In this paper, we discuss the constraints on the reheating temperature supposing an early postreheating cosmological phase dominated by one or more simple scalar fields produced from inflaton decay and decoupled from matter and radiation. In addition, we explore the combined effects of the reheating and non-standard scalar field phases on the inflationary number of e-foldings.

We discuss the effects on the cosmic microwave background (CMB), cosmic infrared background (CIB), and thermal Sunyaev-Zeldovich effect due to the peculiar motion of an observer with respect to the CMB rest frame, which induces boosting effects. After a brief review of the current observational and theoretical status, we investigate the scientific perspectives opened by future CMB space missions, focussing on the Cosmic Origins Explorer (CORE) proposal. The improvements in sensitivity offered by a mission like CORE, together with its high resolution over a wide frequency range, will provide a more accurate estimate of the CMB dipole. The extension of boosting effects to polarization and cross-correlations will enable a more robust determination of purely velocity-driven effects that are not degenerate with the intrinsic CMB dipole, allowing us to achieve an overall signal-to-noise ratio of 13; this improves on the Planck detection and essentially equals that of an ideal cosmic-variancelimited experiment up to a multipole 2000. Precise inter-frequency calibration will offer the opportunity to constrain or even detect CMB spectral distortions, particularly from the cosmological reionization epoch, because of the frequency dependence of the dipole spectrum, without resorting to precise absolute calibration. The expected improvement with respect to COBE-FIRAS in the recovery of distortion parameters (which could in principle be a factor of several hundred for an ideal experiment with the CORE configuration) ranges from a factor of several up to about 50, depending on the quality of foreground removal and relative calibration. Even in the case of 1 % accuracy in both foreground removal and relative calibration at an angular scale of 1 • , we find that dipole analyses for a mission like CORE will be able to improve the recovery of the CIB spectrum amplitude by a factor 17 in comparison with current results based on COBE-FIRAS. In addition to the scientific potential of a mission like CORE for these analyses, synergies with other planned and ongoing projects are also discussed.

We present constraints on the reheating era within the string Fiber Inflation scenario, in terms of the effective equation-of-state parameter of the reheating fluid, w reh . The results of the analysis, completely independent on the details of the inflaton physics around the vacuum, illustrate the behavior of the number of e-foldings during the reheating stage, N reh , and of the final reheating temperature, T reh , as functions of the scalar spectral index, ns. We analyze our results with respect to the current bounds given by the PLANCK mission data and to upcoming cosmological experiments. We find that large values of the equation-of-state parameter (w reh > 1/3) are particularly favored as the scalar spectral index is of the order of ns ∼ 0.9680, with a σn s ∼ 0.002 error. Moreover, we compare the behavior of the general reheating functions N reh and T reh in the fiber Inflation scenario with the one extracted by the class of the α-attractor models with α = 2. We find that the corresponding reheating curves are very similar in the two cases.