Friedmann Equation and Stability of Inflationary Higher Derivative Gravity

TL;DR

This paper analyzes the stability of the De Sitter universe in higher derivative gravity theories, extending previous proofs and deriving generalized Friedmann equations applicable to various cosmological models.

Contribution

It completes the proof of stability conditions using a non-redundant Friedmann equation and generalizes the approach to include scalar field interactions.

Findings

Stability conditions are applicable to $k e 0$ Friedmann-Robertson-Walker spaces.

Derived a simple effective Lagrangian for the Friedmann equation in pure gravity.

Extended the stability analysis to models with scalar field interactions.

Abstract

Stability analysis on the De Sitter universe in pure gravity theory is known to be useful in many aspects. We first show how to complete the proof of an earlier argument based on a redundant field equation. It is shown further that the stability condition applies to $k \ne 0$ Friedmann-Robertson-Walker spaces based on the non-redundant Friedmann equation derived from a simple effective Lagrangian. We show how to derive this expression for the Friedmann equation of pure gravity theory. This expression is also generalized to include scalar field interactions.