Reconstructing $f(R)$ gravity from the spectral index
  Recent cosmological observations are in good agreement with the scalar
spectral index $n_s$ with $n_s-1\simeq -2/N$, where $N$ is the number of
e-foldings. In the previous work, the reconstruction of the inflaton potential
for a given $n_s$ was studied, and it was found that for $n_s-1=-2/N$, the
potential takes the form of either $\alpha$-attractor model or chaotic
inflation model with $\phi^2$ to the leading order in the slow-roll
approximation. Here we consider the reconstruction of $f(R)$ gravity model for
a given $n_s$ both in the Einstein frame and in the Jordan frame. We find that
for $n_s-1=-2/N$ (or more general $n_s-1=-p/N$), $f(R)$ is given parametrically
and is found to asymptote to $R^2$ for large $R$. This behavior is generic as
long as the scalar potential is of slow-roll type.
