Mikhail Shaposhnikov, Andrey Shkerin, Inar Timiryasov, Sebastian Zell
备注：
26 pages, 8 figures, 1 appendix; v2: updated figures and references, added short comparison with arXiv:2007.12595, minor corrections to formulas in sections 6.2 and 6.3, other small improvements; matches published version (including erratum)
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 study the phenomenology of the Higgs-Dilaton model in the context of Einstein-Cartan gravity, focusing on the separate impact of the Holst and Nieh-Yan terms on the inflationary observables. Using analytical and numerical techniques, we show the predictions of these scenarios to display an attractor-like behaviour intrinsically related to the curvature of the field-space manifold in the metric formulation of the theory. Beyond that, the analysis of the Nieh-Yan case reveals the existence of an additional attractor solution induced by a cubic pole in the inflaton kinetic term that becomes re…
We propose a realization of cosmic inflation with the Higgs field when the Higgs potential has degenerate vacua by employing the recently proposed idea of hillclimbing inflation. The resultant inflationary predictions exhibit a sizable deviation from those of the ordinary Higgs inflation.
We study the cosmological perturbations created during the New Higgs inflationary phase. In the New Higgs Inflation, the Higgs boson is kinetically coupled to the Einstein tensor and only three perturbative degrees of freedom, a scalar and two tensorial (gravitational waves), propagate during Inflation. Scalar perturbations are found to match the latest WMAP-7yrs data within Standard Model Higgs parameters. Primordial gravitational waves also, although propagating with superluminal speed, are consistent with present data. Finally, we estimate the values of the parameter of the New Higgs Inflat…
Higgs G-inflation is a Higgs inflation model with a generalized Galileon term added to the standard model Higgs field, which realizes inflation compatible with observations. Recently, it was claimed that the generalized Galileon term induces instabilities during the oscillation phase, and that the simplest Higgs G-inflation model inevitably suffers from this problem. In this paper, we extend the original Higgs G-inflation Lagrangian to a more general form, namely introducing a higher-order kinetic term and generalizing the form of the Galileon term, so that the Higgs field can oscillate after …
In the absence of new physics around $10^{10}$ GeV, the electroweak vacuum is at best metastable. This represents a major challenge for high scale inflationary models as, during the early rapid expansion of the universe, it seems difficult to understand how the Higgs vacuum would not decay to the true lower vacuum of the theory with catastrophic consequences if inflation took place at a scale above $10^{10}$ GeV. In this paper we show that the non-minimal coupling of the Higgs boson to curvature could solve this problem by generating a direct coupling of the Higgs boson to the inflationary pot…
Stimulated with the recent discovery of B-mode by BICEP2, we discuss the relation between a Higgs inflation and a chaotic inflation with quadratic potential. Starting with a generalized Higgs inflation model, we derive a condition for obtaining the quadratic chaotic inflation. It is shown that the running of the Higgs self-coupling constant in the Jordan frame plays a decisive role when the generalized Higgs inflation model coincides with the Higgs inflation model in a small-field limit.
In this paper we point out that Starobinky inflation could be induced by quantum effects due to a large non-minimal coupling of the Higgs boson to the Ricci scalar. The Higgs Starobinsky mechanism provides a solution to issues attached to large Higgs field values in the early universe which in a metastable universe would not be a viable option. We verify explicitly that these large quantum corrections do not destabilize Starobinsky's potential.
In this paper we show that the Germani-Kehagias model of Higgs inflation (or New Higgs Inflation), where the Higgs boson is kinetically non-minimally coupled to the Einstein tensor is in perfect compatibility with the latest Planck and BICEP2 data. Moreover, we show that the tension between the Planck and BICEP2 data can be relieved within the New Higgs inflation scenario by a negative running of the spectral index. Regarding the unitarity of the model, we argue that it is unitary throughout the evolution of the Universe. Weak couplings in the Higgs-Higgs and Higgs-graviton sectors are provide…
We obtain the bound on the Higgs and top masses to have Higgs inflation (where the Higgs field is non-minimally coupled to gravity) at full next-to-next-to-leading order (NNLO). Comparing the result obtained with the experimental values of the relevant parameters we find some tension, which we quantify. Higgs inflation, however, is not excluded at the moment as the measured values of the Higgs and top masses are close enough to the bound once experimental and theoretical uncertainties are taken into account.
