Constant-roll $f(R)$ inflation compared with Cosmic Microwave Background anisotropies and swampland criteria.

Inflationary models derived from $f(R)$ gravity, where the scalaron rolls down with a constant rate from the top to the minimum of the effective potential, are considered. Specifically, we take into account three $f(R)$ models \textit{i.e.}\,Starobinsky $R^{2}$, $R^{2p}$ and the logarithmic corrected models. We compare the inflationary parameters derived from the models with the observational data of CMB anisotropies \textit{i.e.} the Planck and Keck/array datasets in order to find observational constraints on the parameters space. We find that although our $f(R)$ constant-roll models for $\gamma=0$ show observationally acceptable values of $r$, they do not predict favoured values of the spectral index. In particular, we have $n_{s}>1$ for the Starobinsky $R^{2}$ and $R^{2p}$ models and $0.996

Keywords:

• Physics
• Planck
• Mathematical physics
• constant
• Spectral index
• Cosmic microwave background
• Logarithm
• order
• Space (mathematics)
• Inflation (cosmology)

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