Cosmological Implications of Gauged $U(1{)}_{B-L}$ on $\hat{I}”N_{\mathrm{eff}}$ in the CMB and BBN

Abstract

We calculate the effects of a light, very weakly-coupled boson $X$ arising from a spontaneously broken $U(1{)}_{B-L}$ symmetry on $\hat{I}”N_{\mathrm{eff}}$ as measured by the CMB and $Y_p$ from BBN. Our focus is the mass range $1\mathrm{eV}\lesssim m_X\lesssim 100\mathrm{MeV}$; masses lighter than about an $\mathrm{eV}$ have strong constraints from fifth-force law constraints, while masses heavier than about 100 MeV are constrained by other probes. We do not assume $X$ began in thermal equilibrium with the SM; instead, we allow $X$ to freeze-in from its very weak interactions with the SM. We find $U(1{)}_{B-L}$ is more strongly constrained by $\hat{I}”N_{\mathrm{eff}}$ than previously considered. The bounds arise from the energy density in electrons and neutrinos slowly siphoned off into $X$ bosons, which become nonrelativistic, redshift as matter, and then decay, dumping their slightly larger energy density back into the SM bath causing $\hat{I}”N_{\mathrm{eff}}>0$. While some of the parameter space has complementary constraints from stellar cooling, supernova emission, and terrestrial experiments, we find future CMB observatories can access regions of mass and coupling space not probed by any other method. In gauging $U(1{)}_{B-L}$, we assume the $[U(1{)}_{B-L}{]}^3$ anomaly is canceled by right-handed neutrinos, and so our $\hat{I}”N_{\mathrm{eff}}$ calculations have been carried out in two scenarios: neutrinos have Dirac masses, or, right-handed neutrinos acquire Majorana masses. In the latter scenario, we comment on the additional implications of thermalized right-handed neutrinos decaying during BBN. We also briefly consider the possibility that $X$ decays into dark sector states. If these states behave as radiation, we find weaker constraints, whereas if they are massive, there are stronger constraints, though now from $\hat{I}”N_{\mathrm{eff}}<0$.

44 pages, 9 figures. v2: Accepted by JCAP. Minor changes: implemented finite temperature effects into the Boltzmann evolution and added an appendix explaining the dynamics. This change slightly modifies some of the subdominant contours in our parameter space. Results and conclusions remain unchanged