Higgs–Palatini inflation and unitarity

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 unitarity violation since the UV cutoff lies parametrically much higher than the Hubble rate so that unknown UV physics does not disrupt the inflationary dynamics. Higgs–Palatini inflation, as we call it, is, therefore, UV-safe, minimal and endowed with predictive power.     

Inflation,LHC and the Higgs boson

After the Higgs boson has been discovered, the Standard Model of particle physics became a confirmed theory, potentially valid up to the Planck scale and allowing one to trace the evolution of the Universe from the inflationary stage till the present days. We discuss the relation between the results from the LHC and the inflationary cosmology. We overview the Higgs inflation, and its relation to the possible metastability of the electroweak vacuum. A short overview of the bounds on the metastability of the electroweak vacuum in the models with inflation not related to the Higgs boson is presented.     

The Standard Model Higgs boson as the inflaton

We argue that the Higgs boson of the Standard Model can lead to inflation and produce cosmological perturbations in accordance with observations. An essential requirement is the non-minimal coupling of the Higgs scalar field to gravity; no new particle besides already present in the electroweak theory is required.     

Holographic bounds and Higgs inflation

In a recently proposed scenario for primordial inflation, where the Standard Model (SM) Higgs boson plays a role of the inflation field, an effective field theory (EFT) approach is the most convenient for working out the consequences of breaking of perturbative unitarity, caused by the strong coupling of the Higgs field to the Ricci scalar. The domain of validity of the EFT approach is given by the ultraviolet (UV) cutoff, which, roughly speaking, should always exceed the Hubble parameter in the course of inflation. On the other hand, applying the trusted principles of quantum gravity to a local EFT demands that it should only be used to describe states in a region larger than their corresponding Schwarschild radius, manifesting thus a sort of UV/IR correspondence. We consider both constraints on EFT, to ascertain which models of the SM Higgs inflation are able to simultaneously comply with them. We also show that if the gravitational coupling evolves with the scale factor, the holographic constraint can be alleviated significantly with minimal set of canonical assumptions, by forcing the said coupling to be asymptotically free.     

A possible interpretation of the Higgs mass by the cosmological attractive relaxion

Recently, a novel idea [1] has been proposed to relax the electroweak hierarchy problem through the cosmological inflation and the axion periotic potential. Here, we further assume that only the attractive inflation is needed to explain the light mass of the Higgs boson, where we do not need a specified periodic potential of the axion field. Attractive inflation during the early universe drives the Higgs boson mass from the large value in the early universe to the small value at present, where the Higgs mass is an evolving parameter of the Universe. Thus, the small Higgs mass can technically originate from the cosmological evolution rather than dynamical symmetry or anthropics. Further, we study the possible collider signals or constraints at a future lepton collier and the possible constraints from the muon anomalous magnetic moment. A concrete attractive relaxion model is also discussed, which is consistent with the data of Planck 2015.     

Non-minimal Coupling of the Higgs Boson to Curvature in an Inflationary Universe

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 potential thereby stabilizing the electroweak vacuum. For specific values of the Higgs field initial condition and of its non-minimal coupling, inflation can drive the Higgs field to the electroweak vacuum quickly during inflation.     

Remarks on Higgs inflation

We discuss models where the Higgs boson of the electroweak standard model plays the role of the inflaton. We focus on the question of the violation of perturbative unitarity due to the coupling of the Higgs boson either to the Ricci scalar or to the Einstein tensor and discuss the background dependence of the unitarity bounds. Our conclusion is that the simplest model which restricts itself to the standard model Higgs boson without introducing further degrees of freedom has a serious problem. However, in the asymptotically safe gravity scenario, the Higgs boson of the standard model could be the inflaton and no physics beyond the standard model is required to explain both inflation and the spontaneous breaking of the electroweak symmetry of the standard model.     

Inflation,large scale structure and particle physics

We review experimental and theoretical developments in inflation and its application to structure formation, including the curvaton idea. We then discuss a particle physics model of supersymmetric hybrid inflation at the intermediate scale in which the Higgs scalar field is responsible for large scale structure, show how such a theory is completely natural in the framework extra dimensions with an intermediate string scale.     

Phase transitions from preheating in gauge theories

We show by studying the Abelian Higgs model with numerical lattice simulations that nonthermal phase transitions arising out of preheating after inflation are possible in gauge-Higgs models under rather general circumstances. This may lead to the formation of gauged topological defects and, if the scale at which inflation ends is low enough, to electroweak baryogenesis after preheating.     

