Abstract
A model of vector dark matter that communicates with the Standard Model only through gravitational interactions has been investigated. It has been shown in detail how does the canonical quantization of the vector field in varying FLRW geometry implies a tachyonic enhancement of some of its momentum modes. Approximate solutions of the mode equation have been found and verified against exact numerical ones. De Sitter geometry has been assumed during inflation while after inflation a non-standard cosmological era of reheating with a generic equation of state has been adopted which is followed by the radiation-dominated universe. It has been shown that the spectrum of dark vectors produced gravitationally is centered around a characteristic comoving momentum k⋆ that is determined in terms of the mass of the vector mX, the Hubble parameter during in- flation HI, the equation of state parameter w and the efficiency of reheating γ. Regions in the parameter space consistent with the observed dark matter relic abundance have been determined, justifying the gravitational production as a viable mechanism for vector dark matter. The results obtained in this paper are applicable within various possible models of inflation/reheating with non-standard cosmology parametrized effectively by the corresponding equation of state and efficiency of reheating.
Highlights
DM production due to quantum fluctuations [9, 10]
It has been shown that the spectrum of dark vectors produced gravitationally is centered around a characteristic comoving momentum k that is determined in terms of the mass of the vector mX, the Hubble parameter during inflation HI, the equation of state parameter w and the efficiency of reheating γ
A very heavy DM can be produced during the (p)reheating period — the last stage of inflation — where the inflaton field transfers its energy density to the visible and dark sectors through coherent oscillations [11,12,13]
Summary
During an epoch of rapidly expanding universe (inflation and partially reheating) the gravitational production dominates over other DM production mechanisms. During the reheating the energy density of the universe is dominated by the energy density ρφ of the inflaton/reheaton field φ In this period, we assume that the inflaton equation of state is parametrized by a parameter w describing the non-standard cosmology that we will vary and investigate its relevance: pφ = wρφ,. Assuming ρφ ρSM and Γφ 3(1 + w)H, the generic form of the equation of state for the inflaton/reheaton (2.10) implies that during the reheating period the scale factor aRH evolves as a function of the conformal time τ as aRH(τ ) ∝ τ 1+3w. Note that the SM energy density ρSM is zero during the inflationary period and is continuous at the end of reheating since a−4 term in the middle line of (2.20) is negligible in comparison to a−3(1+w)/2 term for −1/3 < w < 1. (1+w) during the non-standard reheating, shown as dashed green curve
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