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In the context of the Palatini formalism of gravity with an $R^{2}$ term, a $phi^{2}$ potential can be consistent with the observed bound on $r$ whilst retaining the successful prediction for $n_{s}$. Here we show that the Palatini $phi^{2} R^2$ inflation model can also solve the super-Planckian inflaton problem of $phi^{2}$ chaotic inflation, and that the model can be consistent with Planck scale-suppressed potential corrections. If $alpha gtrsim 10^{12}$, where $alpha$ is the coefficient of the $R^2$ term, the inflaton in the Einstein frame, $sigma$, remains sub-Planckian throughout inflation. In addition, if $alpha gtrsim 10^{20}$ then the predictions of the model are unaffected by Planck-suppressed potential corrections in the case where there is a broken shift symmetry, and if $alpha gtrsim 10^{32}$ then the predictions are unaffected by Planck-suppressed potential corrections in general. The value of $r$ is generally small, with $r lesssim 10^{-5}$ for $alpha gtrsim 10^{12}$. We calculate the maximum possible reheating temperature, $T_{R;max}$, corresponding to instantaneous reheating. For $alpha approx 10^{32}$, $T_{R; max}$ is approximately $10^{10}$ GeV, with larger values of $T_{R;max}$ for smaller $alpha$. For the case of instantaneous reheating, we show that $n_{s}$ is in agreement with the 2018 Planck results to within 1-$sigma$, with the exception of the $alpha approx 10^{32}$ case, which is close to the 2-$sigma$ lower bound. Following inflation, the inflaton condensate is likely to rapidly fragment and form oscillons. Reheating via inflaton decays to right-handed neutrinos can easily result in instantaneous reheating. We determine the scale of unitarity violation and show that, in general, unitarity is conserved during inflation.
It has recently been suggested that the Standard Model Higgs boson could act as the inflaton while minimally coupled to gravity - given that the gravity sector is extended with an $alpha R^2$ term and the underlying theory of gravity is of Palatini,
We present two cases where the addition of the $R^2$ term to an inflationary model leads to single-field inflation instead of two-field inflation as is usually the case. In both cases we find that the effect of the $R^2$ term is to reduce the value of the tensor-to-scalar ratio $r$.
We present a comparative study of inflation in two theories of quadratic gravity with {it gauged} scale symmetry: 1) the original Weyl quadratic gravity and 2) the theory defined by a similar action but in the Palatini approach obtained by replacing
We study quantum effects in Higgs inflation in the Palatini formulation of gravity, in which the metric and connection are treated as independent variables. We exploit the fact that the cutoff, above which perturbation theory breaks down, is higher t
We study quadratic gravity $R^2+R_{[mu u]}^2$ in the Palatini formalism where the connection and the metric are independent. This action has a {it gauged} scale symmetry (also known as Weyl gauge symmetry) of Weyl gauge field $v_mu= (tildeGamma_mu-Ga