A Lower Bound on the Mass of Cold Thermal Dark Matter from Planck

TL;DR

This work shows that Planck's measurement of $N_{ m eff}$ can place robust lower bounds on the mass of cold thermal dark matter in the MeV range, provided the DM remains in thermal equilibrium with either neutrinos or electrons/photons after neutrino decoupling. By deriving how such DM shifts the neutrino-photon temperature ratio and thus $N_{ m eff}$, the authors derive mass bounds that hold regardless of whether the annihilation is $s$- or $p$-wave, and they explicitly compare these bounds to BBN-derived constraints. As a concrete application, they analyze a supersymmetric model with a light bino-like neutralino and a light mixed left-right sneutrino mediator that maintains equilibrium with neutrinos through $p$-wave annihilation, obtaining a 95% CL lower bound of $m_{ ilde{ ilde{chi}}_1^0}\gtrsim 3.5$ MeV. The results demonstrate the power of cosmological data to constrain light DM scenarios and highlight viable evasion channels, such as non-thermal production or equilibrium with all SM sectors, which would erase the $N_{ m eff}$ shift.

Abstract

We show that the new measurement of the effective number of neutrinos Neff by the Planck satellite can be used to set a robust lower bound on the mass of cold thermal dark matter of O(MeV). Our limit applies if the dark matter remains in thermal equilibrium by coupling to electrons and photons or through interactions with neutrinos, and applies regardless of whether the dark matter annihilation cross-section is s-wave or p-wave. To illustrate our bounds we apply them to a model of a supersymmetric neutralino annihilating to neutrinos, via a light mixed left-right handed sneutrino mediator. While this scenario was not constrained by previous data, the Planck limits on Neff allow us to set a lower bound on the neutralino dark matter mass of 3.5 MeV.

Figures (7)

• Figure 1: Left panel: $N_{\rm{eff}}$ as a function of the cold thermal dark matter mass $m$. The green (red) lines are for the case when the dark matter is in thermal equilibrium with neutrinos (electrons and photons) and show that $N_{\rm{eff}}$ increases (decreases) as $m$ is reduced. Right panel: The blue regions show the $68\%$ and $95\%$ regions determined from Planck+WP+highL+BAO when both $N_{\rm{eff}}$ and $Y_p$ are varied freely. The green (red) lines indicate the relationship between $Y_p$ and $N_{\rm{eff}}$ for particles in thermal equilibrium with neutrinos (electrons and photons). As $m$ decreases, the prediction for $N_{\rm{eff}}$ and $Y_p$ falls outside of the Planck confidence regions.
• Figure 2: The left [right] panels show the calculated abundances of helium (upper segment) and deuterium (lower segment) for cold dark matter in thermal equilibrium with neutrinos [photons and electrons] respectively. The dotted lines label by $N_{\nu}$ show the predicted abundances for $N_{\nu}$ massless neutrinos.
• Figure 3: Feynman diagrams showing the interaction that keep the neutralino in chemical equilibrium with the neutrinos in the early universe. The mediator $\tilde{\nu}_1$ is a light mixed left-right handed sneutrino.
• Figure 4: A schematic diagram showing the structure of the neutralino and sneutrino sectors that we consider in this paper. As well as a sub-GeV bino-like neutralino, we have a light mixed left-right handed sneutrino. The other neutralinos and mixed sneutrinos have soft masses around the electroweak scale $\mathcal{O}(100)$ GeV. We assume that the other sparticles are heavy enough to have evaded direct search constraints from the LHC and LEP.
• Figure 5: The mixed sneutrino mass $m_{\tilde{\nu}_1}$ required to achieve $\Omega_{\tilde{\chi}_1^0}h^2=0.11$ as a function of the neutralino mass $m_{\tilde{\chi}_1^0}$ for three different values of $\sin\theta$. The upper dashed blue line is for $\sin\theta=0.1$, the middle solid red line for $\sin\theta=0.06$, and the bottom dash-dotted black line for $\sin\theta=0.04$. The required sneutrino mass is typically $m_{\tilde{\nu}_1}\sim\text{few}\times m_{\tilde{\chi}_1^0}$.