Gauge-Invariant Gravitational Waves from Cogenesis in a $B-L$ Conserving Universe

TL;DR

This work proposes a $U(1)_x$-extended Standard Model with a B-L conserving hidden sector to achieve cogenesis of baryons and asymmetric dark matter. It develops a gauge-invariant, low-temperature framework for first-order phase transitions in the hidden sector and uses the Metaxas–Weinberg approach to predict stochastic gravitational wave spectra, showing that gauge-invariant results are essential for reliable predictions. Parameter scans reveal regions where successful cogenesis coincides with supercooled transitions, yielding GW signals potentially detectable by PTA experiments and future detectors, while a cogenesis constraint narrows the viable space and disfavors LISA-scale signals. The model furthermore accommodates active neutrino masses, sub-GeV dark photons, and consistent DM relic densities, offering a multi-messenger portal linking cosmology, particle physics, and gravitational-wave astronomy.

Abstract

An analysis of baryogenesis and stochastic gravitational wave production is presented for an extension of the standard model where the dark sector consists of dark matter particles charged under a $U(1)_x$ gauge symmetry, while a subset of dark fields also carry lepton number but no $U(1)_x$ charge. We demonstrate that with CP violation induced by Yukawa couplings, equal and opposite lepton asymmetries are generated in the visible and hidden sectors. Subsequent evolution preserves lepton number separately in each sector, and sphaleron interactions partially convert the lepton asymmetry into baryon asymmetry near the temperature of the first-order phase transition. Further, we discuss stochastic gravitational wave background production for the first-order phase transition using a gauge-independent bubble nucleation dynamics which yields spectra also valid in the supercooled low-temperature regime with {$T_p/m_{A_x} \ll 1$} where $T_p$ is the percolation temperature and $m_{A_x}$ is the dark photon mass. A parameter-space scan identifies regions that simultaneously account for cogenesis of baryon asymmetry and dark matter and predict stochastic gravitational wave signals within reach of current (NANOGrav, EPTA, PPTA) and future detectors at higher frequencies, providing a unified framework for cogenesis and associated gravitational wave production.

Figures (10)

• Figure 1: Thermal evolution of $Y_{A_x}, Y_X, Y_{sym}, Y_{sym^\prime}$ for four benchmark models labeled by $\epsilon, g_x, m_{A_x}$ as given in each of the four panels. The plots show the comoving number densities of asymmetric dark matter $X$, its symmetric component ($Y_{sym}=2Y_{\overline{X}}$), and the dark photon $A_x$ as functions of the universe temperature. $Y_{sym^\prime}$ denotes the symmetric abundance of the dark matter in the absence of dark matter asymmetry, i.e., when $Y_X - Y_{\overline{X}} = 0$. The final abundance of $Y_X$ corresponds to a relic density $\Omega_X h^2 = 0.06$, as shown by the light blue dotted line, while $X^\prime$ contributes the other half. In the presence of dark matter asymmetry, the symmetric component is more efficiently annihilated through the process $\overline{X}X\to A_x A_x$. The $U(1)_x$ dark photon $A_x$ which mixes with the hypercharge gauge field via a kinetic term with kinetic parameter $\epsilon$ will eventually decay into Standard Model fermion pairs before BBN.
• Figure 2: Left panel: $g_x$ versus the dark photon mass $m_{A_x}$. Right panel: $g_x$ versus the vacuum expectation value of the $U(1)_x$ Higgs field, $v_x$. The shaded light-green regions in both panels indicate the parameter space of $g_x$ that yields sufficient secluded annihilation of the symmetric dark matter component, for dark photon masses in the range $20~{\rm MeV}-1~{\rm GeV}$. The kinetic mixing between $U(1)_x$ and the hypercharge gauge field is fixed at $\epsilon = 10^{-4}$, consistent with current experimental constraints.
• Figure 3: A display of effective bounce actions $S^{\rm G.D.}_{\rm eff}$ defined in Eq. (\ref{['SG.D.']}) in Landau gauge ($\xi = 0$), along with $S_0$ and $S_0+S_1$ with different choices of $\xi$. From left to right, the models are (*),(a), (b) and (c) where the models are defined in Table \ref{['tab:benchmark1']}.
• Figure 4: Analysis of gravitational wave power spectra for models (*), (a), (b), and (c) defined in Table \ref{['tab:benchmark1']} which shows variations in the gravitational wave power spectrum $\Omega_{GW} h^2$ on the gauge parameter $\xi$ across the range $(-1,1)$ exhibited by the color bands for each model. The solid line displays the gauge-invariant solution.The dashed line displays the Landau gauge solution. Shaded regions represent pulsar timing array signals from NANOGrav NANOGrav:2023gor, PPTA Reardon:2023gzh, and EPTA EPTA:2023fyk, while detection regions for planned space-based gravitational wave detectors are shown, including LISA LISA:2017pwjBaker:2019niaAmaroSeoane:2012km, BBOGrojean:2006bp, DecigoKawamura:2006up, TaijiRuan:2018tsw, TianQinTianQin:2015yph, and $\mu$AresSesana:2019vho.
• Figure 5: Upper left panel: Parameter scan within the $g_x - \lambda_x$ parameter plane, with $v_x$ fixed at 1 GeV. It presents results obtained using gauge-dependent effective action with Landau gauge selection ($\xi = 0$). Upper right panel: Parameter scan within the $g_x - \lambda_x$ parameter plane, with $v_x$ fixed at 1 GeV. It presents results obtained using gauge invariant analysis. The color coding along the left vertical axis indicates the ratio $T_p/m_{A_x}$ for both left and right panels. Lower panels: Theoretical predictions for gravitational wave power spectra $\Omega_{GW} h^2$ as a function of the frequency corresponding to the parameter configurations displayed in the upper panels. Each point marks the peak of the power spectrum.