We propose a hybrid type of the conventional Higgs inflation and new Higgs inflation models. We perform a disformal transformation into the Einstein frame and analyze the background dynamics and the cosmological perturbations in the truncated model, in which we ignore the higher-derivative terms of the Higgs field. From the observed power spectrum of the density perturbations, we obtain the constraint on the non-minimal coupling constant $ξ$ and the mass parameter $M$ in the derivative coupling. Although the primordial tilt $n_s$ in the hybrid model barely changes, the tensor-to-scalar ratio $…
We construct a new inflation model in which the standard model Higgs boson couples minimally to gravity and acts as the inflaton. Our construction of Higgs inflation incorporates the standard model with Einstein gravity which exhibits asymptotic safety in the ultraviolet region. The slow roll condition is satisfied at large field value due to the asymptotically safe behavior of Higgs self-coupling at high energies. We find that this minimal construction is highly predictive, and is consistent with both cosmological observations and collider experiments.
We investigate whether Higgs inflation can occur in the Standard Model starting from natural initial conditions or not. The Higgs has a non-minimal coupling to the Ricci scalar. We confine our attention to the regime where quantum Einstein gravity effects are small in order to have results that are independent of the ultraviolet completion of gravity. At the classical level we find no tuning is required to have a successful Higgs inflation, provided the initial homogeneity condition is satisfied. On the other hand, at the quantum level we obtain that the renormalization for large non-minimal c…
Higgs inflation is attractive because it identifies the inflaton with the electroweak Higgs boson. In this work, we construct a new class of supersymmetric Higgs inflationary models in the no-scale supergravity with an SU(5) GUT group. Extending the no-scale Kahler potential and SU(5) GUT superpotential, we derive a generic potential for Higgs inflation that includes the quadratic monomial potential and a Starobinsky-type potential as special limits. This type of models can accommodate a wide range of the tensor-to-scalar ratio $r = O(10^{-3}-10^{-1})$, as well as a scalar spectral index $n_s …
We consider an extension of Higgs inflation in which the Higgs field is coupled to the Gauss-Bonnet term. Working solely in the Jordan frame, we firstly recover the standard predictions of Higgs inflation without a Gauss-Bonnet term. We then calculate the power spectra for scalar and tensor perturbations in the presence of a coupling to a Gauss-Bonnet term. We show that generically the predictions of Higgs inflation are robust and the contributions to the power spectra coming from the Gauss-Bonnet term are negligible. We find, however, that the end of inflation can be strongly modified and tha…
We analyze a two-field inflationary model consisting of the Ricci scalar squared ($R^2$) term and the standard Higgs field non-minimally coupled to gravity in addition to the Einstein $R$ term. Detailed analysis of the power spectrum of this model with mass hierarchy is presented, and we find that one can describe this model as an effective single-field model in the slow-roll regime with a modified sound speed. The scalar spectral index predicted by this model coincides with those given by the $R^2$ inflation and the Higgs inflation implying that there is a close relation between this model an…
We point out that a light scalaron dynamically emerges if scalar fields have a sizable non-minimal coupling to the Ricci scalar as in the Higgs inflation model. We support this claim in two ways. One is based on the renormalization group equation; the non-minimal coupling inevitably induces a Ricci scalar quadratic term due to the renormalization group running. The other is based on scattering amplitudes; a scalar four-point amplitude develops a pole after summing over a certain class of diagrams, which we identify as the scalaron. Our result implies that the Higgs inflation is actually a two-…
We derive one- and two-loop renormalization group equations (RGEs) of Higgs-$R^2$ inflation. This model has a non-minimal coupling between the Higgs and the Ricci scalar and a Ricci scalar squared term on top of the standard model. The RGEs derived in this paper are valid as long as the energy scale of interest (in the Einstein frame) is below the Planck scale. We also discuss implications to the inflationary predictions and the electroweak vacuum metastability.
