Quintessential inflation from 5D warped product spaces on a dynamical foliation

TL;DR

This paper explores how a 5D warped space with a scalar field can produce both inflationary and dark energy-like behaviors in 4D by using a dynamical foliation of the extra dimension, offering a unified geometric model.

Contribution

It introduces a novel approach of using dynamical foliation in 5D warped spaces to generate both inflation and quintessence scenarios in 4D, extending previous constant foliation models.

Findings

Dynamical foliation enables a transition from inflation to late-time acceleration.

Induced scalar potential supports chaotic inflation in 4D.

Model reproduces current accelerated expansion with deceleration parameter near -1.

Abstract

Assuming the existence of a 5D purely kinetic scalar field on the class of warped product spaces we investigate the possibility of mimic both an inflationary and a quintessential scenarios on 4D hypersurfaces, by implementing a dynamical foliation on the fifth coordinate instead of a constant one. We obtain that an induced chaotic inflationary scenario with a geometrically induced scalar potential and an induced quasi-vacuum equation of state on 4D dynamical hypersurfaces is possible. While on a constant foliation the universe can be considered as matter dominated today, in a family of 4D dynamical hypersurfaces the universe can be passing for a period of accelerated expansion with a deceleration parameter nearly -1. This effect of the dynamical foliation results negligible at the inflationary epoch allowing for a chaotic scenario and becomes considerable at the present epoch allowing a quintessential scenario.