Loop quantum cosmology, non-Gaussianity, and CMB power asymmetry

We argue that the anomalous power asymmetry observed in the cosmic microwave background (CMB) may have originated in a cosmic bounce preceding inflation. In loop quantum cosmology (LQC) the big bang singularity is generically replaced by a bounce due to quantum gravitational effects. We compute the spectrum of inflationary non-Gaussianity and show that strong correlation between observable scales and modes with longer (super-horizon) wavelength arise as a consequence of the evolution of perturbations across the LQC bounce. These correlations are strongly scale dependent and induce a dipole-dominated modulation on large angular scales in the CMB, in agreement with observations.Comment: 7 pages, 3 figur

Loop Quantum Cosmology

This Chapter provides an up to date, pedagogical review of some of the most relevant advances in loop quantum cosmology. We review the quantization of homogeneous cosmological models, their singularity resolution and the formulation of effective equations that incorporate the main quantum corrections to the dynamics. We also summarize the theory of quantized metric perturbations propagating in those quantum backgrounds. Finally, we describe how this framework can be applied to obtain a self-consistent extension of the inflationary scenario to incorporate quantum aspects of gravity, and to explore possible phenomenological consequences.Comment: To appear as a Chapter of "The Springer Handbook of Spacetime," edited by A. Ashtekar and V. Petkov. (Springer-Verlag, at Press). 52 pages, 5 figure

Unitarity and ultraviolet regularity in cosmology

Quantum field theory in curved space-times is a well developed area in mathematical physics which has had important phenomenological applications to the very early universe. However, it is not commonly appreciated that on time dependent space-times ---including the simplest cosmological models--- dynamics of quantum fields is not unitary in the standard sense. This issue is first explained with an explicit example and it is then shown that a generalized notion of unitarity does hold. The generalized notion allows one to correctly pass to the Schr\"odinger picture starting from the Heisenberg picture used in the textbook treatments. Finally, we indicate how these considerations can be extended from simple cosmological models to general globally hyperbolic space-timesComment: 30 pages, 0 figures. Version to be published in PR

Detailed analysis of the predictions of loop quantum cosmology for the primordial power spectra

We provide an exhaustive numerical exploration of the predictions of loop quantum cosmology (LQC) with a post-bounce phase of inflation for the primordial power spectrum of scalar and tensor perturbations. We extend previous analysis by characterizing the phenomenologically relevant parameter space and by constraining it using observations. Furthermore, we characterize the shape of LQC-corrections to observable quantities across this parameter space. Our analysis provides a framework to contrast more accurately the theory with forthcoming polarization data, and it also paves the road for the computation of other observables beyond the power spectra, such as non-Gaussianity.Comment: 24 pages, 5 figure

An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era

Cosmological perturbations are generally described by quantum fields on (curved but) classical space-times. While this strategy has a large domain of validity, it can not be justified in the quantum gravity era where curvature and matter densities are of Planck scale. Using techniques from loop quantum gravity, the standard theory of cosmological perturbations is extended to overcome this limitation. The new framework sharpens conceptual issues by distinguishing between the true and apparent trans-Planckian difficulties and provides sufficient conditions under which the true difficulties can be overcome within a quantum gravity theory. In a companion paper, this framework is applied to the standard inflationary model, with interesting implications to theory as well as observations.Comment: 50 pages, no figures. This is first of the two detailed papers which form the basis of Phys. Rev. Lett. 109, 251301 (2012). A few references and clarifications added. Version to appear in Phys. Rev.

Preferred instantaneous vacuum for linear scalar fields in cosmological space-times

We discuss the problem of defining a preferred vacuum state at a given time for a quantized scalar field in Friedmann, Lema\^itre, Robertson Walker (FLRW) space-time. Among the infinitely many homogeneous, isotropic vacua available in the theory, we show that there exists at most one for which every Fourier mode makes vanishing contribution to the adiabatically renormalized energy-momentum tensor at any given instant. For massive fields such a state exists in the most commonly used backgrounds in cosmology, and provides a natural candidate for the ground state at that instant of time. The extension to the massless and the conformally coupled case are also discussed.Comment: 19 pages, 4 figures. Section VI was expanded to include a discussion on semi-classical gravity. Version to appear in PR

Non-Gaussianity in Loop Quantum Cosmology

We extend the phenomenology of loop quantum cosmology (LQC) to second order in perturbations. Our motivation is twofold. On the one hand, since LQC predicts a cosmic bounce that takes place at the Planck scale, the second order contributions could be large enough to jeopardize the validity of the perturbative expansion on which previous results rest. On the other hand, the upper bounds on primordial non-Gaussianity obtained by the Planck Collaboration are expected to play a significant role on explorations of the LQC phenomenology. We find that the bounce in LQC produces an enhancement of non-Gaussianity of several orders of magnitude, on length scales that were larger than the curvature radius at the bounce. Nonetheless, we find that one can still rely on the perturbative expansion to make predictions about primordial perturbations. We discuss the consequences of our results for LQC and its predictions for the cosmic microwave background.Comment: Minor updates: current version matches the accepted PRD manuscrip