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Register a new userQuantum Effects in Palatini Higgs Inflation
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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 than the scale of inflation. Unless new physics above the cutoff leads to unnaturally large corrections, we can directly connect low-energy physics and inflation. On the one hand, the lower bound on the top Yukawa coupling due to collider experiments leads to an upper bound on the non-minimal coupling of the Higgs field to gravity: $xi lesssim 10^8$. On the other hand, the Higgs potential can only support successful inflation if $xi gtrsim 10^6$. This leads to a fairly strict upper bound on the top Yukawa coupling of $0.925$ (defined in the $overline{text{MS}}$-scheme at the energy scale $173.2,text{GeV}$) and constrains the inflationary prediction for the tensor-to-scalar ratio. Additionally, we compare our findings to metric Higgs inflation.
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We review the recent progress in Higgs inflation focusing on Higgs-$R^2$ inflation, primordial black hole production and the $R^3$ term.
We study inflation driven by the Higgs field in the Einstein-Cartan formulation of gravity. In this theory, the presence of the Holst and Nieh-Yan terms with the Higgs field non-minimally coupled to them leads to three additional coupling constants. For a broad range of parameters, we find that inflation is both possible and consistent with observations. In most cases, the spectral index is given by $n_s=1-2/N_star$ (with $N_star$ the number of e-foldings) whereas the tensor-to-scalar ratio $r$ can vary between about $10^{-10}$ and $1$. Thus, there are scenarios of Higgs inflation in the Einstein-Cartan framework for which the detection of gravitational waves from inflation is possible in the near future. In certain limits, the known models of Higgs inflation in the metric and Palatini formulations of gravity are reproduced. Finally, we discuss the robustness of inflationary dynamics against quantum corrections due to the scalar and fermion fields.
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 the Weyl connection by its Palatini counterpart. These theories have different vectorial non-metricity induced by the gauge field ($w_mu$) of this symmetry. Both theories have a novel spontaneous breaking of gauged scale symmetry, in the absence of matter, where the necessary scalar field is not added ad-hoc to this purpose but is of geometric origin and part of the quadratic action. The Einstein-Proca action (of $w_mu$), Planck scale and metricity emerge in the broken phase after $w_mu$ acquires mass (Stueckelberg mechanism), then decouples. In the presence of matter ($phi_1$), non-minimally coupled, the scalar potential is similar in both theories up to couplings and field rescaling. For small field values the potential is Higgs-like while for large fields inflation is possible. Due to their $R^2$ term, both theories have a small tensor-to-scalar ratio ($rsim 10^{-3}$), larger in Palatini case. For a fixed spectral index $n_s$, reducing the non-minimal coupling ($xi_1$) increases $r$ which in Weyl theory is bounded from above by that of Starobinsky inflation. For a small enough $xi_1leq 10^{-3}$, unlike the Palatini version, Weyl theory gives a dependence $r(n_s)$ similar to that in Starobinsky inflation, while also protecting $r$ against higher dimensional operators corrections.
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.
In this work, we revisit the non-minimally coupled Higgs Inflation scenario and investigate its observational viability in light of the current Cosmic Microwave Background, Baryon Acoustic Oscillation and type Ia Supernovae data. We explore the effects of the Coleman-Weinberg approximation to the Higgs potential in the primordial universe, connecting the predictions for the Lagrangian parameters at inflationary scales to the electroweak observables through Renormalization Group methods at two-loop order. As the main result, we find that observations on the electroweak scale are in disagreement with the constraints obtained from the cosmological data sets used in the analysis. Specifically, an $approx 8sigma$-discrepancy between the inflationary parameters and the electroweak value of the top quark mass is found, which suggests that a significant deviation from the scenario analysed is required by the cosmological data.
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