. We emphasize that neither loop quantum cosmology in general nor loop quantum gravity are disfavored by this study but their falsifiability is established.Comment: 5 pages, 2 figur

Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves

Loop quantum cosmology provides an efficient framework to study the evolution of the Universe beyond the classical Big Bang paradigm. Because of holonomy corrections, the singularity is replaced by a "bounce". The dynamics of the background is investigated into the details, as a function of the parameters of the model. In particular, the conditions required for inflation to occur are carefully considered and are shown to be generically met. The propagation of gravitational waves is then investigated in this framework. By both numerical and analytical approaches, the primordial tensor power spectrum is computed for a wide range of parameters. Several interesting features could be observationally probed.Comment: 11 pages, 14 figures. Matches version published in Phys. Rev.

Vers une construction microphysique du paradigme cosmologique : prédictions et observations dans un univers quantique

Cosmological physics is currently recognized as a high precision branch of science. It is based on two theoretical frameworks (namely general relativity and the standard model of particles physics), on a symmetry principle (stating that our Universe is statistically homogeneous and isotropic), and on a large set of cosmological observables (among which the cosmic microwave background anisotropies play a key role). The current cosmological paradigm is very efficient at a phenomenological level but still lacks of microphysical explanations. More specifically, the initial Big Bang singularity should be viewed as a pathology of general relativity pointing towards the necessity of a quantum theory of gravitation. In the framework of loop quantum cosmology -a minisuperspace model of the Universe inspired by loop quantum gravity ideas-, this initial singularity is replaced by a regular quantum bounce. Moreover, if the matter content of the loopy universe is dominated by a scalar field during the pre-bounce contracting phase and the bounce, the Universe naturally enters in a phase of cosmological inflation shortly after the bounce. This means that loop quantum cosmology offers a promising extension of the standard inflationnary paradigm backwards to the Planck era. Thanks to a dedicated building of the theory of cosmological perturbations evolving in a quantum background which is fully coherent at the semiclassical level, it is shown that the quantum bounce could leave a typical footprint on the anisotropies of the cosmic microwave background, opening the window for observing in principle quantum gravity in the microwave sky. This tentative proposal is however made possible only if one could extract the cosmological information from the observation of the cosmic microwave background anisotropies with a very high accuracy. Though its secondary component has been recently detected, the case of the B-mode of polarized anisotropies is still particularly challenging du to its minute amplitude signal plagued by many statistical and systematic uncertainties. An accurate enough reconstruction of such a mode from the observed maps of the Stokes parameters requires an exact separation of B-modes from the much larger E-modes. Thanks to a dedicated pseudospectrum estimator filtering out E-modes and using optimized sky apodizations -the so-called pure pseudospectrum estimator-, the angular power spectrum of B-mode can be recovered with high precision in a reasonnable amount of computational time. Using numerical experiments, it appears that such an approach is mandatory for analyzing forthcoming or ongoing small-scale CMB experiments -- covering at most few percents of the celestial sphere -- as well as a potential, future satellite mission dedicated to the primordial B-mode. Using such a pseudospectrum based estimation of the B-mode, the fundamental parameters of the primordial Universe such as the tensor-to-scalar ratio (directly proportionnal to the energy scale of inflation) would be constrained with a high accuracy from the statistical viewpoint since e.g. for a future satellite mission this would allow for measuring r~0.001 at 98% of confidence level.La cosmologie physique a acquis le statut de science de précision. Elle se base actuellement sur deux théories cadre (la relativité générale et le modèle standard de la physique des particules), un principe fondamentale de symétrie (l'Univers est statistiquement homogène et isotrope), et un ensemble d'observables astronomiques (parmi lesquelles les anisotropies du fond diffus cosmologique jouent un rôle majeur). Le paradigme actuel est incroyablement effectif à un niveau phénoménologique mais manque d'explications microphysiques. En particulier, la question de la singularité de Big Bang pointe vers la nécessité d'une théorie quantique de la gravitation. Dans le cadre de la cosmologie quantique à boucles -un modèle de minisuperespace inspiré de la gravité quantique à boucles}- cette singularité de Big Bang est remplacée par un rebond quantique régulier. De plus, si le contenu en matière pendant la phase pré-rebond et le rebond est dominé par un champ scalaire, alors l'Univers entre naturellement en phase d'inflation primordiale après le rebond ; la cosmologie quantique à boucles offrant ainsi une extension du paradigme inflationnaire standard jusqu'à l'ère de Planck. Par la construction d'un cadre théorique cohérent à un niveau semiclassique traitant des perturbations cosmologiques évoluant dans un Univers quantifié, il est alors possible de prédire les traces que laisserait le rebond quantique dans les anisotropies du fond diffus cosmologique, ouvrant la voie vers une observation possible de la gravité quantique dans le ciel micro-onde. Ce programme n'est toutefois réalisable que dans la mesure où l'information cosmologique contenue dans les anisotropies du fond diffus cosmologique peut être reconstruite avec une très grande précision. Plus précisément, le cas du mode B de polarisation, bien que récemment détecté (sa composante secondaire !), reste un défi observationnel compte tenu de la petitesse de son signal affecté par de nombreuses incertitudes statistiques et systématiques. Une reconstruction précise de ce mode partant des cartes du ciel des paramètres de Stokes, suppose de pouvoir le séparer exactement des modes E, bien plus intense que les modes B. Par un estimateurs de pseudospectre spécifique, appelé estimateur de pseudospectre pur, pour lequel les modes E sont exactement filtrés et utilisant des fonctions de poids optimisées, le spectre de puissance angulaire de mode B peut être reconstruit avec une grande précision et en un temps de calcul raisonnable. Par simulations numériques, il apparaît que l'utilisation d'une telle méthode est nécessaire pour reconstruire le mode B partant des données prises par les expériences couvrant une faible portion de la voûte céleste -de l'ordre de quelques pourcents au plus- ainsi que pour une possible future mission satellite dédiée à la mesure du mode B primordial. Avec une reconstruction par pseudospectre pur du mode B, une valeur de r~0.001 du rapport tenseur-sur-scalaire, paramètre cosmologique de l'Univers primordial directement lié à l'échelle d'énergie de l'inflation, pourrait être mesurée à 98% de niveau de confiance d'un strict point de vue statistique partant des données prises par une possible mission satellite

