Back reaction of the neutrino field in an Einstein universe

TL;DR

This paper investigates how the neutrino field's back reaction influences the Einstein universe's properties at finite temperature, revealing a critical relationship between temperature, radius, and the universe's state transitions.

Contribution

It extends previous studies by analyzing the neutrino field's back reaction in the Einstein universe, establishing a temperature-radius relationship and identifying critical points for universe state changes.

Findings

Existence of a minimum radius for self-consistent solutions.

Identification of a maximum temperature for state transition.

Comparison with scalar and photon field back reactions.

Abstract

The back reaction effect of the neutrino field at finite temperature in the background of the static Einstein universe is investigated. A relationship between the temperature of the universe and its radius is found. As in the previously studied cases of the massless scalar field and the photon field, this relation exhibit a minimum radius below which no self-consistent solution for the Einstein field equation can be found. A maximum temperature marks the transition from a vacuum dominated state to the radiation dominated state universe. In the light of the results obtained for the scalar, neutrino and photon fields the role of the back reaction of quantum fields in controling the value of the cosmological constant is briefly discussed.