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 a unitary non-local UV completion of the original Higgs inflation model while the inflationary stage is kept stable with respect to quantum corrections.
We reconsider perturbative unitarity violation in the standard model Higgs inflation model. We show that the Cutkosky cutting rule implied by perturbative unitarity is fulfilled at one-loop. This is a strong indication that unitarity is restored order by order in perturbation theory. We then resum certain one-loop diagrams and show that the relevant dressed amplitude fulfills the Cutkosky rule exactly. This is an example of the self-healing mechanism. The original Higgs inflation model is thus consistent and does not require any new physics beyond the standard model at least up to the Planck s…
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.
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.
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 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 work, we study unified picture of inflation and dark matter in the Higgs-Starobinsky (HS) model. As pointed out in the literature, Starobinsky $R^2$ inflation is induced by quantum correction effect from the large Higgs-curvature (graviton) coupling. We start with non-minimal coupling HS action in Jordan frame. We then transform the Jordan frame action into the Einstein one using the conformal transformation. The inflation potential is derived from the gravitational action of non-minimal-Higgs coupling and Starobinsky term in Einstein frame where the $R^2$ term is dominated in the infl…
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 consequences of (beyond) positivity of scattering amplitudes in the effective field theory description of the Higgs-Dilaton inflationary model. By requiring the EFT to be compatible with a unitary, causal, local and Lorentz invariant UV completion, we derive constraints on the Wilson coefficients of the first higher order derivative operators. We show that the values allowed by the constraints are consistent with the phenomenological applications of the Higgs-Dilaton model.
We study preheating following Higgs inflation in the Palatini formulation of gravity. We numerically evolve perturbations of the radial mode of the Higgs field and that of three scalars modeling the gauge bosons. We compare the two non-perturbative mechanisms of growth of excitations -- parametric resonance and tachyonic instability -- and confirm that the latter plays the dominant role. Our results provide further evidence that preheating in Palatini Higgs inflation happens within a single oscillation of the Higgs field about the bottom of its potential, consistent with the approximation of a…
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 investigate an inflationary model involving a gauge singlet scalar and fermionic dark matter. The mixing between the singlet scalar and the Higgs boson provides a portal to dark matter. The inflaton could either be the Higgs boson or the singlet scalar, and slow roll inflation is realized via its non-minimal coupling to gravity. In this setup, the effective scalar potential is stabilized by the mixing between two scalars and coupling with dark matter. We study constraints from collider searches, relic density and direct detection, and find that dark matter mass should be around half the mas…
We develop the formalism for computing gravitational corrections to vacuum decay from de Sitter space as a sub-Planckian perturbative expansion. Non-minimal coupling to gravity can be encoded in an effective potential. The Coleman bounce continuously deforms into the Hawking-Moss bounce, until they coincide for a critical value of the Hubble constant. As an application, we reconsider the decay of the electroweak Higgs vacuum during inflation. Our vacuum decay computation reproduces and improves bounds on the maximal inflationary Hubble scale previously computed through statistical techniques.
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 …
Hybrid Higgs inflation model is a hybrid type of the so-called Higgs inflation model with the conventional non-minimal $ξ$ coupling to a scalar curvature $R$ and new Higgs inflation model with the derivative coupling to the Einstein curvature tensor $G_{μν}$. This model can explain all possible value of the tensor-to-scalar ratio $r$ allowed by the present CMB constraints with an appropriate choice of coupling parameters. However the derivative coupling may causes a gradient instability during oscillation phase after inflation just as in new Higgs inflation model. Analyzing the behaviours of p…
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…
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.
We discuss a simple unitarization of Higgs inflation that is genuinely weakly coupled up to Planckian energies. A large non-minimal coupling between the Higgs and the Ricci curvature is induced dynamically at intermediate energies, as a simple ratio of mass scales. Despite not being dominated by the Higgs field, inflationary dynamics simulates the `Higgs inflation' one would get by blind extrapolation of the low-energy effective Lagrangian, at least qualitatively. Hence, Higgs inflation arises as an approximate `mirage' picture of the true dynamics. We further speculate on the generality of th…
Starobinsky inflation and Higgs inflation in gravity, and their equivalence based on the common inflationary potential are extended to supergravity in the proper framework, where the Starobinsky and Higgs descriptions of inflation arise in two different gauges of the same supergravity model.