The abundance of the QCD axion is known to be suppressed if the Hubble parameter during inflation, $H_{\rm inf}$, is lower than the QCD scale, and if the inflation lasts sufficiently long. We show that the tight upper bound on the inflation scale can be significantly relaxed if the eternal old inflation is driven by the standard-model Higgs field trapped in a false vacuum at large field values. Specifically, $H_{\rm inf}$ can be larger than $100\,$GeV if the false vacuum is located above the intermediate scale. We also discuss the slow-roll inflation after the tunneling from the false vacuum t…
We derive lower bounds for the Higgs-curvature coupling from vacuum stability during inflation in three inflationary models: quadratic and quartic chaotic inflation, and Starobinsky-like power-law inflation. In contrast to most previous studies we take the time-dependence of the Hubble rate into account both in the geometry of our past light-cone and in the Higgs effective potential, which is approximated with three-loop renormalisation group improvement supplemented with one-loop curvature corrections. We find that in all three models, the lower bound is $ξ\gtrsim 0.051\ldots 0.066$ depending…
The measured values of the Higgs and top quark masses imply that the Standard Model potential is very likely to be unstable at large Higgs values. This is particularly problematic during inflation, which sources large perturbations of the Higgs. The instability could be cured by a threshold effect induced by a scalar with a large vacuum expectation value and directly connected to the Standard Model through a Higgs portal coupling. However, we find that in a minimal model in which the scalar generates inflation, this mechanism does not stabilize the potential because the mass required for infla…
We investigate the UV-completion of the Higgs inflation in the metric and the Palatini formalisms. It is known that the cutoff scales for the perturbative unitarity of these inflation models become much smaller than the Planck scale to be consistent with observations. Expecting that the low cutoff scale originates in the curvature of a field-space spanned by the Higgs fields, we consider embedding the curved field-space into a higher dimensional flat space and apply this procedure to the metric-Higgs and the Palatini-Higgs scenarios. The new field introduced in this way successfully flattens t…
We propose a new inflation model in which a gauge singlet inflaton turns into the Higgs condensate after inflation. The inflationary path is characterized by a moduli space of supersymmetric vacua spanned by the inflaton and Higgs field. The inflation energy scale is related to the soft supersymmetry breaking, and the Hubble parameter during inflation is smaller than the gravitino mass. The initial condition for the successful inflation is naturally realized by the pre-inflation in which the Higgs plays a role of the waterfall field.
We study Higgs inflation in the context of generalized G-inflation, i.e. the most general single-field inflation model with second-order field equations. The four variants of Higgs inflation proposed so far in the literature can be accommodated at one time in our framework. We also propose yet another class of Higgs inflation, the running Einstein inflation model, that can naturally arise from the generalized G-inflation framework. As a result, five Higgs inflation models in all should be discussed on an equal footing. Concise formulas for primordial fluctuations in these generalized Higgs inf…
It has been argued that the mixed Higgs-$R^2$ model acts as the UV extension of the Higgs inflation, pushing up its cut-off scale in the vacuum close up to the Planck scale. In this letter, we study the inflaton oscillation stage after inflation, focusing on the effective mass of the phase direction of the Higgs field, which can cause a violent preheating process. We find that the "spikes" in the effective mass of the phase direction observed in the Higgs inflation still appear in the mixed Higgs-$R^2$ model. While the spikes appear above the cut-off scale in the Higgs-only case, they appear b…
In the Higgs inflation scenario the Higgs field is strongly coupled to the Ricci scalar in order to drive primordial inflation. However, in its original form in pure metric formulation of gravity, the ultraviolet (UV) cutoff of the Higgs interactions and the Hubble rate are of the same magnitude, and this makes the whole inflationary evolution dependent of the unknown UV completion of the Higgs sector. This problem, the unitarity violation, plagues the Higgs inflation scenario. In this letter we show that, in the Palatini formulation of gravitation, Higgs inflation does not suffer from unitari…
