Discrete Modes in Gravitational Waves from the Big-Bang

TL;DR

This paper introduces a new approach to gravitational waves in a closed universe with a cosmological constant, revealing discrete modes and analyzing their dynamics during the early universe's inflationary phase.

Contribution

It develops a novel framework linking Einstein equations with a cosmological constant to a closed manifold, identifying discrete polarization modes in primordial gravitational waves.

Findings

Existence of infinite polarization modes for quantization

Dynamics of gravitational waves during pre-inflationary stage

Calculation of gravitational wave energy density in early universe

Abstract

We develop a new approach to gravitational waves in which the Einstein equations are governed by the cosmological constant which is related to the existence of a manifold which is closed. We study an example in which the matter Lagrangian is described by the scalar (inflaton) field. There are only three dynamical solutions. In one of them the universe is initially static but begins to increase until an inflationary stage. We calculate the dynamics of GW in this primordial pre-inflationary stage of the universe. We found that there should be an infinite number of polarization modes in order to the fields can be quantized. Finally, we calculate the energy density due to the gravitational waves.