Damping of tensor mode in spatially closed cosmology

TL;DR

This paper derives an integro-differential equation to study how free-streaming neutrinos damp tensor modes of gravitational waves in a spatially closed universe, showing significant amplitude reduction during radiation domination.

Contribution

It introduces a new formalism for analyzing gravitational wave damping in closed cosmology with neutrino anisotropic stress, including short and long wavelength regimes.

Findings

Neutrino anisotropic stress reduces GW amplitude by 76% during radiation era.

Damping effect is less significant for waves entering the horizon later.

Results provide insight into gravitational wave evolution in closed universe models.

Abstract

We derive an integro-differential equation for propagation of cosmological gravitation waves in spatially closed cosmology whereas the traceless transverse tensor part of the anisotropic stress tensor is free streaming neutrinos (including antineutrinos), which have been traveling essentially without collision since temperature dropped below about $ 10^{10} K$. We studied the short wavelengths and long wavelengths of gravitational waves (GWs) that enter the horizon in closed spacetime. The solution shows that the anisotropic stress reduces the squared amplitude by 76% for wavelengths that enter the horizon during radiation-dominated phase and this reduction is less for the wavelength that enter the horizon at later times. At the end we compare the results to the