Unification of inflation and dark matter in the Higgs–Starobinsky model

In this work, we propose unified picture of inflation and dark matter in the Higgs–Starobinsky (HS) model. As pointed out in the literature, Starobinsky $$R^2$$ inflation is induced by quantum correction effect from the large Higgs-curvature (graviton) coupling. We start with non-minimal coupling HS action in Jordan frame. We then transform the Jordan frame action into the Einstein one using the conformal transformation. The inflation potential is derived from the gravitational action of non-minimal-Higgs coupling and Starobinsky term in Einstein frame where the $$R^2$$ term is dominated in the inflationary phase of the universe. For model of inflation, we compute the inflationary parameters and confront them with Planck 2015 data. We discover that the predictions of the model are in excellent agreement with the Planck analysis. In addition, we find that the HS model is equivalent to a scalar singlet dark matter (SSDM) or Higgs-portal model. The renormalization group equations (RGEs) of HS scenario with standard model at one-loop level is qualitatively analyzed. By using the solutions of parameter spaces from RGE analysis, the coupling constants of the HS model will be verified and can be used to constrain the SSDM using dark matter relic abundance