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 $\gamma\gamma$, with a rather particular lifetime $0.05\,{\rm s}\lesssim \tau \lesssim 3\,{\rm min}$, mass $250\,{\rm MeV}\lesssim m \lesssim 600\,{\rm MeV}$, and abundance $\rho/\rho_\gamma\sim 0.1$ 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.