Cosmological mass limits on neutrinos, axions, and other light particles

TL;DR

This paper develops a generalized cosmological framework to constrain light, stable particles that contribute as hot dark matter, extending beyond standard neutrinos to include generic thermal relics such as axions and sterile species. By modifying CMBFAST to handle arbitrary numbers of massless degrees of freedom and massive flavors, and by performing a likelihood analysis against large-scale structure data and CMB measurements, the authors derive robust upper bounds on particle masses and abundances across several scenarios, including: (i) three degenerate massive neutrinos with $m_\nu<0.34$ eV, (ii) a 3+1 scheme with one fully thermalized massive neutrino giving $m_\nu<\sim1.0$ eV, and (iii) thermally produced QCD axions with $m_a<3.0$ eV. They also show how $\Omega_\nu h^2$ and $N_\nu$ are frequently degenerate in their impact on the matter power spectrum, reducing the sensitivity of $m_\nu$ alone to the exact flavor count. Extending to general thermal relics, they find that fermionic or scalar relics decoupling after the QCD epoch are constrained to the eV scale (e.g., $m_X\lesssim$ a few eV for post-QCD decoupling), while earlier decoupling yields weaker bounds. Overall, the work highlights how cosmological small-scale power, together with CMB data, tightly constrains the presence and properties of light, thermally produced particles, with implications for neutrino physics, axion phenomenology, and beyond-Standard Model scenarios.

Abstract

The small-scale power spectrum of the cosmological matter distribution together with other cosmological data provides a sensitive measure of the hot dark matter fraction, leading to restrictive neutrino mass limits. We extend this argument to generic cases of low-mass thermal relics. We vary the cosmic epoch of thermal decoupling, the radiation content of the universe, and the new particle's spin degrees of freedom. Our treatment covers various scenarios of active plus sterile neutrinos or axion-like particles. For three degenerate massive neutrinos, we reproduce the well-known limit of m_nu < 0.34 eV. In a 3+1 scenario of 3 massless and 1 fully thermalized sterile neutrino we find m_nu < 1.0 eV. Thermally produced QCD axions must obey m_a < 3.0 eV, superseding limits from a direct telescope search, but leaving room for solar eV-mass axions to be discovered by the CAST experiment.

Figures (6)

• Figure 1: Likelihood contours (68% and 95%) for the case of $N_\nu$ neutrinos with equal masses $m_\nu$. Left panel: $N_\nu$-$\Omega_\nu h^2$-plane. Right panel: Equivalent $N_\nu$-$m_\nu$-plane.
• Figure 2: Likelihood contours (68% and 95%) for the case of $N_\nu$ flavors with exactly one of them carrying a mass $m_\nu$. Left panel: $N_\nu$-$\Omega_\nu h^2$-plane. Right panel: Equivalent $N_\nu$-$m_\nu$-plane.
• Figure 3: Likelihood contours (68% and 95%) for the case of $N_\nu$ flavors, $N_\nu-3$ each carrying mass $m_\nu$, and an additional 3 massless flavors.
• Figure 4: Power spectra for $\Lambda$CDM models with $\Omega_b = 0.05$, $\Omega = 1$, $h=0.7$, $n_s=1$, and $N_{\nu,{\rm massive}}=1$ and a common large-scale normalization. The full line is for $\Omega_\nu=0$, $\Omega_m=0.25$, $N_\nu=3$, dashed is for $\Omega_\nu=0.05$, $\Omega_m=0.25$, $N_\nu=3$, dotted is for $\Omega_\nu=0.05$, $\Omega_m=0.25$, $N_\nu=8$, and long-dashed is for $\Omega_\nu=0.05$, $\Omega_m=0.35$, $N_\nu=8$.
• Figure 5: Likelihood contours (68% and 95%) for a generic thermal relic with $g_X=2$, characterized by its density, $\Omega_X h^2$, and effective temperature, $T_X$. The dashed line shows $\Delta \chi^2 = 4$, corresponding to the 95% confidence limit for fixed$T_X$. In the left panel, the solid lines correspond to the indicated values of the particle mass in eV, whereas in the right panel they denote the parameters for which the free streaming scale according to Eq. (\ref{['eq:freestream']}) is $k_{\rm FS}=0.1$, 0.2, and $0.3\,$$h\,\rm Mpc^{-1}$.