The Status of Gravitational Vector Perturbations with Recent CMB Data

TL;DR

This paper uses recent CMB data to set new constraints on gravitational vector perturbations, exploring different initial conditions and their implications for cosmological models.

Contribution

It provides the strongest observational constraints on $ u$-modes using combined datasets, considering various initial conditions and tensor mode scenarios.

Findings

95% CL upper limits: $r_v < 1.3\times10^{-4}$ (ISO), $r_v < 6.8$ (OCT), $r_v < 4.2$ (SMD)

SPTpol $B$-modes alone suggest $r_v=4.7\pm2.1$, consistent with zero

Current data do not fully exclude $ u$-modes, which should be considered in primordial signal analysis.

Abstract

We present new constraints on gravitational vector perturbations ($\mathcal{V}$-modes) using Cosmic Microwave Background (CMB) data, including temperature and $E$-mode polarization from SPT-3G D1, ACT-DR6, and $Planck$, as well as $B$-mode data from BICEP/Keck and SPTpol, which provide the strongest constraints on $\mathcal{V}$-modes. We consider three initial conditions (ICs) that source $\mathcal{V}$-modes: neutrino isocurvature (ISO), neutrino octupole (OCT), and a sourced mode (SMD) generated by an anisotropic stress before matter-radiation equality. We also consider including tensor modes along with $\mathcal{V}$-modes for each of these ICs. Combining all datasets, we obtain 95\% confidence level upper limits of $r_\mathrm{v} < 1.3\times10^{-4}$ (ISO), $r_\mathrm{v} < 6.8$ (OCT), and $r_\mathrm{v} < 4.2$ (SMD), with slightly tighter bounds when tensors are included, at a pivot scale $k_p\ =\ 0.05$ Mpc$^{-1}$. Interestingly, for SMD without tensors, using SPTpol $B$-modes alone yields $r_\mathrm{v} = 4.7 \pm 2.1$, consistent with zero at $2.2\sigma$. Similar result is found for SMD when including tensor perturbations. No statistically significant deviation from $\Lambda$CDM is found. However, $\mathcal{V}$-modes are not fully excluded by current $B$-mode data and should be considered when interpreting primordial signals.