A Universal CMB $B$-Mode Spectrum from Early Causal Tensor Sources

Abstract: Many early universe scenarios predict post-inflationary tensor perturbations from causality-limited, sub-horizon sources. While the microphysical details may differ, as long as these sources are bounded in duration and correlation length, their tensor power spectra exhibit a universal scaling behavior at small wavenumber: $P_h(k) \propto k^3$, corresponding to white noise on super-horizon scales at the time of production. If these early causal tensor sources (ECTs) exclusively produce gravitational waves before redshift $z \sim 10^5$, this scaling is realized on all of the scales observed in the cosmic microwave background (CMB), and thus yields a universal multipole distribution for the $B$-mode angular power spectrum. Unlike the scale-invariant distributions of inflationary $B$ modes, ECTs generically predict enhanced power on small scales and suppressed power on large scales, which allows these source classes to be distinguished given measurements over a sufficient range of angular scales. In this paper, we introduce a unified framework for characterizing ECTs and demonstrate how their universal infrared scaling manifests in low-frequency observables, including CMB $B$ modes and stochastic gravitational wave spectral densities. We illustrate this mapping with representative case studies of this universality class involving first-order phase transitions, topological defects, and enhanced scalar perturbations, which source tensor modes at second order in perturbation theory.