Reheating constraints to modulus mass for single field inflationary models

We consider string and supergravity motivated scenarios in which moduli fields dominate the energy density of the Universe in a post-inflationary epoch. For the case of a single light modulus it has been shown that considering the evolution of a specific scale from the time of its Hubble crossing during inflation to the present time, a relation can be obtained among the lightest modulus mass, the reheating parameters ($T_{\text{reh}}$, $\bar{w}_{\text{reh}}$ and $N_{\text{reh}}$) and the inflationary observables. By paying closer attention to the role of the $\bar{w}_{\text{reh}}$, we obtain more stringent constraints on the value of the modulus mass and the reheating parameters using the CMB data. Next, the analysis is extended to include features in the inflaton potential as a source of CMB low multipole anomalies, which further constrains the mass of the modulus to be substantially higher than without such a constraint. By both considerations and for several inflation models considered, we find a constraint on the mass of the lightest modulus particle, $m_{\chi}$, generically $\gtrsim10^{15}$GeV, with possible low values $\sim10^{12}$GeV. While a simplification of the reheating phase is assumed, the bounds are reliably suggestive, and the study may be taken as a demonstration that substantial knowledge about reheating phase buried deep in the early epochs of the Universe is accessible through the use of CMB observables today.