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

Loop Quantum Cosmology with Complex Ashtekar Variables

22 pagesInternational audienceWe construct and study Loop Quantum Cosmology (LQC) when the Barbero-Immirzi parameter takes the complex value $\gamma=\pm i$. We refer to this new quantum cosmology as complex Loop Quantum Cosmology. We proceed in making an analytic continuation of the Hamiltonian constraint (with no inverse volume corrections) from real $\gamma$ to $\gamma=\pm i$ in the simple case of a flat FLRW Universe coupled to a massless scalar field with no cosmological constant. For that purpose, we first compute the non-local curvature operator (defined by the trace of the holonomy of the connection around a fundamental plaquette) evaluated in any spin $j$ representation and we find a new close formula for it. This allows to define explicitly a one parameter family of regularizations of the Hamiltonian constraint in LQC, parametrized by the spin $j$. It is immediate to see that any spin $j$ regularization leads to a bounce scenario. Then, motivated particularly by previous results on black hole thermodynamics, we perform the analytic continuation of the Hamiltonian constraint defined by $\gamma=\pm i$ and $j=-1/2+is$ where $s$ is real. Even if the area spectrum is now continuous, we show that the so-defined complex LQC removes also the original singularity which is replaced by a quantum bounce. In addition, the maximal density and the minimal volume of the Universe are obviously independent of $\gamma$. Furthermore, the dynamics before and after the bounce are no more symmetric, which makes a clear distinction between these two phases of the evolution of the Universe