In this letter, we show for the first time that the perfect state of our present universe can be obtained through gravitational interaction between inflaton and all fundamental fields during reheating without invoking new physics. Our analysis revealed that gravitational reheating is consistent for a very restricted class of inflation models and narrow ranges of reheating temperature and dark matter mass.

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.