Fourth order deformed general relativity

TL;DR

This paper derives a fourth-order deformed gravitational Lagrangian within loop quantum cosmology, exploring conditions for a big bounce and inflation, highlighting the impact of anomaly freedom on general covariance.

Contribution

It introduces a fourth-order deformation of the gravitational Lagrangian consistent with anomaly freedom in loop quantum cosmology.

Findings

Derived effective gravitational Lagrangian up to fourth order in extrinsic curvature.

Identified conditions for a cosmological big bounce.

Analyzed scenarios for inflation with different matter contents.

Abstract

Whenever the condition of anomaly freedom is imposed within the framework of effective approaches to loop quantum cosmology, one seems to conclude that a deformation of general covariance is required. Here, starting from a general deformation we regain an effective gravitational Lagrangian including terms up to fourth order in extrinsic curvature. We subsequently constrain the form of the corrections, and then investigate the conditions for the occurrence of a big bounce and the realisation of an inflationary era, in the presence of a perfect fluid or scalar field.