Probing interactions within the dark matter sector via extra radiation contributions

TL;DR

This work investigates how a dark sector containing massless gauge bosons and other relativistic species contributes to dark radiation, encoded in $N_{ m eff}$, and how cosmological data constrain such hidden sectors. By employing entropy conservation, it relates the dark-sector temperature to the visible sector and the dark matter freeze-out temperature, deriving a semi-analytic expression for $\Delta N_{ m eff}$ as a function of dark-sector degrees of freedom, e.g. $\Delta N_{ m eff} \approx 2.201\, g_D\left(\frac{3.91}{g^*_{s,\mathrm{f.o.}}-g_{s,D}}\right)^{4/3}$. Using Planck+BAO and, when available, $H_0$ data, the paper places current bounds on the number of dark gauge bosons: for instance, $N \lesssim 14$ when $T_{ m DM}^{\rm f.o.} > m_t$ and $N \lesssim 20$ with $H_0$ data, with future Planck releases expected to reduce uncertainties by about a factor of 3. Two simple toy models illustrate how additional dark fermions or equal-temperature dark gauge bosons modify $\Delta N_{ m eff}$ and tighten the bounds, indicating that cosmology can rule out broad classes of hidden-sector scenarios. The results highlight a concrete link between early-universe cosmology and dark-sector model-building, providing a pathway to test unseen gauge interactions with current and forthcoming CMB data.

Abstract

The nature of dark matter is one of the most thrilling riddles for both cosmology and particle physics nowadays. While in the typical models the dark sector is composed only by weakly interacting massive particles, an arguably more natural scenario would include a whole set of gauge interactions which are invisible for the standard model but that are in contact with the dark matter. We present a method to constrain the number of massless gauge bosons and other relativistic particles that might be present in the dark sector using current and future cosmic microwave background data, and provide upper bounds on the size of the dark sector. We use the fact that the dark matter abundance depends on the strength of the interactions with both sectors, which allows one to relate the freeze-out temperature of the dark matter with the temperature of {this cosmic background of dark gauge bosons}. This relation can then be used to calculate how sizable is the impact of the relativistic dark sector in the number of degrees of freedom of the early Universe, providing an interesting and testable connection between cosmological data and direct/indirect detection experiments. The recent Planck data, in combination with other cosmic microwave background experiments and baryonic acoustic oscillations data, constrains the number of relativistic dark gauge bosons, when the freeze-out temperature of the dark matter is larger than the top mass, to be N \lesssim 14 for the simplest scenarios, while those limits are slightly relaxed for the combination with the Hubble constant measurements to N \lesssim 20. Future releases of Planck data are expected to reduce the uncertainty by approximately a factor 3, what will reduce significantly the parameter space of allowed models.

Figures (2)

• Figure 1: Number of d.o.f. $g_{\ast s}^{\mathrm{f.o.}}$ versus number of dark gauge bosons. The red dashed line corresponds to the current 95% C.L. upper value on $N_{\mathrm{eff}}$ using CMB+BAO planck, while the upper/lower blue solid lines shows the combination CMB+$H_0$ (see text for details). Diagonal dotted lines represent $g_{\ast s}^{\mathrm{f.o.}}$ levels associated to $T_{\rm D}$ for the SM particle content. Notice that for a given range of $T_{\rm DM}^{\rm f.o.}$, models exist only along the corresponding line.
• Figure 2: Number of d.o.f. $g_{\ast s}^{\mathrm{f.o.}}$ versus number $N$ of dark gauge bosons for the case with additional $3 N$ dark fermions. Line-styles are equivalent to the ones shown in Fig. \ref{['fig:neffb']}.