Bouncing cosmology in f(Q) symmetric teleparallel gravity

Francesco Bajardi,Salvatore Capozziello,Daniele Vernieri

doi:10.1140/epjp/s13360-020-00918-3

Abstract

We consider f(Q) extended symmetric teleparallel cosmologies, where Q is the non-metricity scalar, and constrain its functional form through the order reduction method. By using this technique, we are able to reduce and integrate the field equations and thus to select the corresponding models giving rise to bouncing cosmology. The selected Lagrangian is then used to develop the Hamiltonian formalism and to obtain the Wave Function of the Universe which suggests that classical observable universes can be recovered according to the Hartle Criterion.

Highlights

The gravitational interaction, described by Einstein’s General Relativity (GR), is the only fundamental force escaping a formulation according to Quantum Field Theory
We focus on STEGR and on a modified action containing a function of the non-metricity scalar Q
GR still remains the best candidate to describe the gravitational interaction in the classical regime, despite some shortcomings related to IR and UV behaviors

Summary

Introduction

The gravitational interaction, described by Einstein’s General Relativity (GR), is the only fundamental force escaping a formulation according to Quantum Field Theory. −(1/2) √−g f (Q) d4x can be considered; even if STEGR, TEGR and GR are interchangeable, their extensions are different from each other: while f (Q) is equivalent to f (T ), f (R) gravity leads to a different dynamics In view of this difference, it is useful to study related cosmologies with the aim to reconstruct cosmic histories capable of matching large datasets at any epoch and select a self-consistent theory of gravity. According to the Hartle Criterion, the Wave Function describes correlations among cosmological observables: if it oscillates, cosmological parameters are correlated and can give rise to observables universes, whose dynamics is described by classical trajectories In this perspective, studying generalized STEGR models is useful since non-metricity can enlarge the set of viable minisuperspaces. The Hamiltonian formulation of GR and the ADM formalism are summarized in “Appendix 1”

Modified non-metric theories of gravity

Bouncing cosmology via order reduction of the field equations

N2 a 2 a2

Findings

Conclusions