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Ultraviolet Freeze-in and Non-Standard Cosmologies

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 Publication date 2019
  fields Physics
and research's language is English




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A notable feature of UV freeze-in is that the relic density is strongly dependent on the highest temperatures of the thermal bath, and a common assumption is that the relevant highest temperature should be the reheating temperature after inflation $T_text{RH}$. However, the temperature of the thermal bath can be significantly higher in certain scenarios, reaching a value denoted T max , a fact which is only apparent away from the instantaneous decay approximation. Interestingly, it has been shown that if the operators are of sufficiently high mass dimension then the dark matter abundance can be enhanced by a boost factor depending on ($T_text{max}/T_text{RH}$) relative to naive estimates assuming instantaneous reheating. We highlight here that in non-standard cosmological histories the critical mass dimension of the operator above at which the instantaneous decay approximation breaks down, and the exponent of the boost factor, depend on the equation of state $omega$ prior to reheating. We highlight four examples in which the dark matter abundance receives a significant enhancement in the context of gravitino dark matter, the moduli portal, the Higgs portal, and the spin-2 portal (as might arise in bimetric gravity models). We comment on the transition from kination domination to radiation domination as a motivated example of non-standard cosmologies.



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Using the upper bound on the inelastic reaction cross-section implied by S-matrix unitarity, we derive the thermally averaged maximum dark matter (DM) annihilation rate for general $k rightarrow 2$ number-changing reactions, with $k geq 2$, taking place either entirely within the dark sector, or involving standard model fields. This translates to a maximum mass of the particle saturating the observed DM abundance, which, for dominantly $s$-wave annihilations, is obtained to be around $130$ TeV, $1$ GeV, $7$ MeV and $110$ keV, for $k=2,3,4$ and $5$, respectively, in a radiation dominated Universe, for a real or complex scalar DM stabilized by a minimal symmetry. For modified thermal histories in the pre-big bang nucleosynthesis era, with an intermediate period of matter domination, values of reheating temperature higher than $mathcal{O}(200)$ GeV for $k geq 4$, $mathcal{O}(1)$ TeV for $k=3$ and $mathcal{O}(50)$ TeV for $k=2$ are strongly disfavoured by the combined requirements of unitarity and DM relic abundance, for DM freeze-out before reheating.
Once dark matter has been discovered and its particle physics properties have been determined, a crucial question rises concerning how it was produced in the early Universe. If its thermally averaged annihilation cross section is in the ballpark of few$times 10^{-26}$ cm$^3$/s, the WIMP mechanism in the standard cosmological scenario (i.e. radiation dominated Universe) will be highly favored. If this is not the case one can either consider an alternative production mechanism, or a non-standard cosmology. Here we study the dark matter production in scenarios with a non-standard expansion history. Additionally, we reconstruct the possible non-standard cosmologies that could make the WIMP mechanism viable.
We undertake a careful analysis of stochastic gravitational wave production from cosmological phase transitions in an expanding universe, studying both a standard radiation as well as a matter dominated history. We analyze in detail the dynamics of the phase transition, including the false vacuum fraction, bubble lifetime distribution, bubble number density, mean bubble separation, etc., for an expanding universe. We also study the full set of differential equations governing the evolution of plasma and the scalar field during the phase transition and generalize results obtained in Minkowski spacetime. In particular, we generalize the sound shell model to the expanding universe and determine the velocity field power spectrum. This ultimately provides an accurate calculation of the gravitational wave spectrum seen today for the dominant source of sound waves. For the amplitude of the gravitational wave spectrum visible today, we find a suppression factor arising from the finite lifetime of the sound waves and compare with the commonly used result in the literature, which corresponds to the asymptotic value of our suppression factor. We point out that the asymptotic value is only applicable for a very long lifetime of the sound waves, which is highly unlikely due to the onset of shocks, turbulence and other damping processes. We also point out that features of the gravitational wave spectral form may hold the tantalizing possibility of distinguishing between different expansion histories using phase transitions.
We study a minimal scenario to realize non-thermal leptogenesis and UV freeze-in of a Standard Model (SM) gauge singlet fermionic dark matter (DM) simultaneously, with inflaton field playing a non-trivial role in their yields. The renormalizable interactions are restricted to the SM fields, two right handed neutrinos (RHN) and inflaton coupling exclusively to the RHNs, while the DM couples to both the SM and the RHNs only via operators of dimension $d>4$. Considering two separate cases of $d={5,6}$, we show that for $d=5$, inflaton decay into RHNs followed by their subsequent decay into SM particles lead to both reheating as well as DM production from the SM bath. This requires a cut-off scale as large as $Lambdasim 10^{17}~rm GeV$ depending on the DM mass. On the other hand, for $d=6$, DM production happens directly from scattering of RHNs (for $Lambdagtrsim 10^{14}~rm GeV$) that results in a very non-trivial evolution of the DM yield. In both these cases, it is possible to explain the observed baryon asymmetry through successful non-thermal leptogenesis via the decay of the RHNs, together with the PLANCK observed relic density of the DM via pure UV freeze-in mechanism. Taking into account both instantaneous as well as non-instantaneous reheating separately, we constrain the parameter space of this minimal scenario from relevant phenomenological requirements including sub-eV scale active neutrino masses and their mixing.
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