Critical Cosmology in Higher Order Gravity

TL;DR

This paper develops higher order curvature terms in the Lagrangian for FLRW cosmology, demonstrating inflationary solutions without scalar fields and exploring applications to thick brane models.

Contribution

It introduces a systematic construction of higher order curvature terms from Lovelock tensors in cosmological Lagrangians, enabling inflationary solutions without scalar degrees of freedom.

Findings

Higher order curvature terms can produce inflationary behavior.

The constructed Lagrangians relate to Lovelock tensors.

Applications to thick brane solutions are demonstrated.

Abstract

We construct the higher order terms of curvatures in Lagrangians of the scale factor for the Friedmann-Lemaitre-Robertson-Walker universe, which are linear in the second derivative of the scale factor with respect to cosmic time. It is shown that they are composed from the Lovelock tensors at the first step; iterative construction yields arbitrarily high order terms. The relation to the former work on higher order gravity is discussed. Despite the absence of scalar degrees of freedom in cosmological models which come from our Lagrangian, it is shown that an inflationary behavior of the scale factor can be found. The application to the thick brane solutions is also studied.