Gravitational Coleman-Weinberg Potential and It's Finite Temperature Counterpart

TL;DR

This paper investigates the Coleman-Weinberg potential for gravitons coupled to a scalar field, analyzing its stability, imaginary parts, and thermal behavior, revealing temperature-dependent effects and potential symmetry restoration.

Contribution

It provides the first detailed analysis of the gravitational Coleman-Weinberg potential at finite temperature, including its imaginary part and thermal damping effects.

Findings

One-loop effective potential vanishes without matter self-interaction.

Imaginary part indicates instability due to tachyonic poles.

Finite temperature effects damp out as temperature approaches zero.

Abstract

Coleman-Weinberg (CW) phenomena for the case of gravitons minimally coupled to massless scalar field is studied. The one loop effect completely vanishes if there is no self interaction term present in the matter sector. The one loop effective potential is shown to develop an instability in the form of acquiring an imaginary part, which can be traced to the tachyonic pole in the graviton propagator. The finite temperature counterpart of this CW potential is computed to study the behaviour of the potential in the high and low temperature regimes with respect to the typical energy scale of the theory. Finite temperature contribution to the imaginary part of gravitational CW potential exhibits a damped oscillatory behaviour; all thermal effects are damped out as the temperature vanishes, consistent with the zero-temperature result. Possibility of symmetry restoration at high temperature is also depicted.