Observational constraints on power law Starobinsky inflation

In this work we revisit power law, $\frac{1}{M^2}{R}^{\beta }$, inflation to find the deviations from $R^2$ inflation allowed by current cosmic microwave background (CMB) and large-scale structure (LSS) observations. We compute the power spectra for scalar and tensor perturbations numerically and perform Markov chain Monte Carlo analysis to put constraints on parameters $M$ and $\beta$ from Planck-2018, BICEP3 and other LSS observations. We consider general reheating scenario and also vary the number of $e$-foldings during inflation, $N_{\text{pivot}}$, along with the other parameters. We find $\beta ={1.966}_{-0.042}^{+0.035}$, $M=({3.31}_{-2}^{+5})\times {10}^{-5}$ and $N_{\text{pivot}}={41}_{-10}^{+10}$ with 95% C.L. This indicates that the current observations allow deviation from Starobinsky inflation. The scalar spectral index, $n_s$, and tensor-to-scalar ratio, $r$, derived from these parameters, are consistent with the Planck and BICEP3 observations.

Figure 1

The potential (9) for various values of $\beta$. The value of M is fixed at $M=5\times {10}^{-5}$, and the values of potential and scalar field are in $M_p=1$ units.

Figure 2

Marginalized constraints on the potential parameters and $N_{\text{pivot}}$ using Planck-2018, BICEP3 and BAO data.

Figure 3

Joint 68% C.L., and 95% C.L. constraints on parameters of potential and $N_{\text{pivot}}$ using Planck-2018, BICEP3, and BAO data.

Figure 4

Joint 68% C.L., and 95% C.L. constraints on potential parameter $M$ and $N_{\text{pivot}}$ from Planck-2018, BICEP3, and BAO data.

Figure 5

Joint 68% C.L., and 95% C.L. constraints on $n_s$ and $r$ from Planck-2018, BICEP3, and BAO data.