Gauge-Invariant Tensor Perturbations Induced from Baryon-CDM Relative Velocity and the B-mode Polarization of the CMB

TL;DR

This paper investigates gauge-invariant tensor perturbations induced by baryon-CDM relative velocity and their impact on CMB B-mode polarization, emphasizing the importance of gauge-invariant observables despite the effect being too small to detect.

Contribution

It provides a gauge-invariant calculation of tensor perturbations from baryon-CDM relative velocity and explores their potential influence on CMB polarization.

Findings

Induced gravitational wave spectrum is extremely small and unobservable.

Highlights the necessity of gauge-invariant methods in cosmological perturbation analysis.

Demonstrates that non-propagating tensor perturbations can have observable effects on CMB polarization.

Abstract

At second-order, scalar perturbations can source traceless and transverse perturbations to the metric, called induced gravitational waves (IGW). The apparent gauge-dependence of the IGW obscures the interpretation of the stochastic gravitational-wave signal. To elucidate the gauge dependence, we study the IGW from manifestly gauge-invariant scalar perturbations, namely, the relative velocity between the baryon and cold dark matter. From this relative velocity perturbation, we compute the dimensionless gravitational wave power spectrum and the corresponding expected angular power spectrum of the B-mode polarization of the cosmic microwave background. Although the effect turns out to be unobservably small, the calculation demonstrates both the importance of using observable quantities to remove the gauge ambiguity and the observable consequences of tensor perturbations which are not propagating gravitational waves.