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…
We explore two saddle point inflationary scenarios in the context of higher order corrections related to different generalisations of general relativity. Firstly, we deal with Jordan frame Starobinsky potential, for which we identify a portion of a parameter space of inflection point inflation, which can accommodate all the experimental results. Secondly, we analyse Higgs inflation and more specifically the influence of non-renormalisible terms on the standard quartic potential. All results were verified with the PLANCK 2015 data.
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-…
In the conventional metric formulation of gravity, the Higgs Inflation model violates unitarity in the electroweak vacuum in Higgs scattering at the energy scale $Λ\sim M_{Pl}/ξ$, where $ξ\sim 10^4$ is the non-minimal coupling of the Higgs to the Ricci scalar. In the Palatini formulation it is commonly believed that $Λ\sim M_{Pl}/\sqrtξ$, where $ξ\sim 10^{9}$. Here we reconsider unitarity violation in the electroweak vacuum in the Palatini formulation. We argue that there is no unitarity violation in Higgs scattering in the Palatini non-minimally coupled Standard Model in the electroweak vacuu…
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…
We study whether the inflation is realized based on the radion gauge-Higgs potential obtained from the one-loop calculation in the 5-dimensional gravity coupled to a $U(1)$ gauge theory. We show that the gauge-Higgs can give rise to inflation in accord with the astrophysical data and the radion plays a role in fixing the values of physical parameters. We clarify the reason why the radion dominated inflation and the hybrid inflation cannot occur in our framework.
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…
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…
The refined de Sitter derivative conjecture provides constraints to potentials that are low energy effective theories of quantum gravity. It can give direct bounds on inflationary scenarios and determine whether the theory is in the Landscape or the Swampland. We consider the `Higgs inflation' scenario taking the refined de Sitter derivative conjecture into account. Obtaining the critical lines for the potential, we find a conjecture parameter space in which the `Higgs inflation' is to be in the Landscape. Comparing with the model independent observational bounds from recent data we find that …
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 a scalar field with non-minimal kinetic coupling to itself and to the curvature. The slow rolling conditions allowing an inflationary background have been found. The quadratic and Higgs type potentials have been considered, and the corresponding values for the scalar fields at the end of inflation allows to recover the connection with particle physics.
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 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 Ein…
We consider a single scalar field inflation model with Higgs potential and curvature corrections given by non-minimal derivative coupling to gravity and coupling to the Gauss-Bonnet invariant. Exact analytical expressions, within the slow-roll approximation, are obtained for the main physical quantities. These corrections lead to successful inflation driven by the $ϕ^4$-potential with the main inflationary observables in the regions restricted by the latest Planck data. It is shown that these curvature corrections can make the $ϕ^4$ potential not only compatible with the current CMB observatio…
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…
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 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…
The issue of electroweak vacuum stability is studied in presence of a scalar field which participates in modifying the minimal chaotic inflation model. It is shown that the threshold effect on the Higgs quartic coupling originating from the Higgs-inflaton sector interaction can essentially make the electroweak vacuum stable upto the Planck scale. On the other hand we observe that the new physics parameters in this combined framework are enough to provide deviation from the minimal chaotic inflation predictions so as to keep it consistent with recent observation by Planck 2015.
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…
It is of great interest to connect cosmology in the early universe to the Standard Model of particle physics. In this paper, we try to construct a bounce inflation model with the standard model Higgs boson, where the one loop correction is taken into account in the effective potential of Higgs field. In this model, a Galileon term has been introduced to eliminate the ghost mode when bounce happens. Moreover, due to the fact that the Fermion loop correction can make part of the Higgs potential negative, one naturally obtains a large equation of state(EoS) parameter in the contracting phase, whi…
In this letter we study the dynamics of the late Universe when a nonminimally coupled Higgs field is present. In general, the nonminimal coupling leads to a nontrivial mixing between the gravitational degrees of freedom and the Goldstone massless bosons. We know that this is irrelevant during the inflationary phase. In contrast, in the late Universe the nonminimal coupling affects the classical equations of motion, leading to an acceleration of the expansion rate or to a collapse that forms Q-balls.
