Gravitational dark matter: free streaming and phase space distribution

Abstract

Gravitational dark matter (DM) is the simplest possible scenario that has recently gained interest in the early universe cosmology. In this scenario, DM is assumed to be produced from the decaying inflaton through the gravitational interaction during reheating. Gravitational production from the radiation bath will be ignored as our analysis shows it to be suppressed for a wide range of reheating temperature (T re ).Ignoring any other internal parameters except the DM mass (m Y ) and spin, a particular inflation model such as α-attractor, with a specific scalar spectral index (n s ) has been shown to uniquely fix the dark matter mass of the present universe. For fermion type dark matter we found the mass m f should be within (10 4 − 10 13 ) GeV, and for boson type DM, the mass m s/X turned out to be within (10 −8 − 10 13 ) GeV.Interestingly, if the inflaton equation of state ω φ → 1/3, the DM mass also approaches towards unique value, m f ∼ 10 10 GeV and m s/X ∼ 10 3 ( 8 × 10 3 ) GeV irrespective of the value of ω φ . We further analyzed the phase space distribution (f Y ), and free streaming length (λ f s ) of these gravitationally produced DM. f Y , which is believed to encode important information about DM, is shown to contain a characteristic primary peak at the initial time where the gravitational production is maximum for both fermion/boson. Apart from this fermionic phase-space distribution function contains an additional peak near the inflaton and fermion mass equality (m Y = m φ ) arising for ω φ > 5/9. Furthermore, the height of this additional peak turned out to be increasing with decreasing T re , and at some point dominates over the primary one. Since reheating is a causal process and dark matter is produced during this phase, gravitational instability forming small-scale DM structures during this period will encode those phase space information and be observed at present. Crucial condition λ f s < λ re of forming such small scale DM structure during reheating has been analyzed in detail. We further estimate in detail the range of scales within which the above condition will be satisfied for different dark matter masses. Finally, we end by stating the fact that all our results are observed to be insensitive on the parameter α of the inflaton potential within the allowed range set by the latest Planck and BICEP/Keck results.

Scalar Dark Matter Production from Preheating and Structure Formation Constraints

“…On the perturbative side, gravitational production of dark matter with a graviton mediator has been studied in [26-28, 113, 114], where it was shown that such processes play a dominant role during reheating. Similar processes involving the inflaton condensate scattering to thermal bath particles were studied in [27,115]. However, we argue here that such a simple perturbative picture of gravitational production of dark matter is insufficient since it does not account for the tachyonic growth of the superhorizon modes.…”

Gravitational Reheating

“…Our conclusion so far seems to be independent of any new physics in the visible sector. However, if one introduces explicit coupling (say β) between DM and radiation bath, the DM masses obtained in our analysis become the maximum possible value m max Y in (β, m Y ) space, above which the universe will be over-abundant (see detail discussion in [2]). Therefore, an important conclusion we can arrive at is that detection of DM with m Y > m max Y will automatically rule out the possibility of purely gravitational reheating, at least in the framework of de-Sitter inflation.…”

“…Therefore, peak appears for fermionic PDFs at m φ (t) = m Y . However, this distinguishing feature happens only for ω φ > 5/9 (see [2] for detailed discussions) Conclusions: GRe phenomena appeared to be a unique scenario through which our present state of the universe can be obtained after inflation. Because of DM mass being a only free parameter during this phase, realizing such scenario put stringent constraint on the possible models of inflation and DM mass.…”

“…Given the constraints of our present state of the universe, GRe appeared to be consistent with a very limited class of inflation models and a narrow range of DM mass. GRe is not sensitive to any new physics in the observable sector, except if the DM couples with the radiation bath, gravitational production has been shown to set a maximum limit on the DM mass [2] It is the s-channel graviton exchange process through which inflaton converts its energy to radiation and DM during reheating. Gravitaton exchange processes between radiation bath and DM will be ignored due to its sub-dominant contribution (see detailed study in [1][2][3]).…”

“…Here, we first discuss the generic bounds on de-Sitter type inflation without specifying any particular model. Using the following approximate relation 2 H end (under the assumption φ end ∼ M p ), one immediately gets ω φ within (0.60, 0.99) and H end within (1×10 9 , 5×10 13 ) GeV. This narrow and closed bound are derived form the minimum reheating temperature T min re = T BBN = 10 −2 GeV and maximum possible value of the de-sitter Hubble scale at the end of inflation, H max end πM p rA s /2 calculated at upper limit on r = 0.036 [15] (see Fig.…”