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Register a new userThe Conformal Transformation in General Single Field Inflation with Non-Minimal Coupling
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The method of a conformal transformation is applied to a general class of single field inflation models with non-minimal coupling to gravity and non-standard kinetic terms, in order to reduce the cosmological perturbative calculation to the conventional minimal coupling case to all orders in perturbation theory. Our analysis is made simple by the fact that all perturbation variables in the comoving gauge are conformally invariant to all orders. The structure of the vacuum, on which cosmological correlation functions are evaluated, is also discussed. We show how quantization in the Jordan frame for non-minimally coupled inflation models can be equivalently implemented in the Einstein frame. It is thereafter argued that the general N-point cosmological correlation functions (of the curvature perturbation) are independent of the conformal frame.
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The predictions of standard Higgs inflation in the framework of the metric formalism yield a tensor-to-scalar ratio $r sim 10^{-3}$ which lies well within the expected accuracy of near-future experiments $ sim 10^{-4}$. When the Palatini formalism is employed, the predicted values of $r$ get highly-suppressed $rsim 10^{-12}$ and consequently a possible non-detection of primordial tensor fluctuations will rule out only the metric variant of the model. On the other hand, the extremely small values predicted for $r$ by the Palatini approach constitute contact with observations a hopeless task for the foreseeable future. In this work, we propose a way to remedy this issue by extending the action with the inclusion of a generalized non-minimal derivative coupling term between the inflaton and the Einstein tensor of the form $m^{-2}(phi) G_{mu u} abla^{mu}phi abla^{ u}phi$. We find that with such a modification, the Palatini predictions can become comparable with the ones obtained in the metric formalism, thus providing ample room for the model to be in contact with observations in the near future.
We perform adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation with varying speed of sound. The subtraction is performed within the framework of earlier study by Urakawa and Starobinsky dealing with the canonical inflation. Inspired by Fakir and Unruhs model on nonminimally coupled chaotic inflation, we find upon imposing near scale-invariant condition, that the subtraction term exponentially decays with the number of $ e $-folds. As in the result for the canonical inflation, the regularized power spectrum tends to the bare power spectrum as the Universe expands during (and even after) inflation. This work justifies the use of the bare power spectrum in standard calculation in the most general context of slow-roll single-field inflation involving non-minimal coupling and varying speed of sound.
We derive the consistency relations for a chaotic inflation model with a non-minimal coupling to gravity. For a quadratic potential in the limit of a small non-minimal coupling parameter $xi$ and for a quartic potential without assuming small $xi$, we give the consistency relations among the spectral index $n_s$, the tensor-to-scalar ratio $r$ and the running of the spectral index $alpha$. We find that unlike $r$, $alpha$ is less sensitive to $xi$. If $r<0.1$, then $xi$ is constrained to $xi<0$ and $alpha$ is predicted to be $alphasimeq -8times 10^{-4}$ for a quartic potential. For a general monomial potential, $alpha$ is constrained in the range $-2.7times 10^{-3}<alpha< -6times 10^{-4}$ as long as $|xi|leq 10^{-3}$ if $r<0.1$.
We investigate warm inflationary scenario in which the accelerated expansion of the early Universe is driven by chameleon-like scalar fields. Due to the non-minimal coupling between the scalar field and the matter sector, the energy-momentum tensor of each fluid component is not conserved anymore, and the generalized balance equation is obtained. The new source term in the energy equation can be used to model warm inflation. On the other hand, if the coupling function varies slowly, the model reduces to the standard model used for the description of cold inflation. To test the validity of the warm chameleon inflation model, the results for warm inflationary scenarios are compared with the observational Planck2018 Cosmic Microwave Background data. In this regard, the perturbation parameters such as the amplitude of scalar perturbations, the scalar spectral index and the tensor-to-scalar ratio are derived at the horizon crossing in two approximations, corresponding to the weak and strong dissipative regimes. As a general result it turns out that the theoretical predictions of the chameleon warm inflationary scenario are consistent with the Planck 2018 observations.
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 $r$.
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