The measurements of the Higgs mass and top Yukawa coupling indicate that we live in a very special Universe, at the edge of the absolute stability of the electroweak vacuum. If fully stable, the Standard Model (SM) can be extended all the way up to the inflationary scale and the Higgs field, non-minimally coupled to gravity with strength $ξ$, can be responsible for inflation. We show that the successful Higgs inflation scenario can also take place if the SM vacuum is not absolutely stable. This conclusion is based on two effects that were overlooked previously. The first one is associated with…
The recently suggested Festina-Lente (FL) bound provides a lower bound on the masses of ${\rm U(1)}$ charged particles in terms of the positive vacuum energy. Since the charged particle masses in the Standard Model (SM) are generated by the Higgs mechanism, the FL bound provides a testbed of consistent Higgs potentials in the current dark energy-dominated universe as well as during inflation. We study the implications of the FL bound on the UV behavior of the Higgs potential for a miniscule vacuum energy, as in the current universe. We also present values of the Hubble parameter and the Higgs …
We examine the class of initial conditions which give rise to inflation. Our analysis is carried out for several popular models including: Higgs inflation, Starobinsky inflation, chaotic inflation, axion monodromy inflation and non-canonical inflation. In each case we determine the set of initial conditions which give rise to sufficient inflation, with at least $60$ e-foldings. A phase-space analysis has been performed for each of these models and the effect of the initial inflationary energy scale on inflation has been studied numerically. This paper discusses two scenarios of Higgs inflation…
The properties of the recently discovered Higgs boson together with the absence of new physics at collider experiments allows us to speculate about consistently extending the Standard Model of particle physics all the way up to the Planck scale. In this context, the Standard Model Higgs non-minimally coupled to gravity could be responsible for the symmetry properties of the Universe at large scales and for the generation of the primordial spectrum of curvature perturbations seeding structure formation. We overview the minimalistic Higgs inflation scenario, its predictions, open issues and exte…
Based on the current experimental data, the Standard Model predicts that the current vacuum state of the Universe is metastable, leading to a non-zero rate of vacuum decay through nucleation of bubbles of true vacuum. Our existence implies that there cannot have been any such bubble nucleation events anywhere in our whole past lightcone. We consider a minimal scenario of the Standard Model together with Starobinsky inflation, using three-loop renormalization group improved Higgs effective potential with one-loop curvature corrections. We show that the survival of the vacuum state through infla…
A non-minimal coupling xi of the Standard Model Higgs field to gravity can give rise to inflation, but large xi is required and thus leads to a violation of perturbative unitarity at Mp/xi, which is well below the inflationary scale Mp/sqrt(xi). We re-examine this claim for a Higgs mass in the range 125-126 GeV for which lambda_eff(mu) runs to very small values near the Planck scale and can significantly reduce the value of xi required for inflation. Using the two-loop renormalization group equations and effective potential for Higgs xi-inflation, we find that familiar inflationary solutions c…
We consider how Higgs Inflation can be observationally distinguished from variants based on gauge singlet scalar extensions of the Standard Model, in particular where the inflaton is a non-minimally coupled gauge singlet scalar (S-inflation). We show that radiative corrections generally cause the spectral index n to decrease relative to the classical value as the Higgs mass is increased if the Higgs boson is the inflaton, whereas n increases with increasing Higgs mass if the inflaton is a gauge singlet scalar. The accuracy to which n can be calculated in these models depends on how precisely t…
The constraint on the mass of Higgs field in the Standard Model at the minimal interaction with the gravity is derived in the form of lower bound $m_H> 150$ GeV by the strict requirement of decoupling the Higgs boson from the inflation of early Universe: the inflation produced by the Higgs scalar could crucially destroy visible properties of large scale structure of Universe, while the large mass makes the Higgs particle not able to produce the inflation and shifts its cosmological role into the region of quantum gravity.
