R^2-inflation with conformal SM Higgs field
  We introduce conformal coupling of the Standard Model Higgs field to gravity
and discuss the subsequent modification of $R^2$-inflation. The main
observation is a lower temperature of reheating which happens mostly through
scalaron decays into gluons due to the conformal (trace) anomaly. This modifies
all predictions of the original $R^2$-inflation. To the next-to-leading order
in slow roll parameters we calculate amplitudes and indices of scalar and
tensor perturbations produced at inflation. The results are compared to the
next-to-leading order predictions of $R^2$-inflation with minimally coupled
Higgs field and of Higgs-inflation. We discuss additional features in gravity
wave signal that may help to distinguish the proposed variant of
$R^2$-inflation. Remarkably, the features are expected in the region available
for study at future experiments like BBO and DECIGO. Finally, we check that
(meta)stability of electroweak vacuum in the cosmological model is consistent
with recent results of searches for the Higgs boson at LHC.
