Cannibal domination and the matter power spectrum

Decoupled hidden sectors can easily and generically result in a period of cannibal domination, during which the dominant component of the Universe has an equation of state intermediate between radiation and matter due to self-heating by number-changing interactions. We present for the first time the consequences of a cannibal-dominated era prior to big bang nucleosynthesis for structure formation on small scales. We find that an early cannibal-dominated era imprints a characteristic peak on the dark matter power spectrum, with scale and amplitude directly determined by the mass, lifetime, and number-changing interaction strength of the cannibal field. This enhancement to the small-scale matter power spectrum will generate early-forming dark matter microhalos, and we provide a detailed and transparent map between the properties of the cannibal species and the characteristic mass and formation time of these structures. These relations demonstrate how the internal workings of a hidden sector leave a potentially observable imprint on the matter power spectrum even if dark matter has no direct couplings to the Standard Model.

Figure 1

Evolution of the cannibal sound speed $c_s^2$ and equation of state $w$ from initial cannibal temperature $T_c(a_i)=10m$. The red (yellow) dashed line shows the evolution of $c_s^2$ ($w$) in thermal equilibrium, the gray (cyan) dot-dashed lines show the asymptotic post-freeze-out evolution, and the solid black (blue) line shows the full numerical result.

Figure 2

This figure takes $m=1.8\mathrm{TeV}$, $T_{\mathrm{rh}}=10\mathrm{MeV}$ and ${\alpha }_c=0.1$ in order to realize large separations of scales, to better highlight the physics. Results are shown for DM and cannibal fluids that only interact gravitationally, except at bottom right. Modes that enter the horizon at $a_i$ have comoving wave number $k_{\mathrm{hor},i}=a_{i}H(a_i)$. Top left: evolution of the comoving horizon scale (solid blue) and cannibal Jeans length (solid orange) relative to $k_{\mathrm{hor},i}^{-1}$. Horizontal dashed lines mark the comoving wave numbers corresponding to the perturbations ${\delta }_c$ and ${\delta }_{\mathrm{DM}}$ shown in the bottom left panel. Bottom left: evolution of ${\delta }_c$ (solid) and ${\delta }_{\mathrm{DM}}$ (dash-dotted) for three selected comoving wave numbers, relative to primordial metric perturbation amplitude ${\varphi }_p$. Bottom right: absolute value of the transfer function. The vertical blue dashed line marks the mode that enters the horizon at $a_{\mathrm{rh}}$, while the vertical black dashed line marks the mode corresponding to $k_{\mathrm{pk}}^{-1}=1.4k_J^{-1}(2a_{\mathrm{fz}})$. The blue curve shows results for DM coupled only gravitationally to the cannibal, while the orange curve shows results for DM tightly coupled to the cannibal through reheating. Top right: same as bottom right panel, but with axes inverted for comparison with top left panel.

Figure 3

Colored contours of $T(k_{\mathrm{pk}})$ as a function of $m$ and $T_{\mathrm{rh}}$ for fixed ${\alpha }_c=0.02$. White contours show the microhalo mass $M_{\mathrm{pk}}$ corresponding to $k_{\mathrm{pk}}$. Above the red lines thermal-relic DM becomes nonperturbative for fixed $m_{\mathrm{DM}}/m=10$ (dashed) and 100 (dot-dashed). Above the black lines, DM free streaming determines the small-scale cutoff for fixed $m_{\mathrm{DM}}/m=10$ (dashed) and 100 (dot-dashed) if DM kinetically decouples from the cannibal after cannibal freeze-out.

Figure 4

Same as Fig. 3 but for different values of ${\alpha }_c$. Smaller values of ${\alpha }_c$ reduce the parameter space for cannibalism.