Current measurements of the Higgs boson mass and top Yukawa coupling suggest that the effective Higgs potential develops an instability below the Planck scale. If the energy scale of inflation is as high as the GUT scale, inflationary quantum fluctuations of the Higgs field can easily destabilize the standard electroweak vacuum and produce a lot of AdS domains. This destabilization during inflation can be avoided if a relatively large nonminimal Higgs-gravity or inflaton-Higgs coupling is introduced. Such couplings generate a large effective mass term for the Higgs, which can raise the effecti…
The Standard Model Higgs becomes tachyonic at high energy scales according to current measurements. This unstable regime of the Higgs potential can be realized in the early Universe during high scale inflation, potentially with catastrophic consequences. This letter highlights a crucial inherent feature of such configurations that has so far remained ignored: Higgs particle production out of vacuum induced by the rapidly evolving Higgs field, which gets exponentially enhanced due to the tachyonic instability. Such explosive particle production can rapidly drain energy away from the Higgs field…
Higgs inflation is known to be a minimal extension of the Standard Model allowing for the description of the early Universe inflation. This model is considered as an effective field theory since it has a relatively low cutoff scale, thus requiring further extensions to be a valid description of the reheating phase. We present a novel unified approach to the problem of unitarization and UV completion of the Higgs inflation model without introducing new massive degrees of freedom. This approach is based on an analytic infinite derivative modification of the Higgs field kinetic term. We construct…
We propose a scenario of spontaneous leptogenesis in Higgs inflation with help from two additional operators: the Weinberg operator (Dim 5) and the derivative coupling of the Higgs field and the current of lepton number (Dim 6). The former is responsible for lepton number violation and the latter induces chemical potential for lepton number. The period of rapidly changing Higgs field, naturally realized in Higgs inflation during the reheating, allows large enhancement in the produced asymmetry in lepton number, which is eventually converted into baryon asymmetry of the universe. This scenario …
We study the dynamics of $SU(2)_L$ times $U(1)_Y$ electroweak gauge fields during and after Higgs inflation. In particular, we investigate configurations of the gauge fields during inflation and find the gauge fields remain topologically non-trivial. We also find that the gauge fields grow due to parametric resonances caused by oscillations of a Higgs field after inflation. We show that the Chern-Simons number also grows significantly. Interestingly, the parametric amplification gives rise to sizable magnetic fields after the inflation whose final amplitudes depend on the anisotropy survived d…
Scalar field models of inflation based on a large nonminimal coupling to gravity xi, in particular, Higgs inflation, may violate unitarity at an energy scale ~ M_p / xi << M_p. In this case the model is incomplete at energy scales relevant to inflation. Here we propose a new unitarity-conserving model of Higgs inflation. The completion of the theory is achieved via additional interactions which are proportional to products of the derivatives of the Higgs doublet. The resulting model differs from the original version of Higgs inflation in its prediction for the spectral index, with a classical …
We show that the dynamics of the Higgs field during inflation is not affected by metric fluctuations if the Higgs is an energetically subdominant light spectator. For Standard Model parameters we find that couplings between Higgs and metric fluctuations are suppressed by $\mathcal{O}(10^{-7})$. They are negligible compared to both pure Higgs terms in the effective potential and the unavoidable non-minimal Higgs coupling to background scalar curvature. The question of the electroweak vacuum instability during high energy scale inflation can therefore be studied consistently using the Jordan fra…
We propose a new construction of the supergravity inflation as an UV completion of the Higgs-$R^2$ inflation. In the dual description of $R^2$-supergravity, we show that there appear dual chiral superfields containing the scalaron or sigma field in the Starobinsky inflation, which unitarizes the supersymmetric Higgs inflation with a large non-minimal coupling up to the Planck scale. We find that a successful slow-roll inflation is achievable in the Higgs-sigma field space, but under the condition that higher curvature terms are introduced to cure the tachyonic mass problems for spectator singl…
In this article, we intend to find a specific model which can satisfy the further refining dS swampland conjecture and scalar weak gravity conjecture (SWGC) simultaneously, in particular, Higgs inflation model and its two extensions: Higgs-Dilaton model and Palatini Higgs inflation. We find that although Higgs inflation model and Higgs-Dilaton model could satisfy the further refining dS swampland conjecture, the two models cannot satisfy SWGC and its strong version. While Palatini Higgs inflation could satisfy these conjectures simultaneously. Therefore Palatini Higgs inflation could be a "rea…
We show that introducing $R^2$-term makes the Higgs-inflation and Higgs-dilaton inflation consistent models: the strong coupling energy scales in scalar, gauge and gravity sectors all are lifted up to the Planck scale.
We study gravitational interaction of Higgs boson through the unique dimension-4 operator $ξH^†H R$, with $H$ the Higgs doublet and $R$ the Ricci scalar curvature. We analyze the effect of this dimensionless nonminimal coupling $ξ$ on weak gauge boson scattering in both Jordan and Einstein frames. We explicitly establish the longitudinal-Goldstone boson equivalence theorem with nonzero $ξ$ coupling in both frames, and analyze the unitarity constraints. We study the $ξ$-induced weak boson scattering cross sections at O(1-30)TeV scales, and propose to probe the Higgs-gravity coupling via weak bo…
