First constraints on causal sources of primordial gravitational waves from BICEP/Keck, SPTpol, SPT-3G, Planck and WMAP $B$-mode data

TL;DR

This paper presents the first constraints on non-inflationary, causality-limited primordial gravitational wave sources using CMB B-mode polarization data from multiple experiments, significantly limiting their possible contribution.

Contribution

It provides the first observational upper limit on the amplitude of early causal tensor spectra, constraining a broad class of early universe gravitational wave models.

Findings

95% CL upper limit of r_{ect} < 0.0077

Constraints on gravitational wave energy density at ultra-low frequencies

Limits on models like phase transitions and topological defects

Abstract

Non-inflationary sources of gravitational waves in the early Universe generically predict causality-limited tensor power spectra at low frequencies. We report the first-ever constraints on such sources based on cosmic microwave background (CMB) $B$-mode polarization measurements. Using data from BICEP/Keck, SPTpol, SPT-3G, Planck, and WMAP, we constrain the amplitude of an early causal tensor (ECT) power spectrum parameterized by $r_{ect}$, the ratio of causal tensor power to total scalar power at $k~=~0.01$ Mpc$^{-1}$, and obtain a 95% CL upper limit of $r_{ect}<$ 0.0077. Since $r_{ect}$ can easily be related to the parameters of a given theory, our bound robustly constrains a broad class of well-motivated gravitational wave sources in the early universe, including first-order cosmological phase transitions, enhanced small-scale density perturbations, and various topological defects. Finally, we translate our limit into a bound on the present-day energy density in gravitational waves at ultra-low frequencies otherwise inaccessible to traditional gravitational wave detection strategies, including pulsar timing arrays, interferometers, and resonant cavities.