Starobinsky model in rainbow gravity

In this paper, we study the Starobinsky model of inflation in the context of gravity’s rainbow theory. We propose that gravity rainbow functions can be written in the power-law form of the Hubble parameter. We present a detailed derivation of the spectral index of curvature perturbation and the tensor-to-scalar ratio and compare the predictions of our models with Planck 2015 data. We discover that in order to be consistent with Planck data up to $2\sigma$ C.L., the viable values of $N_k$ $e$-folds would satisfy $42\lesssim N_k\lesssim 87$ and the rainbow parameter $\lambda$ is nicely constrained to be $\lambda \lesssim 6.0$.

Figure 1

We compare the theoretical predictions in the $(r-n_s)$ plane for different values of $\lambda$ with Planck’15 results for TT, TE, EE, $+\mathrm{lowP}$ and assuming $\mathrm{\Lambda }\mathrm{CDM}+\mathrm{r}$ [19].

Figure 2

We compare the theoretical predictions in the $(r-n_s)$ plane for different values of $N_k$ for each $\lambda$ with Planck’15 results for TT, TE, EE, $+\mathrm{lowP}$ and assuming $\mathrm{\Lambda }\mathrm{CDM}+\mathrm{r}$ [19].

Figure 3

We compare the theoretical predictions in the $(r-n_s)$ plane for different values of $\lambda$ for each $N_k$ with Planck’15 results for TT, TE, EE, $+\mathrm{lowP}$ and assuming $\mathrm{\Lambda }\mathrm{CDM}+\mathrm{r}$ [19].