The Existence of Godel, Einstein and de Sitter Universes

TL;DR

This paper derives conditions for the existence of Godel, Einstein static, and de Sitter universes within generalized gravity theories based on arbitrary curvature invariants, including criteria for time-travel in Godel universes.

Contribution

It provides explicit solution expressions and conditions on the Lagrangian for these universes in theories with arbitrary curvature functions.

Findings

Conditions for Godel, Einstein static, and de Sitter universes derived.

Explicit solutions expressed in terms of Lagrangian parameters.

Criteria for time-travel in Godel universes established.

Abstract

We determine the general conditions for the existence of Godel, Einstein static, and de Sitter universes in gravity theories derived from a Lagrangian that is an arbitrary function of the scalar curvature and Ricci and Riemann curvature invariants. Explicit expressions for the solutions are found in terms of the parameters defining the Lagrangian. We also determine the conditions on the Lagrangian of the theory under which time-travel is allowed in the Godel universes.