Applications of Nash's Theorem to Cosmology

TL;DR

This paper explores how Nash's theorem can resolve the cosmological constant problem by addressing curvature ambiguity in general relativity, offering a new perspective compatible with cosmic acceleration and structure formation.

Contribution

It introduces a novel application of Nash's theorem to cosmology, linking extra-dimensional perturbations to resolving the cosmological constant issue.

Findings

Nash's theorem eliminates the direct link between vacuum energy and the cosmological constant.

The approach is compatible with universe's accelerated expansion.

It supports structure formation within a modified gravitational framework.

Abstract

The cosmological constant problem is seen as a symptom of the ambiguity of the Riemann curvature in general relativity. The solution of that ambiguity provided by Nash's theorem on gravitational perturbations along extra dimensions eliminate the direct comparison between the vacuum energy density and Einstein's cosmological constant, besides being compatible with the formation of structures and the accelerated expansion of the universe.