Analysis of inflationary models in higher-dimensional uniform inflation

We consider higher-dimensional uniform inflation, in which the extra dimensions expand at the same rate as three-dimensional non-compact space during inflation. We compute the cosmological perturbation in $D+4$ dimensions and derive the spectral index $n_s$ and the tensor-scalar ratio $r$. We analyze five inflationary models: chaotic inflation, natural inflation, quartic hilltop inflation, inflation with spontaneously broken SUSY, and $R^2$ inflation. By combining the results from these models with the Planck 2018 constraints, we discuss that it is not desirable for the extra-dimensional space to expand at the same rate as the three-dimensional non-compact space, except for the case of one extra dimension.