Observational Viability of Anisotropic Inflation Revisited

We investigate anisotropic inflation within the single-field model featuring an intermediate scale factor. Our analysis reveals that the anisotropic nature of the Friedmann equations in this framework affects the slow-roll parameters, which in turn influence key perturbation parameters. Using a numerical approach, we derive constraints on the intermediate parameter $\beta$ and the anisotropic parameter $c$. Our results show that the model is consistent with Planck2018 TT, TE, EE +lowE+lensing+BK14+BAO data at $68\%$ CL, for $0.84<\beta<1$ and $7.34<c<27.7$. At $95\%$ CL the consistency holds for $0.77<\beta<1$ and $7.17<c<28.9$. The model is also consistent with Planck2018 TT, TE, EE +lowE+lensing+BK18+BAO data, for $0.91<\beta<1$ and $8.00<c<27.4$ (at $68\%$ CL), and $0.88<\beta<1$ and $7.40<c<28.8$ (at $95\%$ CL). Additionally, we examine the reheating phase using these constraints on constraints on $\beta$ and $c$ and determine the observationally consistent ranges for the number of e-folds and the temperature during the reheating phase.