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

Estimation of imprints of the bounce in loop quantum cosmology on the bispectra of cosmic microwave background

Primordial non-Gaussianity has set strong constraints on models of the early universe. Studies have shown that Loop Quantum Cosmology (LQC), which is an attempt to extend inflationary scenario to planck scales, leads to a strongly scale dependent and oscillatory non-Gaussianity. In particular, the non-Gaussianity function $f_{_{\rm NL}} (k_1,\, k_2,\, k_3)$ generated in LQC, though similar to that generated during slow roll inflation at small scales, is highly scale dependent and oscillatory at long wavelengths. In this work, we investigate the imprints of such a primordial bispectrum in the bispectrum of Cosmic Microwave Background (CMB). Inspired by earlier works, we propose an analytical template for the primordial bispectrum in LQC. We write the template as a sum of strongly scale dependent and oscillatory part, which captures the contribution due to the bounce, and a part which captures the scale invariant behaviour similar to that of slow roll. We then compute the reduced bispectra of temperature and electric polarisation and their three-point cross-correlations corresponding to these two parts. We show that the contribution from the bounce to the reduced bispectrum is negligible compared to that from the scale-independent part. Thus, we conclude that the CMB bispectra generated in LQC will be similar to that generated in slow roll inflation. We conclude with a discussion of our results and its implications to LQC.Comment: v1:17 pages, 8 figures; v2: 23 pages, 9 figures, improved template of bispectrum, new subsections added, version accepted for publication in JCA

Predictions for the CMB from an anisotropic quantum bounce

We introduce an extension of the standard inflationary paradigm on which the big bang singularity is replaced by an anisotropic bounce. Unlike in the big bang model, cosmological perturbations find an adiabatic regime in the past. We show that this scenario accounts for the observed quadrupolar modulation in the temperature anisotropies of the cosmic microwave background (CMB), and we make predictions for the remaining angular correlation functions E-E, B-B and T-E, together with non-zero temperature-polarization correlations T-B and E-B, that can be used to test our ideas. We base our calculations on the bounce predicted by loop quantum cosmology, but our techniques and conclusions apply to other bouncing models as well.Comment: 5 pages, 4 figures, minor changes to match published versio