Nonadiabatic evolution of primordial perturbations and non-Gaussinity in hybrid approach of loop quantum cosmology

Abstract

While loop quantum cosmology (LQC) predicts a robust quantum bounce of the background evolution of a Friedmann-Robertson-Walker (FRW) spacetime prior to the standard slow-roll inflation, whereby the big bang singularity is resolved, there are several different quantization procedures to cosmological perturbations, for instance, the deformed algebra, dressed metric, and hybrid quantizations. This paper devotes to study the quantum bounce effects of primordial perturbations in the hybrid approach. The main discrepancy of this approach is the effective positive mass at the quantum bounce for the evolution of the background that is dominated by the kinetic energy of the inflaton field at the bounce, while this mass is always nonpositive in the dressed metric approach. It is this positivity of the effective mass that violates the adiabatic evolution of primordial perturbations at the initial moments of the quantum bounce. With the assumption that the evolution of the background is dominated by the kinetic energy of the inflaton at the bounce, we find that the effective potentials for both scalar and tensor perturbations can be well approximately described by a Pöschl-Teller (PT) potential, which allows us to find analytical solutions of perturbations, and from these analytical expressions we are able to study the non-adiabatic evolution of primordial perturbations in details. In particular, we derive their quantum bounce effects and investigate their observational constraints. In addition, the impacts of quantum bounce effects on the non-Gaussinity and their implication on the explanations of observed power asymmetry in CMB have also been explored.

Phenomenological Implications of Modified Loop Cosmologies: An Overview

“…(Gupt and Singh, 2012;Gupt and Singh, 2013; and references therein.]. In particular, the last two approaches have been widely studied and found that they are all consistent with current cosmological observations (Agullo and Morris, 2015;de Blas and Olmedo, 2016;Castelló Gomar et al, 2017;Agullo et al, 2018;Elizaga Navascués et al, 2018;Navascues et al, 2018;Wu et al, 2018;Zhu et al, 2018). In addition, within the framework of the dressed metric approach recently it has been also shown that some anomalies from the CMB data (Akrami and Planck collaboration, 2020;Akrami and Planck collaboration, 2020;Schwarz et al, 2016) can be reconciled purely due to the quantum geometric effects (Ashtekar et al, 2020;Ashtekar et al, 2021).…”

Genericness of pre-inflationary dynamics and probability of the desired slow-roll inflation in modified loop quantum cosmologies

“…Finally, we note that the linear perturbations of mLQCs were recently studied numerically in [25]. It would be very interesting to study the same problem analytically along the lines presented in [28,29,[58][59][60], by using the analytical solutions obtained in our analysis along with the method recently developed in [61][62][63]. This exercise will be performed in a future publication.…”

Preinflationary dynamics in loop quantum cosmology: monodromy potential

“…Now LQC is in a position to undergo experimental tests and to look for observational signature of quantum bounce, pre-inflationary dynamics in current/forth-coming observations. In fact three major streams of calculations of cosmological perturbations, namely, dressed metric, deformed algebra and hybrid approaches [44], [50], [51] have been carried out and studied numerically and analytically in [52], [53], [54], [55], [56]. It has been reported that the deformed algebra approach is already inconsistent with current observations [57].…”