Nonthermal histories and implications for structure formation

We examine the evolution of cosmological perturbations in a nonthermal inflationary history with a late-time matter domination period prior to big bang nucleosynthesis. Such a cosmology could arise naturally in the well-motivated moduli scenario in the context of supersymmetry (SUSY)—in particular in models of split SUSY. Subhorizon dark matter perturbations grow linearly during the matter dominated phase before reheating and can lead to an enhancement in the growth of substructure on small scales, even in the presence of dark matter annihilations. This suggests that a new scale (the horizon size at reheating) could be important for determining the primordial matter power spectrum. However, we find that in many nonthermal models free-streaming effects or kinetic decoupling after reheating can completely erase the enhancement leading to small-scale structures. In particular, in the moduli scenario with wino or Higgsino dark matter we find that the dark matter particles produced from moduli decays would thermalize with radiation and kinetically decouple below the reheating temperature. Thus, the growth of dark matter perturbations is not sustained, and the predictions for the matter power spectrum are similar to a standard thermal history. We comment on possible exceptions, but these appear difficult to realize within standard moduli scenarios. We conclude that although enhanced structure does not provide a new probe for investigating the cosmic dark ages within these models, it does suggest that nonthermal histories offer a robust alternative to a strictly thermal post inflationary history.

Figure 1

Evolution of the background energy densities compared to the total density (as discussed in the text) for two different nonthermal cosmologies. In both figures we take $m_{\chi }=500\mathrm{GeV}$, $B_{\chi }=1/3$, $g_{*}=30$, and $⟨\sigma v⟩=3\times 10^{-8}{\mathrm{GeV}}^{-2}$. On the left we chose the initial dimensionless decay rate as ${\mathrm{\Gamma }}_{\sigma }/H_0\simeq 2\times 10^{-7}$ and the moduli mass $m_{\sigma }=10^6\mathrm{GeV}$. On the left the Universe becomes radiation dominated at $N_{rh}\simeq 10.6$ and the reheat temperature is $T_r\simeq 707\mathrm{MeV}$, whereas on the right we have ${\mathrm{\Gamma }}_{\sigma }/H_0=0.5\times 10^{-12}$ and $m_{\sigma }=10^5\mathrm{GeV}$, with $N_{rh}\simeq 19$ at reheating and $T_r\simeq 22\mathrm{MeV}$.

Figure 2

Evolution of the density perturbations in radiation fluid for modes with $k/H_0=0.1$ and for different rates of decay and annihilation. The bottom blue curve corresponds to the evolution of radiation perturbations in the absence of scalar decay and annihilation terms in a matter dominated universe, whereas green and red curves show the evolution with enhanced decay and annihilations. Particularly, the values of $A$ and $\alpha$ for the red curve are implied by SUSY model building.

Figure 3

Evolution of radiation density contrast and velocity perturbation (both normalized) for the modes $k/H_0=0.1$ (left), $k/H_0=0.04$ (right). This mode crosses the horizon at $N_h=\ln (k/H_0{)}^{-2}\simeq 4.6$ (Left), $N_h=\ln (k/H_0{)}^{-2}\simeq 6.4$ (right). In this nonthermal cosmology the Universe is effectively matter dominated until $N_{rh}\simeq 10.6$ $e$-foldings after which the Universe becomes radiation dominated. Well after reheating, the density perturbation oscillates with an amplitude $A_{{\delta }_r}\simeq 0.0005{\mathrm{\Phi }}_0$ (left), $A_{{}_d}r\mathrm{bac}{\mathrm{\Phi }}_0$ (right). For these modes, the ratio of the size of the comoving horizon $k_{rh}^{-1}$ at the time of reheating to the size $k^{-1}$ of the fluctuation is given by $k/k_{rh}\simeq 20$ (left) and $k/k_{rh}\simeq 8$ (right).

Figure 4

Evolution of DM density contrast (normalized) in a nonthermal cosmology for modes with $k/H_0=0.1$ (left) and $k/H_0=0.04$ (right). As the mode enters the horizon, it grows linearly with the scale factor $e^N\sim a$. We see that the solution (36) (red dot-dashed curve) we derived in the previous section is an excellent fit during the scalar dominated era. After the Universe becomes radiation dominated at $N_{rh}\simeq 10.6$, the amplitude of the density contrast decreases due to rapid annihilations of DM particles. For $N\gtrsim 12$, the density contrast then begins to grow logarithmically as expected.

Figure 5

Elastic/inelastic scattering rates per Hubble (red/blue curves) as a function of the mass splittings fixing $\mu =200\mathrm{GeV}$. Left: energy of DM produced from decay is fixed to be 2 TeV. Right: energy of DM produced from decays is fixed to be 200 GeV. The solid curves correspond to the temperature of the thermal bath to be about $T_{rh}=0.4\mathrm{GeV}$; the dashed curves correspond to a much lower temperature 5 MeV. The gray dashed lines correspond to $\gamma /H=1$.