  Considering the inflation model based on a $f(R)$ gravity theory, we obtain
several important constraints from the large angular scale CMBR observations.
First, the ordinary slow-roll assumption during the inflation together with
Harrison-Zel'dovich spectral conditions chooses $R^2$ gravity as a unique
candidate. Second, the $R^2$ gravity leads to specific near scale-invariant
Harrison-Zel'dovich spectra both for the scalar and the tensor perturbations.
Third, using the COBE-DMR data we derive the strong constraints on the coupling
constant and the energy scale during the inflation. Also, our result shows the
gravitational wave contribution to the CMBR anisotropy is negligible. So, the
future observation can provide the strong constraints on the inflation model
based on $R^2$ gravity. This is a summary of a talk presented in COSMO-01, and
the more completed published version can be found in astro-ph/0102423.
