Abstract
We investigate the sensitivity of Higgs(-like) inflation to higher dimensional operators in the nonminimal couplings and in the potential, both in the metric and Palatini formalisms. We find that, while inflationary predictions are relatively stable against the higher dimensional operators around the attractor point in the metric formalism, they are extremely sensitive in the Palatini one: for the latter, inflationary predictions are spoiled by |ξ4| ≳ 10−6 in the nonminimal couplings (ξ2 ϕ2 + ξ4 ϕ4 + ⋯)R, or by |λ6| ≳ 10−16 in the Jordan-frame potential λ4 ϕ4 + λ6 ϕ6 + ⋯ (both in Planck units). This extreme sensitivity results from the absence of attractor in the Palatini formalism. Our study underscores the challenge of realizing inflationary models with the nonminimal coupling in the Palatini formalism.
Highlights
The inflationary paradigm [1,2,3] is one of the fundamental elements of modern cosmology, providing an elegant solution to the horizon and flatness problems [3] and the dilution of possible unwanted relics [2]
The possibility of induced gravity has been mainly pursued where the Einstein-Hilbert action SEH is absent, and the nonminimal coupling ξ2 between the Higgs field and the Ricci scalar is required to be of order ξ2 ∼ 1034.♦2 The modern version of the Higgs inflation [21] allows SEH, which is not prohibited by any symmetry, and the nonminimal coupling becomes of order ξ2 ∼ 105–6.♦3 This modern version is one of the best fit models of the current observational data [9].♦4 There are variations in addition to this vanilla model: the critical [24, 26,27,28], the hill-climbing [29, 30], and the hill-top
We have investigated the sensitivity of this model to higher dimensional operators in the Weyl rescaling factor (ξ4φ4) or in the potential (λ6φ6) both in the metric and Palatini formalisms
Summary
The inflationary paradigm [1,2,3] is one of the fundamental elements of modern cosmology, providing an elegant solution to the horizon and flatness problems [3] and the dilution of possible unwanted relics [2]. Sharing the virtue of the vanilla model, these variations predict different values of r along with other observables such as dns/d ln k, d2ns/d ln k2 as well as nt, dnt/d ln k, which can possibly be used to distinguish between these models in near-future experiments Such various Higgs inflations have been studied mainly in the so-called metric formalism for past decades. If the inflationary predictions significantly depend on the higher-order terms suppressed by the Planck scale, it means that the model construction is challenging in such setups This is what we find for the Higgs inflation with the Palatini formalism. We summarize two independent formalisms of Higgs-like inflation, namely the metric and Palatini formalisms, and review the standard predictions without higher order corrections for each case
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