Reinventing spacetime on a dynamical hypersurface

TL;DR

This paper demonstrates that the FRW spacetime can be modeled on a non-orthogonal, dynamical hypersurface in 5D, leading to new physics and a cosmological model consistent with late-time acceleration and observational data.

Contribution

It introduces a novel approach to embedding FRW spacetime on a non-orthogonal hypersurface, revealing higher-dimensional effects on 4D matter and cosmological evolution.

Findings

The new hypersurface approach modifies matter density and pressure in 4D.

The model aligns with observed late-time cosmic acceleration.

Predicted effective equation of state matches observational constraints.

Abstract

In braneworld models, Space-Time-Matter and other Kaluza-Klein theories, our spacetime is devised as a four-dimensional hypersurface {\it orthogonal} to the extra dimension in a five-dimensional bulk. We show that the FRW line element can be "reinvented" on a dynamical four-dimensional hypersurface, which is {\it not} orthogonal to the extra dimension, without any internal contradiction. This hypersurface is selected by the requirement of continuity of the metric and depends explicitly on the evolution of the extra dimension. The main difference between the "conventional" FRW, on an orthogonal hypersurface, and the new one is that the later contains higher-dimensional modifications to the regular matter density and pressure in 4D. We compare the evolution of the spacetime in these two interpretations. We find that a wealth of "new" physics can be derived from a five-dimensional metric if it is interpreted on a dynamical (non-orthogonal) 4D hypersurface. In particular, in the context of a well-known cosmological metric in $5D$, we construct a FRW model which is consistent with the late accelerated expansion of the universe, while fitting simultaneously the observational data for the deceleration parameter. The model predicts an effective equation of state for the universe, which is consistent with observations.