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Register a new userPalatini-Higgs inflation with non-minimal derivative coupling
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Alexandros Karam Dr.
Publication date
2020
fields
Physics
and research's language is
English
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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.
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We derive the general formulae for the the scalar and tensor spectral tilts to the second order for the inflationary models with non-minimally derivative coupling without taking the high friction limit. The non-minimally kinetic coupling to Einstein tensor brings the energy scale in the inflationary models down to be sub-Planckian. In the high friction limit, the Lyth bound is modified with an extra suppression factor, so that the field excursion of the inflaton is sub-Planckian. The inflationary models with non-minimally derivative coupling are more consistent with observations in the high friction limit. In particular, with the help of the non-minimally derivative coupling, the quartic power law potential is consistent with the observational constraint at 95% CL.
We consider a subclass of Horndeski theories for studying cosmic inflation. In particular, we investigate models of inflation in which the derivative self-interaction of the scalar field and the non-minimal derivative coupling to gravity are present in the action and equally important during inflation. In order to control contributions of each term as well as to approach the single-term limit, we introduce a special relation between the derivative interaction and the coupling to gravity. By calculating observable quantities including the power spectra and spectral tilts of scalar and tensor perturbation modes, and the tensor-to-scalar ratio, we found that the tensor-to-scalar ratio is suppressed by a factor of $(1+1/gamma)$, where $gamma$ reflects the strength of the derivative self-interaction of the inflaton field with respect to the derivative coupling gravity. We placed observational constraints on the chaotic and natural inflation models and showed that the models are consistent with the current observational data mainly due to the suppressed tensor-to-scalar ratio.
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, rather than metric, type. In this paper, we revisit the idea and correct some shortcomings in earlier studies. We find that in this setup the Higgs can indeed act as the inflaton and that the tree-level predictions of the model for the spectral index and the tensor-to-scalar ratio are $n_ssimeq 0.941$, $rsimeq 0.3/(1+10^{-8}alpha)$, respectively, for a typical number of e-folds, $N=50$, between horizon exit of the pivot scale $k=0.05, {rm Mpc}^{-1}$ and the end of inflation. Even though the tensor-to-scalar ratio is suppressed compared to the usual minimally coupled case and can be made compatible with data for large enough $alpha$, the result for $n_s$ is in severe tension with the Planck results. We briefly discuss extensions of the model.
We study non-minimal Coleman-Weinberg inflation in the Palatini formulation of gravity in the presence of an $R^2$ term. The Planck scale is dynamically generated by the vacuum expectation value of the inflaton via its non-minimal coupling to the curvature scalar $R$. We show that the addition of the $R^2$ term in Palatini gravity makes non-minimal Coleman-Weinberg inflation again compatible with observational data.
We derive the reconstruction formulae for the inflation model with the non-minimal derivative coupling term. If reconstructing the potential from the tensor-to-scalar ratio, we could obtain the potential without using the high friction limit. As an example, we reconstruct the potential from the parametrization $r=8alpha/(N+beta)^{gamma}$, which is a general form of the $alpha$-attractor. The reconstructed potential has the same asymptotic behavior as the T- and E-model if we choose $gamma=2$ and $alphall1$. We also discuss the constraints from the reheating phase preceding the radiation domination by assuming the parameter $w_{re}$ of state equation during reheating is a constant. The scale of big-bang nucleosynthesis could put a up limit on $n_s$ if $w_{re}=2/3$ and a low limit on $n_s$ if $w_{re}=1/6$.
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