Inflationary cosmology is the dominant perspective in explaining the early physics of the universe. Along with solving the flatness, homogeneity, and unwanted relics problems, inflationary cosmology interprets inhomogeneities in the Cosmic Microwave Background Radiation. Three models of inflation are considered in this study: Natural inflation, Power-law inflation, and inflationary model based on variations of the strong coupling constant. Unfortunately, in Einstein's gravity, these three models did not match current observational constraints represented by Planck2018 (TT, EE, TE), BK18, and other experiments (lowE, lensing) separately or combined. However, our study demonstrates that by modifying the gravitational sector, represented by F(R) gravity with/without non-minimal coupling between the inflaton field and gravity, the models can be rescued and accommodate the observations. Moreover, the study is conducted within Palatini's formalism of gravity rather than one based on metric formulation. Finally, we demonstrate that the models can produce inherently different results when analyzed within different inflationary scenarios like warm slow-roll inflation, cold constant-roll inflation, or non-canonical inflation. The talk is based on:
M.AlHallak, A.AlRakik, N.Chamoun and M.S.El-Daher, Universe 8 (2022) no.2, 126 doi:10.3390/universe8020126 [arXiv:2111.05075 [astro-ph.CO]].
M.AlHallak, N.Chamoun and M.S.Eldaher, JCAP 10 (2022), 001 doi:10.1088/1475-7516/2022/10/001 [arXiv:2202.01002 [astro-ph.CO]].
M.AlHallak, K.K.A Said, N.CHAMOUN and M.S.El-Daher, [arXiv:2211.07775 [gr-qc]].
And current studies.