What does it take to have $N_{\rm eff} < 3$ at CMB times?

Abstract

The vast majority of extensions of the Standard Model affecting the number of effective relativistic neutrino species ($N_{\rm eff}$) do so additively, namely, they enhance this quantity with some light state contributing to dark radiation. In this work, we consider precisely the opposite case: new physics scenarios that can lead to $N_{\rm eff} < 3$ that are consistent with all known cosmological, astrophysical, and laboratory data. We are motivated by three main reasons: 1) a recent measurement from ACT and SPT in combination with Planck that leads to $N_{\rm eff} = 2.81\pm0.12$, 2) by a new and powerful measurement of the primordial helium abundance, which anchors $N_{\rm eff}$ to be very close to the Standard Model value one second after the Big Bang, 3) by the deployment of the Simons Observatory which will provide precise tests of the radiation content in the Universe and which may detect with a high significance cosmologies with $N_{\rm eff}<3$. We survey the main theoretical possibilities and find that only a few simple scenarios can consistently give $N_{\rm eff}=2.81\pm0.12$. One class consists of thermal electrophilic relics with masses $m\sim 8\!-\!13\,{\rm MeV}$. Another consists of out-of-equilibrium particles decaying to $e^+e^-$ or $γγ$, with a rather particular lifetime $0.05\,{\rm s}\lesssim τ\lesssim 3\,{\rm min}$, mass $250\,{\rm MeV}\lesssim m \lesssim 600\,{\rm MeV}$, and abundance $ρ/ρ_γ\sim 0.1$ at decay. Thermal electrophilic particles are especially interesting because they can account for the dark matter in the Universe and can be tested in experiments such as SENSEI, DAMIC-M, and Oscura, and their portals to the visible sector at experiments such as NA64 and LDMX. We conclude that if the Simons Observatory confirms that $N_{\rm eff} \simeq 2.8$, it will point to very specific extensions of the Standard Model.

Figures (3)

• Figure 1: Summary of the various options from Section \ref{['sec:globalconsiderations']} that can lead to $N_{\rm eff} < 3$ at CMB times. We highlight those which may lead to $N_{\rm eff} \simeq 2.8$ and hence to a good fit of current CMB data as well as to allow a potential $\sim 5\sigma$ detection by the Simons Observatory (SO). As discussed in the text, two clear and simple options are iia) thermal electrophilic species with masses around $m\sim (8-13)\,{\rm MeV}$ (see Fig. \ref{['fig:thermal']}) and which may be tested with dark matter-electron scatterings on Earth, and iib) out-of-equilibrium injections of $e^+e^-/\gamma \gamma$ from particles with lifetimes $\tau_X \sim (0.05-100)\,{\rm s}$ and masses $m_X\sim (250-600)\,{\rm MeV}$, see Section \ref{['sec:nonthermalcase']}.
• Figure 2: $N_{\rm eff}$, $Y_{\rm P}$ and ${\rm D/H}|_{\rm P}$ for the case of a thermal complex scalar $\phi$ interacting with a massive dark photon $A'$ with mass $m_{A'} = 2.7m_\phi$ (upper blue lines) and $m_{A'} = 2.01\,m_\phi$ (lower blue lines). The gray lines indicate the $1\sigma$ and $2\sigma$ confidence levels from observations, and for ${\rm D/H}|_{\rm P}$ we have added the theory uncertainty in quadrature to the measurement error. The lower-right panel shows the combined $\chi^2$ from these three observables (using $\Omega_bh^2$ from CMB observations). The minimum of the $\chi^2\simeq 1.4$ and in red we highlight the $\sim 1\sigma$ preferred region $m_\phi = 8-13\,{\rm MeV}$. This region is statistically preferred over $\Lambda$CDM only at the $\sim 1\sigma$ level.
• Figure 3: $N_{\rm eff}$, $Y_{\rm P}$ and ${\rm D/H}|_{\rm P}$ for the case of a relic decaying out-of-equilibrium to the EM particles $X\to e^+e^-$ or $X\to \gamma\gamma$, as a function of the relic's lifetime $\tau_X$. The particular value of the relic mass is irrelevant as long as $m_{X}<2m_{\mu}$, as these electromagnetic decay products thermalize in the plasma. We show colored lines for certain values of the number density abundance before decay, fixed in a way such that $N_{\rm eff}$ tends to a constant value in the limit $\tau_X \gtrsim 1\text{ s}$. In the region $0.05\,{\rm s}\lesssim \tau_X \lesssim 100\,{\rm s}$ these types of particles are statistically favored over $\Lambda$CDM, although again only at the $\sim 1\sigma$ level. The lower right panel refers to $\Delta\chi^2 = \chi^2-\chi^2|_{\rm min}|_{\rm blue}$ where $\chi^2|_{\rm min}|_{\rm blue}$ is used as it is the scenario with the lowest value of $\chi^2$.