Abstract
We investigate the gravitational production of scalar dark matter particles during the inflationary and reheating epochs. The oscillatory behavior of the curvature scalar R during the reheating phase generates two different enhancement mechanisms in the particle production. On the one hand, as it has been already discussed in previous works, it induces tachyonic instabilities in the field which are the dominant enhancement mechanism for light masses. On the other hand, we have found that it also provokes a resonant effect in the ultraviolet region of the spectrum which becomes dominant for masses in the range 109 GeV to 1013 GeV. We have developed an analytical approximation to describe this resonance effect and its consequences on the ultraviolet regime. Once we have calculated the theoretical gravitational production, we constrain the possible values of the phenomenological field parameters to be considered as a dark matter candidate. We do so by comparing the theoretically predicted abundance with the observed one and ensuring that the theoretical prediction does not lead to overproduction. In particular, we find that there is a region of intermediate masses that is forbidden as they would lead to overproduction.
Highlights
JHEP06(2020)084 energy scale during this phase (m H0)
In [11, 12], they analyse the impact of the scale factor oscillations on the gravitational production, and the works [13, 14] study the tachyonic instability induced on the field by the oscillations of the scalar curvature
We start with an initial de Sitter phase which mimics the inflationary dynamics and where the initial vacuum state for the dark matter field is well defined for values of the coupling to the scalar curvature ξ ≥ 1/6
Summary
The computation of the mode functions during the reheating epoch cannot be performed analytically, as we discuss in section 4, there are certain regions of the parameter space in which we can carry out an analytical approximation. If the mass term is larger than the energy scale of inflation, i.e, m2 > H02 and larger than the interaction term during the oscillatory phase, the resulting spectrum does not differ much from the one obtained in the de Sitter phase In this scenario, the coupling term increases the effective mass during the inflationary epoch, giving rise to a different Planckian spectrum with no instability-enhancements as it is shown in figure 3. The coupling term increases the effective mass during the inflationary epoch, giving rise to a different Planckian spectrum with no instability-enhancements as it is shown in figure 3 In this regime, as the coupling increases, the particle production decreases. It is worth noting that for larger couplings in this regime a resonance enhanced region would be reached eventually and the production would raise again monotonically with the coupling constant value
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