On post-inflation validity of perturbation theory in Horndeski scalar-tensor models

Germani, Cristiano; Kudryashova, Nina; Watanabe, Yuki

doi:10.1088/1475-7516/2016/08/015

Cited by 6 publications

(14 citation statements)

References 55 publications

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“…By looking at the Hubble equations (see for example [3]), on an homogeneous and isotropic background one easily find the boundφ 2 < 2 3 M 2 M 2 p . In fact, in average φ2 2 3 M 2 M 2 p [12]. As discussed before, we are interested in the case in which some canonical scalar quanta could spontaneously scatter with up to the background energy.…”

Section: New Higgs Inflationmentioning

confidence: 99%

Beyond dimensional analysis: Higgs and new Higgs inflations do not violate unitarity

Escrivà

Germani

2017

Phys. Rev. D

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Naïve dimensional analysis seems to suggest possible unitarity violations in the framework of the Higgs and new Higgs inflationary scenarios. These violations seem to happen around the value in which the potential energy, per given Higgs boson's vacuum expectation value, crosses the perturbative cut-off scale calculated around the electroweak vacuum. Conversely to these expectations, in this paper we show that, by using an exact analysis of the background dependent cut-off scale, and by including the contribution of the phase-space volume in the perturbative scattering amplitudes of scalars, no violation of (perturbative) unitarity might ever happen during the whole Universe evolution. THE NAÏVE STORYBecause inflation is supposed to generate a homogeneous and isotropic Universe (at the background level), a natural Inflaton candidate is a spin 0 particle. The standard model of particle physics (SM) contains already a scalar field: the Higgs boson. Therefore one may be tempted to consider the very economical scenario in which the Higgs boson is also the inflaton (this is a very old story, see for example [1]). However, as it is well known, the Higgs boson has a too steep potential to generate a successful inflation. Assuming no extra degrees of freedom in Nature, rather than the ones of the standard model of particle physics and gravity, at least up to the inflationary scale, lead to only two possibilities. The first one is that the actual Higgs potential becomes shallower after certain scales (Higgs inflation) [1] (for this scenario with current precision data see [2]), and the other is that the gravitational friction acting on the Higgs boson is stronger than the one already provided by standard General Relativity (GR) (new Higgs inflation) [3]. After this is achieved at tree-level, loops analysis can be done such to consider the contribution of the running coupling constants to inflation (see [2] for Higgs inflation and [4] for new Higgs inflation).However, it has already been criticised the use of these scenario on the base of a putative perturbative unitarity violation (for the latest rebuttal on this see [5]). The story goes along those lines 1 : Although the Higgs inflationary scenarios make only use of the SM degrees of freedom and gravity, they are non-renormalizable effective field theories (EFT). The Higgs boson and/or the graviton are no canonical degrees of freedom in these EFTs. Therefore, in order to figure out the perturbative unitarity violation scale, one has to diagonalise the gravitonHiggs system and then, check the scales (V m ) suppress- ing the non-renormalizable operators constructed with m powers of the diagonalised field fluctuations. This procedure is however background dependent and so the vertices V m . The diagonalization of the Higgs-gravity system does not have an analytical form. For this reason, the usual approach has been to consider the perturbative cut-offs (Λ m ) constructed on the vertices V m , only around the electroweak (φ = v) and large Higgs vacuum expectation values (v...

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Section: New Higgs Inflationmentioning

confidence: 99%

Beyond dimensional analysis: Higgs and new Higgs inflations do not violate unitarity

Escrivà

Germani

2017

Phys. Rev. D

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“…We note that even though the singular behavior atφ = ±φ c disappears at the solution level, one cannot avoid the blow-up of the curvature perturbation ζ k wheṅ φ = 0. This means that ζ is unphysical and thus, one has to reanalyze the perturbation during the reheating by looking for a physical gauge [23]. This is the Newtonian gauge.…”

Section: (418)mentioning

confidence: 99%

“…This is so because the curvature perturbation ζ blows up atφ = 0 on superhorizon scales. We have to re-analyze the perturbations by choosing a different gauge without problems atφ = 0 [23]. To this end, we consider the scalar perturbation around the background (φ = φ(t) + ϕ(t, x)) and the Newtonian gauge [28].…”

Section: Perturbation Analysis In the Newtonian Gaugementioning

confidence: 99%

“…(5.4) could be recast in terms of the Bardeen potential Φ 6) where the constant C depends on the initial conditions ζ c settled during inflation when changing the Newtonian gauge to the comoving gauge. In the CC+NDC model, one has K = V = λφ 4 /4, [23], where they have shown that the curvature perturbations ζ on superhorizon scales are not generally conserved but the the rescaled Mukhanov-Sasaki variable is conserved, implying a constraint equation for the Newtonian potential. This implies that the superhorizon perturbations of Φ and Ψ are fine with the warning that Ψ could become very large.…”

Section: Perturbation Analysis In the Newtonian Gaugementioning

confidence: 99%

“…Recently, it was proposed that the breakdown of the comoving gauge ϕ = 0 atφ = 0 could be resolved by introducing the cd-gauge which eliminates ϕ in the Hamiltonian formalism of the CC model and thus, provides a well-behaved curvature perturbation ζ [22]. However, it turned out that choosing the Newtonian gauge is necessary to study the perturbation during the oscillating period, since the comoving gauge is not suitable for performing the perturbation analysis during the reheating [23].…”

Section: Introductionmentioning

confidence: 99%

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Inflaton decay and reheating in nonminimal derivative coupling

Myung

Moon²

2016

J. Cosmol. Astropart. Phys.

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Abstract. We investigate the inflaton decay and reheating period after the end of inflation in the non-minimal derivative coupling (NDC) model with chaotic potential. In general, this model is known to provide an enhanced slow-roll inflation caused by gravitationally enhanced friction. We find violent oscillations of Hubble parameter which induces oscillations of the sound speed squared, implying the Lagrangian instability of curvature perturbation ζ under the comoving gauge ϕ = 0. Also, it is shown that the curvature perturbation blows up atφ = 0, leading to the breakdown of the comoving gauge atφ = 0. Therefore, we use the Newtonian gauge to perform the perturbation analysis where the Newtonian potential is employed as a physical variable. The curvature perturbation is not considered as a physical variable which describes a relevant perturbation during reheating.

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Reheating predictions in gravity theories with derivative coupling

Dalianis

Koutsoumbas

Ntrekis

et al. 2017

J. Cosmol. Astropart. Phys.

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We investigate the inflationary predictions of a simple Horndeski theory where the inflaton scalar field has a non-minimal derivative coupling (NMDC) to the Einstein tensor. The NMDC is very motivated for the construction of successful models for inflation, nevertheless its inflationary predictions are not observationally distinct. We show that it is possible to probe the effects of the NMDC on the CMB observables by taking into account both the dynamics of the inflationary slow-roll phase and the subsequent reheating. We perform a comparative study between representative inflationary models with canonical fields minimally coupled to gravity and models with NMDC. We find that the inflation models with dominant NMDC generically predict a higher reheating temperature and a different range for the tilt of the scalar perturbation spectrum n s and scalar-to-tensor ratio r, potentially testable by current and future CMB experiments.

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On post-inflation validity of perturbation theory in Horndeski scalar-tensor models

Cited by 6 publications

References 55 publications

Beyond dimensional analysis: Higgs and new Higgs inflations do not violate unitarity

Beyond dimensional analysis: Higgs and new Higgs inflations do not violate unitarity

Inflaton decay and reheating in nonminimal derivative coupling

Reheating predictions in gravity theories with derivative coupling

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