We examine the power-law Starobinsky model, a generalized version of the Starobinsky inflation model, characterized by a power-law correction to Einstein gravity. Employing the $f(R)$ formalism, the scalar and tensor power spectra were numerically computed as functions of the dimensionless parameters $M$ and $\beta$. A Markov Chain Monte Carlo (MCMC) analysis was conducted using Planck-2018, BICEP3 and BAO observational data, yielding precise constraints on $\beta = 1.987^{ +0.013}_{ -0.016},\, 95\%\, C.\, L.$. and $ \log_{ 10}M = -4.72^{ +0.21}_{ -0.20}$. The derived scalar spectral index $n_s=0.9676^{ +0.0069}_{ -0.0068}$ and tensor-to-scalar ratio $r=0.0074^{ +0.0061}_{ -0.0044}$ lie within the bounds set by Planck observations. We analyse a general reheating scenario while keeping the number of e-folds during inflation, $N_{ pivot}$, fixed. The analysis confirms that deviations from the Starobinsky $R^2$ model are observationaly viable, with implications for high-energy physics and supergravity-based inflationary models.
Categories: astro-ph.CO gr-qc hep-th