Resurrecting Gravitational Vector Modes and their Magnetogenesis

TL;DR

The paper investigates primordial gravitational vector modes ($\mathcal{V}$-modes) as a potential source of magnetogenesis and their signatures in the CMB. It assesses three unconventional initial conditions—neutrino isocurvature velocity, neutrino octupole, and a sourced mode from a dark sector—to sustain $\mathcal{V}$-modes and compute the resulting PMFs and $B$-mode spectra. Across all scenarios, the predicted PMF amplitudes are too small (roughly $\mathcal{B}_1 \sim 10^{-29}$ to $10^{-26}$ G) to seed the observed cosmic magnetic fields, though the vector modes imprint discernible CMB $B$-mode patterns and can be consistent with current data in certain contexts. The study emphasizes the need to constrain $\mathcal{V}$-modes to avoid biasing inflationary tensor inferences while highlighting their fundamental role in early-universe physics and vector perturbations.

Abstract

We revisit the presence of primordial gravitational vector modes (V-modes) and their sourcing of primordial magnetic fields (PMF), i.e. magnetogenesis. As the adiabatic vector mode generically decays with expansion, we consider exotic initial conditions which circumvent this issue and lead to observational imprints. The first initial condition is an isocurvature mode between photons and neutrinos vorticities, and the second one is a non-trivial initial condition on the neutrino octupole. Both types of conditions sustain a constant vector mode on super Hubble scales at early times. We also consider a third scenario in which the adiabatic vector modes are rapidly sourced, at a given early but finite time, by an exotic component which develops an anisotropic stress. We find the best fitting parameters in these three cases to CMB and BAO data. We compare the resulting $B$-mode spectra of the CMB to data from BICEP/Keck and SPTpol. We find that none of the proposed initial conditions can produce large enough PMFs to seed every type of magnetic fields observed. However, V-modes are still consistent with the data and ought to be constrained for a better understanding of the primordial Universe before its hot big-bang phase.

Figures (10)

• Figure 1: Evolution of $\tilde{v}_b,\ \tilde{v}_{\gamma},\ \Phi,\ \mathcal{N}_2,$ and $\tilde{v}_{\nu}$ (relative to $\Phi_0$) with the scale factor $a$. Solid lines correspond to scale $k=0.01$ Mpc$^{-1}$ while dashed ones correspond to $k=0.1$ Mpc$^{-1}$. Cosmological parameters used are from the best-fit to Planck Planck_PrimaryPlanck_Lensing SPT-3G 2018 Dutcher_etalBalkenhol_etal and BAO data 6dFGSBOSS_DR12BOSS_DR7eBOSS_DR16.
• Figure 2: Evolution of the comoving MF $a^2\mathcal{B}$ (relative to $\Phi_0$) with the scale factor $a$ for the four modes listed in the legend. Dashed lines correspond to negative values. Cosmological parameters used are from the best-fit to Planck Planck_PrimaryPlanck_Lensing SPT-3G 2018 Dutcher_etalBalkenhol_etal and BAO data 6dFGSBOSS_DR12BOSS_DR7eBOSS_DR16.
• Figure 3: Best-fit power spectrum of CMB polarization $B$-modes for the case of ISO ICs compared to data. The latter includes data points from BICEP/Keck BICEP_Keck (purple star-shaped) and SPTpol SPTpol (red x-shaped). The solid blue curve is the unlensed $BB$ spectrum coming purely from $\mathcal{V}$-modes, while the dashed orange curve is for the total lensed one. The pink dot-dash curve is the Planck $\Lambda$CDM best-fit lensed spectrum.
• Figure 4: Evolution of $\Phi,\ \delta v,\ \tilde{v}_b,\ \tilde{v}_{\gamma},\ \tilde{v}_{\nu}$ and $\mathcal{N}_2$ (relative to $\Phi_0$) with the scale factor $a$ for neutrino OCT IC. Each term is plotted in comparison with the corresponding term for ISO IC. The plots on the left are for $k = 0.1$ Mpc$^{-1}$, while the ones on the right are for $k = 0.01$ Mpc$^{-1}$. The dashed lines in the top and middle plots correspond to negative values, while the solid lines to positive ones. The bottom plots are presented in semi-log scales to ease visualisation. In producing these plots, we set $r_v=10^{3}$, $n_v=0$ and the Planck best-fit for the $\Lambda$CDM cosmological parameters. In the top and middle plots, a radiation streaming approximation (RSA) CLASSII is applied when oscillations become large at later times. This is equivalent to setting $\Theta_\ell={\cal N}_\ell=0$ for $\ell \geq 1$, which means in particular that $\tilde{v}_\gamma= - \Phi$.
• Figure 5: Same as Figure \ref{['Fig:ISO_B_vs_a']} for the OCT IC, excluding the $k=10$ Mpc$^{-1}$ mode.