Temperature Notion in a Curved Spacetime

TL;DR

This paper investigates the concept of temperature in curved spacetime by analyzing scalar radiation in a Robertson-Walker universe, deriving a time-dependent temperature function, and comparing massless and massive cases, including near-Planck mass scenarios.

Contribution

It introduces a weak non-minimal vacuum definition to derive a dynamic temperature in curved spacetime, connecting cosmological and black hole radiation phenomena.

Findings

Temperature fits the microwave background when universe evolution is near t^{1/2}

Massive case resembles Hawking radiation at high mass and late times

Derived temperature as a function of universe evolution and field mass

Abstract

Scalar radiation, represented by a massless scalar field in a Robertson-Walker metric, is taken into account. By using a weak non minimum vacuum definition, the radiation temperature as a time dependent function is obtained. When the universe evolution is nearly but non equal to $t^{1/2}$, it is possible to fit the temperature of the microwave background. A particular massive case is compared with the massless one. When the mass of the matter field is next to the Planck one and the time is going to infinite, a similar result to the Hawking radiation of the blackhole is obtained.