Friedmann cosmology in Regge-Teitelboim gravity

TL;DR

This paper explores a surface-embedding approach to gravity, reformulating Regge-Teitelboim theory as a scalar field theory in Minkowski space, with exact solutions for Friedmann universes and insights into quantization.

Contribution

It introduces a field-theoretic reformulation of Regge-Teitelboim gravity, providing exact solutions for Friedmann cosmology and discussing quantization aspects.

Findings

Exact scalar field expressions for Friedmann universe

Insights into quantization of the embedding surface theory

Comparison with original Regge-Teitelboim gravity

Abstract

This paper is devoted to the approach to gravity as a theory of a surface embedded in a flat ambient space. After the brief review of the properties of original theory by Regge and Teitelboim we concentrate on its field-theoretic reformulation, which we call splitting theory. In this theory embedded surfaces are defined through the constant value surfaces of some set of scalar fields in high-dimensional Minkowski space. We obtain an exact expressions for this scalar fields in the case of Friedmann universe. We also discuss the features of quantisation procedure for this field theory.