A Cosmological Theory without Singularities

TL;DR

This paper proposes a modified gravitational theory that eliminates singularities in homogeneous and isotropic cosmological solutions by ensuring all curvature invariants are bounded, leading to nonsingular, de Sitter-like universes.

Contribution

It introduces a higher derivative modification of Einstein's theory that guarantees nonsingular solutions with bounded curvature invariants in cosmology.

Findings

All homogeneous and isotropic solutions are nonsingular.

Curvature invariants are bounded and approach de Sitter space.

Potential for generalization to anisotropic cosmologies.

Abstract

A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach de Sitter space. The action for this theory is obtained by a higher derivative modification of Einstein's theory. We expect that our model can easily be generalized to solve the singularity problem also for anisotropic cosmologies.