Inflation and Global Equivalence

TL;DR

This paper proposes an extension of General Relativity using lifted metrics on the cotangent bundle, which unifies inflationary and current cosmological eras through a generalized equivalence principle.

Contribution

It introduces a novel geometric framework extending General Relativity with lifted metrics, connecting fluid dynamics and cosmology in a unified model.

Findings

Reduces to General Relativity as gravitational constant approaches zero

Predicts both inflationary and current cosmological eras

Globalizes the equivalence principle in cosmological models

Abstract

This article investigates an extension of General Relativity based upon a class of lifted metrics on the cotangent bundle of space-time. The dynamics of the theory is determined by a fixed section of the cotangent bundle, representing the momentum of a fluid flow, and Einstein's equations for the fluid applied to the induced space-time metric on the submanifold of the cotangent bundle defined by the image of the section. This construction is formally analogous to the extension of Galilean Relativity by Special Relativity, and is shown to reduce to General Relativity as the gravitational constant approaches zero. By examining the consequences of the model for homogeneous cosmologies, it is demonstrated that this construction globalizes the equivalence principle, in that, the perfect fluid model of Special Relativity is sufficient to predict both the inflationary and the current era.