Origin of Delta N_eff as a Result of an Interaction between Dark Radiation and Dark Matter

TL;DR

The paper investigates whether an apparent excess of dark radiation can arise from dark matter decaying into dark radiation between BBN and CMB decoupling. A covariant interaction $Q_{ m DM}=\Gamma\rho_{ m DM}$ with $\Gamma=\alpha H$ yields background solutions $\rho_{ m DM}\propto a^{-(3+\alpha)}$ and $\rho_{\rm dark}=\beta a^{-4}+(\alpha/(1-\alpha))\rho_{ m DM,0}a^{-(3+\alpha)}$, enabling a late rise in $\Delta N_{\rm eff}$ while keeping early times near standard. The authors compute $\Delta N_{\rm eff}$ as a function of scale factor and constrain $\alpha$ using COSMOMC with WMAP7+ACT and WMAP7+SPT, finding $\alpha<\sim 0.027$–$0.028$, and show that $\Delta N_{\rm eff}^{\rm CMB}$ can be of order unity while $\Delta N_{ m eff}^{\rm BBN}$ remains near zero. They also present a phenomenological DM decay model to realize the interaction and discuss implications for cosmological perturbations and structure formation.

Abstract

Results from the Wilkinson Microwave Anisotropy Probe (WMAP), Atacama Cosmology Telescope (ACT) and recently from the South Pole Telescope (SPT) have indicated the possible existence of an extra radiation component in addition to the well known three neutrino species predicted by the Standard Model of particle physics. In this paper, we explore the possibility of the apparent extra dark radiation being linked directly to the physics of cold dark matter (CDM). In particular, we consider a generic scenario where dark radiation, as a result of an interaction, is produced directly by a fraction of the dark matter density effectively decaying into dark radiation. At an early epoch when the dark matter density is negligible, as an obvious consequence, the density of dark radiation is also very small. As the Universe approaches matter radiation equality, the dark matter density starts to dominate thereby increasing the content of dark radiation and changing the expansion rate of the Universe. As this increase in dark radiation content happens naturally after Big Bang Nucleosynthesis (BBN), it can relax the possible tension with lower values of radiation degrees of freedom measured from light element abundances compared to that of the CMB. We numerically confront this scenario with WMAP+ACT and WMAP+SPT data and derive an upper limit on the allowed fraction of dark matter decaying into dark radiation.

Figures (5)

• Figure 1: For each panel we show the best-fit vanilla 6-parameter model from WMAP+SPT (black), then models with the same parameters but one extra relativistic species (dotted-red), a lower dark matter density of $\Omega_{\rm DM} = 0.085$ (dashed-blue, as opposed to $\Omega_{\rm DM} = 0.112$) and a decaying dark matter model with $\alpha = 0.02$ (dot-dash green) and 0.04 (dot-dot-dash magenta). (Top-left) $\Delta N_{\rm eff}$ as a function of scale factor. (Top-right) Hubble rate compared to the standard model. (Bottom-left) Effective (total) equation of state. (Bottom-right) Ratio of the gravitational potential $\Phi$ for a Fourier mode with $k=0.02\, {\rm Mpc}^{-1}$ compared to the standard model. Horizon entry for this mode is indicated by the dashed vertical line.
• Figure 2: Temperature power spectrum for the models listed in Fig. \ref{['fig:plots']}.
• Figure 3: Marginalized parameter constraints for WMAP + ACT (solid black) and WMAP + SPT (dashed red).
• Figure 4: Marginalized constraints on the 7 fitted cosmological parameters for WMAP + ACT (solid black) and WMAP + SPT (dashed red). Likelihood contours show the 68% and 95% confidence levels.
• Figure 5: Allowed region in the $( m_{\phi}, \lambda)$ plane for a coherently oscillating scalar dark matter decaying into dark radiation. The blue area is excluded from the requirement that the resonance parameter is not high enough to produce dark radiation through parametric resonance. The purple region is excluded from the upper limit on the fraction of dark matter decaying into dark radiation taken from our numerical result in section \ref{['cosmomc']}. The lower grey area is excluded from the requirement $m_{\phi} \gg H (T_{\rm osc})$.