Cosmological implications of inflaton-mediated dark and visible matter scatterings after reheating

The initial density of dark matter (DM) particles, otherwise secluded from the standard model (SM), may be generated at reheating, with an initial temperature ratio for internal thermalizations, ${\xi }_i=T_{\mathrm{DM},\mathrm{i}}/T_{\mathrm{SM},\mathrm{i}}$. This scenario necessarily implies inflaton-mediated scatterings between DM and SM after reheating, with a rate fixed by the relic abundance of DM and the reheat temperature. These scatterings can be important for an inflaton mass and reheat temperature as high as $\mathcal{O}({10}^7\mathrm{GeV})$ and $\mathcal{O}({10}^9\mathrm{GeV})$, respectively, since the thermally averaged collision terms become approximately independent of the inflaton mass when the bath temperature is larger than the mass. The impact of these scatterings on DM cosmology is studied modeling the perturbative reheating physics by a gauge-invariant set of inflaton interactions up to dimension 5 with the SM gauge bosons, fermions, and the Higgs fields. It is observed that an initially lower (higher) DM temperature will rapidly increase (decrease), even with very small couplings to the inflaton. There is a sharp lower bound on the DM mass below which the relic abundance cannot be satisfied due to faster backscatterings depleting DM quanta to SM particles. For low DM masses, the cosmic microwave background constraints become stronger due to the collisions for ${\xi }_i<1$, probing values as small as $\mathcal{O}({10}^{-4})$, and weaker for ${\xi }_i>1$. The big-bang nucleosynthesis constraints become stronger due to the collisions for lower DM masses, probing ${\xi }_i$ as small as $\mathcal{O}(0.1)$, and weaker for higher DM mass. Thus inflaton-mediated collisions with predictable rates, relevant even for high-scale inflation models, can significantly impact the cosmology of light DM.

Figure 1

Two relevant thermally averaged reaction rates appearing in Eqs. (2.8) and (2.9), as a function of $m_{\chi }/T_{\mathrm{SM}}$. Also shown is the ratio of the Hubble rate to the entropy density, for comparison.

Figure 2

Evolution of the DM and SM temperature ratio $\xi =T_{\chi }/T_{\mathrm{SM}}$, as a function of $m_{\chi }/T_{\mathrm{SM}}$ (left), and the corresponding evolution of the DM yield $Y_{\chi }$ (right). The results are shown for an intermediate reheat temperature of $T_{\mathrm{R}}\sim 5\times {10}^6\mathrm{GeV}$ and inflaton mass of $m_{\varphi }={10}^3\mathrm{GeV}$.

Figure 3

Same as Fig. 2 (left panel), for a reheat temperature of $T_{\mathrm{R}}\sim 5\times {10}^8\mathrm{GeV}$ and inflaton mass of $m_{\varphi }={10}^7\mathrm{GeV}$ (left). Comparison of the evolution of $\xi =T_{\chi }/T_{\mathrm{SM}}$ for two different scales of the inflaton mass and reheat temperature (right), starting from the same initial value ${\xi }_i$.

Figure 4

Effect of the collisions on the DM temperature in the beginning of its nonrelativistic regime, as a function of the DM-inflaton coupling ${\mu }_{\chi }$ (left), and an enlarged version of the figure to illustrate the BBN constraints (inset).

Figure 5

Cosmological constraints on the DM mass $m_{\chi }$ and the DM-inflaton coupling ${\mu }_{\chi }$, from considerations of the DM total abundance, the CMB anisotropies, and the BBN, both without and with the effect of the collision processes. The initial values of the temperature ratio ${\xi }_i$ are also shown. Note that the coupling ${\mu }_{\chi }$ decreases upward along the $y$ axis in the convention used.

Figure 6

The temperature ratio $\xi$ (left) and the DM yield $Y_{\chi }$ (right) for choices of parameters in which ${\xi }_i>1$, without (dashed lines) and with (solid lines) the effects of collisions.

Figure 7

Same as Fig. 2, for the scenario in which the inflaton dominantly couples to the SM gauge bosons and fermions.

Figure 8

Same as Fig. 3, for the scenario in which the inflaton dominantly couples to the SM gauge bosons and fermions.

Figure 9

Same as Fig. 4, for the scenario in which the inflaton dominantly couples to the SM gauge bosons and fermions.

Figure 10

Same as Fig. 5, for the scenario in which the inflaton dominantly couples to the SM gauge bosons and fermions.