Increasing Neff with particles in thermal equilibrium with neutrinos

TL;DR

The paper investigates a scenario in which a light particle $\chi$ with $m_\chi \lesssim 10$ MeV remains in thermal equilibrium with neutrinos after their decoupling and becomes non-relativistic, transferring entropy to the neutrinos and increasing the neutrino-to-photon temperature ratio $T_\nu/T_\gamma$. This raises the effective number of neutrino species $N_{\rm eff}$, with $N_{\rm eff}$ at photon decoupling typically larger than at BBN due to the indirect contribution from the hotter neutrinos. The authors compute the impact on BBN yields ($Y_p$ and ${\rm D/H}$) using a modified PArthENoPE code and derive $N_{\rm eff}$ for the CMB, finding current data allow all $m_\chi$ at roughly the 2σ level, while Planck is expected to tightly constrain $m_\chi$ and, in some regions, distinguish between a real scalar, a complex scalar, and a Majorana fermion. The study concludes that this neutrino-reheating mechanism remains a viable explanation for hints of extra radiation and highlights Planck’s potential to resolve degeneracies with standard dark radiation through precise measurements of $N_{\rm eff}$ and helium abundance $Y_p$.

Abstract

Recent work on increasing the effective number of neutrino species (Neff) in the early universe has focussed on introducing extra relativistic species (`dark radiation'). We draw attention to another possibility: a new particle of mass less than 10 MeV that remains in thermal equilibrium with neutrinos until it becomes non-relativistic increases the neutrino temperature relative to the photons. We demonstrate that this leads to a value of Neff that is greater than three and that Neff at CMB formation is larger than at BBN. We investigate the constraints on such particles from the primordial abundance of helium and deuterium created during BBN and from the CMB power spectrum measured by ACT and SPT and find that they are presently relatively unconstrained. We forecast the sensitivity of the Planck satellite to this scenario: in addition to dramatically improving constraints on the particle mass, in some regions of parameter space it can discriminate between the new particle being a real or complex scalar.

Figures (5)

• Figure 1: The evolution of $T_{\nu}/T_{\gamma}$ with $T_{\gamma}$ in the standard concordance model '$\Lambda$CDM' (black solid) and when there is an additional Majorana fermion in thermal equilibrium with neutrinos with mass $m_{\chi}=5$ MeV (blue dot-dashed) and $m_{\chi}=0.05$ MeV (red dashed). Neutrino reheating occurs when $T_{\gamma}\sim m_{\chi}$.
• Figure 2: The red dot-dashed, solid and dashed lines show the predictions for $Y_p$ (upper panel) and $\text{D/H}$ (lower panel) for a complex scalar (B2), Majorana fermion (F2) and real scalar (B1) respectively. The blue shaded region indicates the $1\sigma$ region for $Y_p$ from Izotov:2010ca (with statistical and systematic errors combined linearly) and the $1\sigma$ weighted mean of $\text{D/H}$ from Fumagalli:2011iw. The black dotted lines show the values of $Y_p$ and $\text{D/H}$ for the indicated values of $N_{\rm{eff}}$.
• Figure 3: The red dot-dashed, solid and dashed lines show $N_{\rm{eff}}$ at photon decoupling ($\left. N_{\rm{eff}} \right|_{\rm{CMB}}$) as a function of $m_{\chi}$ for a complex scalar (B2), Majorana fermion (F2) and real scalar respectively. The shaded green and blue hatched regions show the $1\sigma$ range of $N_{\rm{eff}}$ determined from ACT and SPT (in combination with data from WMAP7, BAO and $H_0$) respectively.
• Figure 4: The difference in $N_{\rm{eff}}$ at photon decoupling and BBN (inferred from the value of $Y_p$). The red dot-dashed, solid and dashed lines show the prediction for a complex scalar (B2), Majorana fermion (F2) and real scalar (B1) respectively.
• Figure 5: The upper and lower panels correspond to the fiducial values of '$\Lambda$CDM' and '$\Lambda$CDM$+\chi$' from table \ref{['tab:forecast']} respectively. Both panels: In blue are the Planck $1\sigma$ and $2\sigma$ regions. The red lines show the values of $Y_p$ as a function of $N_{\rm{eff}}$ for a real scalar (B1), complex scalar (B2) and Majorana fermion (F2). The black star indicates the values of $Y_p$ and $N_{\rm{eff}}$ for the stated values of $m_{\chi}$ in the box. Upper panel: In green are the SPT+WMAP7+BAO+$H_0$$1\sigma$ and $2 \sigma$ regions. Lower panel: In green are the $1\sigma$ and $2 \sigma$ regions for $Y_p$ from Izotov et. al. Izotov:2010ca (with statistical and systematic errors combined linearly). The black dotted line marked DR indicates the relation between $Y_p$ and $N_{\rm{eff}}$ for dark radiation in which $\left. N_{\rm{eff}} \right|_{\rm{BBN}}=\left. N_{\rm{eff}} \right|_{\rm{CMB}}$.