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 ($T_{\text{reh}}$, ${\overline{w}}_{\text{reh}}$ and $N_{\text{reh}}$) and the inflationary observables. By paying closer attention to the role of the ${\overline{w}}_{\text{reh}}$, 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 $\gtrsim {10}^{15}$ GeV, with possible low values $\sim {10}^{12}$ 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.

我们考虑了以弦和超重力为动力的场景，其中模量场在通货膨胀后的时代主导着宇宙的能量密度。对于单光模量的情况，已经表明，考虑到从膨胀期间哈勃越过时间到当前时间的特定比例的演变，可以得到最轻的模量，再加热参数之间的关系（${Ť}_{\text{h}}$， ${\overline{w}}_{\text{h}}$ 和 ${ñ}_{\text{h}}$）和通胀观测值。通过密切关注${\overline{w}}_{\text{h}}$，我们使用CMB数据对模量质量值和再加热参数获得了更严格的约束。接下来，将分析扩展到包括作为CMB低多极异常源的充气素势中的特征，这进一步将模量的质量限制为明显高于没有这种约束的情况。通过考虑和考虑的几种充气模型，我们发现了对最轻模量颗粒的质量的约束，${米}_{\chi }$，一般而言 $\gtrsim {10}^{15}$ GeV，可能值较低 $〜{10}^{12}$GeV。尽管假设简化了加热阶段，但界限确实是暗示性的，并且该研究可以作为证明，通过使用今天的CMB观测资料，可以获得有关埋在宇宙早期的深处的加热阶段的大量知识。