Cosmological implications of a Relic Neutrino Asymmetry

TL;DR

The paper tackles how a relic neutrino lepton asymmetry, encapsulated by the degeneracy parameter $\xi$, alters the energy density and perturbation dynamics of the Universe. It extends the Boltzmann treatment to degenerate neutrinos (massless and $m_\nu=0.07$ eV) and computes the resulting CMB and matter power spectra within a flat cosmology with a cosmological constant, using and adapting the code \textsc{cmbfast}. The key findings are that higher $\xi$ increases radiation density, boosts the first CMB peak, shifts acoustic peaks to larger multipoles, and suppresses small-scale power, with the effects modulated by whether neutrinos are massless or massive. Observational comparisons indicate allowed regions in $(\xi,n)$ that depend on $\Omega_\Lambda$, notably $\xi\lesssim3$ for $\Omega_\Lambda\approx0.5-0.7$, and possibly $3.5\lesssim\xi\lesssim6$ in a cosmology with $\Omega_0=1$, highlighting the potential of future CMB/LSS data to constrain relic lepton asymmetry and its interplay with cosmic expansion.

Abstract

We consider some consequences of the presence of a cosmological lepton asymmetry in the form of neutrinos. Relic neutrino degeneracy enhances the contribution of massive neutrinos to the present energy density of the Universe, and modifies the power spectrum of radiation and matter. Comparing with current observations of cosmic microwave background anisotropies and large scale structure, we derive some constraints on the neutrino degeneracy and on the spectral index in the case of a flat Universe with a cosmological constant.

Figures (5)

• Figure 1: Present energy density of massive degenerate neutrinos as a function of the degeneracy $\xi$. The curves correspond to different values of $h^2 \Omega_\nu$ and the horizontal line is the upper bound from eq. (\ref{['lsf']}).
• Figure 2: Same as figure \ref{['ximass']} for the neutrino asymmetry $L_\nu$.
• Figure 3: CMB anisotropy spectrum for different models with one family of degenerate neutrinos. Solid lines account for the case of massless degenerate neutrinos, and correspond, from bottom to top, to $\xi=0,3,5$. Dashed lines correspond to degenerate neutrinos with mass $m_{\nu} = 0.07$ eV. Other parameters are fixed to $h=0.65$, $\Omega_b=0.05$, $\Omega_{\Lambda}=0.70$, $\Omega_{CDM}=1-\Omega_b-\Omega_{\nu}-\Omega_{\Lambda}$, $Q_{rms-ps}=18~\mu$K, $n=1$. We neglect reionization and tensor contribution.
• Figure 4: Present power spectrum of matter density, for the same parameters as in the previous figure. From top to bottom, to $\xi=0,3,5$.
• Figure 5: LSS and CMB constraints in ($\xi$, $n$) space, for different choices of $\Omega_{\Lambda}$: from top left to bottom right, $\Omega_{\Lambda}=0,0.5,0.6,0.7$. The underlying cosmological model is flat, with $h=0.65$, $\Omega_b=0.05$, $Q_{rms-ps}=18~\mu$K, no reionization, no tensor contribution. The allowed regions are those where the labels are. For LSS constraints, we can distinguish between degenerate neutrinos with $m_{\nu} =0$ (solid lines) and $m_{\nu} =0.07$ eV (dotted lines).