Braneworld Baryogenesis and QCD-Era Magnetogenesis: A Predictive Link

TL;DR

This work links a braneworld baryogenesis mechanism in a two-brane $M_4\times Z_2$ spacetime to realistic primordial magnetic fields by treating the PMF as a causal stochastic field with a broken power-law spectrum. Propagating magnetic fluctuations through the interbrane CP-violating dynamics shows that reproducing the observed baryon asymmetry requires a PMF amplitude of order $B_0\sim10^{10}$ T at the QCD epoch, in agreement with causal QCD magnetogenesis. The induced baryon-density fluctuations become universal white noise on large scales, $P_{\delta}(k)\propto k^{0}$ for $k<k_*$, corresponding to a subdominant baryon isocurvature component that remains compatible with Planck constraints. Altogether, the results establish a predictive bridge between beyond-Standard-Model baryogenesis and standard early-Universe magnetogenesis, offering a concrete observational target for primordial magnetic fields.

Abstract

We demonstrate that primordial magnetic fields (PMF) play a decisive role in the braneworld baryogenesis scenario of [Phys. Rev. D $\textbf{110}$, 023520 (2024)], where C/CP violation arises from the coupling of visible and hidden matter-antimatter sectors through a pseudo-scalar field. Although this mechanism generates baryon number efficiently only after the quark-hadron transition, by incorporating a realistic stochastic PMF within a semi-analytical framework, we find that matching the observed baryon-antibaryon asymmetry robustly requires PMF strengths of order $10^{10}$ T right after the transition, in agreement with causal QCD-era magnetogenesis. We further reveal that magnetic fluctuations drive the baryon-density spectrum to white noise on large scales, yielding an isocurvature component compatible with Cosmic Microwave Background (CMB) bounds. This establishes a predictive link between the braneworld baryogenesis model and realistic early-Universe magnetic fields.

Figures (2)

• Figure 1: Baryon ($Y_{B}$ : blue solid line) and antibaryon ($Y_{\overline{B}}$ : red dashed line) comoving densities at $T=20$ MeV against magnetic vector potential $A_{t}$ at $T=160$ MeV for $\kappa =0.99$ (i.e. $\left\vert \Delta T\right\vert /T\lesssim 10\times 10^{-3})$. Horizontal black dash-dotted line: observed baryon comoving density ($8.8\times 10^{-11}$). Horizontal red dotted line: upper limit on the expected antibaryon comoving density ($10^{-16}$).
• Figure 2: The power spectrum of baryon density fluctuations, $P_\delta(k)$, at $T=20 \, \text{MeV}$ and for $\kappa = 0.991$ ($\left\vert \Delta T\right\vert /T = 9 \times 10^{-3}$, see Table \ref{['tab:b0_values']}) as a function of the comoving wave-number $k$. The different curves correspond to PMF models with different spectral indices $n$ and the magnetic field strengths $B_{0}$ tuned to produce the correct mean baryon density. Regardless of the input PMF spectrum, the output is a white-noise spectrum ($P_\delta(k) \approx \text{const}$) for $k < k_*$.