Late-time acceleration and inflation in a Poincar\'e gauge cosmological model

A self-consistent model which can unify Starobinsky inflation and the $\Lambda$CDM model in the framework of Poincar\'e gauge cosmology (PGC) is studied in this work, without extra inflaton and ``dark energy''. We start from the general nine-parameter PGC Lagrangian and get two Friedmann-like analytical solutions with the certain ghost- and tachyon-free conditions on the Lagrangian parameters. The scalar torsion $h$-determined solution is consistent with Starobinsky cosmology in the early-time and the pseudo-scalar torsion $f$-determined solution contains naturally a constant ``dark energy'' density, $3(\alpha-1)^2/8B_0$, which covers the $\Lambda$CDM model in the late-time. According to the latest observations, we estimate the magnitudes of parameters: $\alpha-1\simeq 8.07\times10^{-56}$, $B_0\simeq5.76\times10^{-28}GeV^{-2}$ in the natural units.