Inflaton dark matter from incomplete decay

We show that the decay of the inflaton field may be incomplete, while nevertheless successfully reheating the Universe and leaving a stable remnant that accounts for the present dark matter abundance. We note, in particular, that since the mass of the inflaton decay products is field dependent, one can construct models, endowed with an appropriate discrete symmetry, where inflaton decay is kinematically forbidden at late times and only occurs during the initial stages of field oscillations after inflation. We show that this is sufficient to ensure the transition to a radiation-dominated era and that inflaton particles typically thermalize in the process. They eventually decouple and freeze out, yielding a thermal dark matter relic. We discuss possible implementations of this generic mechanism within consistent cosmological and particle physics scenarios, for both single-field and hybrid inflation.

Figure 1

Feynman diagrams for the two-body decay of the inflaton into (a) gauge bosons, (b) light scalars and (c) light fermions, induced at the one-loop level by gauge and Yukawa interactions of the ${\psi }_{\pm }$ fermions. In (d) we also show the four-body decay of the inflaton induced by the exchange of virtual ${\psi }_{\pm }$ modes with Yukawa interactions with other light species. For clarity, all light fields are represented by green lines.

Figure 2

Results of the numerical integration of the inflaton-radiation dynamical equations for $m_{\varphi }=10^{-3}{M}_P$, $m_f=0.55m_{\varphi }$ and $h=1$, showing the time evolution of (a) the inflaton (solid blue curve) and radiation (solid red curve) energy densities; and (b) the inflaton decay width (solid blue curve) compared to the Hubble parameter (solid green curve). The blue dashed curves in (a) and (b) give the evolution of the inflaton energy density in the absence of decay and the maximum value of the decay width, respectively. All quantities are given in Planck units such that $M_P=1$.

Figure 3

Results of the numerical integration of the inflaton-waterfall-radiation dynamical equations for $M=10^{-2}{M}_P$, $g=10^{-5}$, $h=1$, $h_{\chi }=10^{-5}$ and $m_f=0.51m_{\varphi }$, showing the time evolution of the inflaton (solid blue curve), the waterfall (dashed green curve) and radiation (dotted red curve) energy densities. All quantities are given in Planck units such that $M_P=1$.

Figure 4

Parameter space of the hybrid model of inflaton dark matter with $m_f=m_{\varphi }$. In the orange (blue) region the abundance of the inflaton accounts for the present dark matter energy density and the freeze-out occurs in the radiation (waterfall matter) era. The purple (green) region is excluded because the reheating (freeze-out) temperature is below 100 MeV. Dashed (dash-dotted) lines are curves of constant inflaton mass (reheating temperature). The grey area represents approximately the transition between the regions where the freeze-out takes place in the radiation and waterfall era.