Detecting relic gravitational waves in the CMB: Optimal parameters and their constraints

TL;DR

This paper develops analytical methods to optimize the detection of relic gravitational waves in the CMB, focusing on the joint constraints of key parameters using future experiment data.

Contribution

It introduces the concept of the best pivot multipole to decorrelate parameters and derives formulas for optimal parameter estimation in CMB experiments.

Findings

Analytical expressions for the best pivot multipole and parameter variances.

Verification of analytical results with numerical simulations showing 20% agreement.

Provides a simple estimation method for future relic gravitational wave detection.

Abstract

The prospect of detecting relic gravitational waves (RGWs), through their imprint in the cosmic microwave background radiation, provides an excellent opportunity to study the very early Universe. In simplest viable theoretical models the RGW background is characterized by two parameters, the tensor-to-scalar ratio $r$ and the tensor spectral index $n_t$. In this paper, we analyze the potential joint constraints on these two parameters, $r$ and $n_t$, using the data from the upcoming cosmic microwave background radiation experiments. Introducing the notion of the best pivot multipole $\ell_t^*$, we find that at this pivot multipole the parameters $r$ and $n_t$ are uncorrelated, and have the smallest variances. We derive the analytical formulae for the best pivot multipole number $\ell_t^*$, and the variances of the parameters $r$ and $n_t$. We verify these analytical calculations using numerical simulation methods, and find agreement to within 20%. The analytical results provides a simple way to estimate the detection ability for the relic gravitational waves by the future observations of the cosmic microwave background radiation.