About the Power Spectrum Of Primordial Gravitational Waves

TL;DR

This paper introduces a new method to calculate the spectral energy density of primordial gravitational waves using the scale factor and Lagrange formalism, aiding understanding of the early universe's inflationary energy scale.

Contribution

It presents a novel approach to compute the PGW spectrum based on the scale factor and Lagrange formalism, differing from previous methods that used transfer functions.

Findings

Provides a straightforward calculation method for PGW spectral energy density.

Allows analysis of the power spectrum across different dynamical regimes.

Enhances understanding of inflationary energy scales through spectral analysis.

Abstract

The primordial gravitational waves (\textbf{PGW}) have been generated by inflationary amplification of the primordial (quantum) fluctuations. It is true that they have not been recorded directly so far, but their spectrum can help a lot in solving the basic puzzles of the early universe as Inflation (high) energy scale. In the present work, we give a straightforward method to calculate the spectral energy density (\textbf{SED}) of the relic gravitons different from that used in e.g. \cite{ mirza04,Latham 2005, Yuki 2006}. In our approach, the evolution equations are in terms of the scale factor (instead of conformal time) through the Lagrange formalism (instead of the transfer function). The presence of the Hubble parameter allows to calculate the power spectrum in the different dynamical regimes.