Radiation Like Scalar Field and Gauge Fields in Cosmology for a theory with Dynamical Time

TL;DR

This paper explores cosmological solutions with a scalar field acting as radiation within a dynamical time gravitational framework, revealing unique constraints on spatial curvature and implications for gauge theories in curved spacetime.

Contribution

It introduces a novel cosmological solution with a scalar field behaving as radiation requiring zero spatial curvature, and discusses potential deviations from standard gauge theories in curved spacetime.

Findings

Radiation-like scalar field solutions require zero spatial curvature.

Solutions possess a homothetic Killing vector, unlike standard radiation solutions.

Potential deviations from Maxwell and Yang-Mills equations in general curved spacetimes.

Abstract

Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spacial curvature of the universe. This is because only such $ k=0 $ radiation solutions poses a homothetic Killimg vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved space time, and there are no deviations from standard gauge filed equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang Mills equations, for more general space times.