More flipped SU(5)×U(1) baryosynthesis

We supplement a previous discussion of baryosynthesis in flipped SU(5)×U(1) GUTs by including (1) the large incoherent field energy density which is likely SU(5) is broken, and (2) the possibility of additional Higgs triplet fields suggested by four dimensional string model-building. We consider strong (weak) reheating scenarios in which the Universe is (is not) SU(5) symmetric after inflation. We find an adequate baryon asymmetry subsequent to strong reheating, whatever the number of Higgs triplets (although beware of possible difficulties with quasi-stable relic particles), whereas weak reheating requires at least two Higgs triplets.     

Quadratic,Higgs and hilltop potentials in Palatini gravity

In this work, we study the theory of inflation with the non-minimally coupled quadratic, standard model Higgs, and hilltop potentials, through ξφ~2R term in Palatini gravity. We first analyze observational parameters of the Palatini quadratic potential as functions of ξ for the high-N scenario. In addition to this, taking into account that the inflaton field f has a non-zero vacuum expectation value v after inflation, we display observational parameters of well-known symmetry-breaking potentials. The types of potentials considered are the Higgs potential and its generalizations, namely hilltop potentials in the Palatini formalism for the high-N scenario and the low-N scenario. We calculate inflationary parameters for the Palatini Higgs potential as functions of v for different ξ values, where inflaton values are both φv and φv during inflation, as well as calculating observational parameters of the Palatini Higgs potential in the induced gravity limit for high-N scenario. We illustrate differences between the Higgs potential's effect on ξ versus hilltop potentials, which agree with the observations for the inflaton values for φv and ξ, in which v1 for both these high and low N scenarios. For each considered potential, we also display n_s-r values fitted to the current data given by the Keck Array/BICEP2 and Planck collaborations.     

Higgs mass implications on the stability of the electroweak vacuum

We update instability and metastability bounds of the Standard Model electroweak vacuum in view of the recent ATLAS and CMS Higgs results. For a Higgs mass in the range 124–126 GeV, and for the current central values of the top mass and strong coupling constant, the Higgs potential develops an instability around 10¹¹ GeV, with a lifetime much longer than the age of the Universe. However, taking into account theoretical and experimental errors, stability up to the Planck scale cannot be excluded. Stability at finite temperature implies an upper bound on the reheat temperature after inflation, which depends critically on the precise values of the Higgs and top masses. A Higgs mass in the range 124–126 GeV is compatible with very high values of the reheating temperature, without conflict with mechanisms of baryogenesis such as leptogenesis. We derive an upper bound on the mass of heavy right-handed neutrinos by requiring that their Yukawa couplings do not destabilize the Higgs potential.     

Inflation and reheating in the Starobinsky model with conformal HiggsField

This is a talk presented by A.A. Tokareva at Baikal summer school on physics of elementary particles and astrophysics 2012. We studied the reheating after the Starobinsky inflation and have found that the main process is the inflaton decay to SM gauge fields due to the conformal anomaly. The reheating temperature is low leading to the possibility to detect the gravity wave signal from inflation and evaporation of structures formed after inflation in DECIGO and BBO experiments. Also we give predictions for the parameters of scalar perturbation spectrum at the next-to-leading order of slow roll and obtain a bound on the Higgs mass.     

Exploring the hyperchargeless Higgs triplet model up to the Planck scale

We examine an extension of the SM Higgs sector by a Higgs triplet taking into consideration the discovery of a Higgs-like particle at the LHC with mass around 125 GeV. We evaluate the bounds on the scalar potential through the unitarity of the scattering matrix. Considering the cases with and without \(\mathbb {Z}_2\)-symmetry of the extra triplet, we derive constraints on the parameter space. We identify the region of the parameter space that corresponds to the stability and metastability of the electroweak vacuum. We also show that at large field values the scalar potential of this model is suitable to explain inflation.     

Inflation and cosmic strings in models with dynamical symmetry breaking

We derive the effective action for the composite field which in dynamical symmetry breaking plays the role of the Higgs field. We show that this effective action does not give rise to inflation. It is, however, possible to obtain topological defects such as cosmic strings. There will be fermionic zero modes trapped on the strings, and the strings will therefore be superconducting in a generalized sense.     

Baryogenesis,proton decay and fermion masses in supergravity guts

In realistic N = 1 supergravity theories with a gravitino mass of order 1 TeV, the reheat temperature after inflation is bounded to be no greater than 10⁸ GeV. We construct an N = 1 supergravity model with realistic fermion masses and mixings in which D = 5 operators are suppressed by a Peccei-Quinn symmetry. We compute the ensuing proton decay and show that the dominant modes involve strange particles in the final state. Efficient baryogenesis is induced by Higgs decay to massive right-handed neutrinos and we find an upper bound on the proton lifetime if the Higgs are light enough to be reheated.     

Fluctuations in a supersymmetric inflationary universe

It has been demonstrated that fluctuations in the new inflationary universe may be almost scale-invariant, but are unfortunately too large. We show that supersymmetric inflationary models allow the fluctuations to be smaller. In a toy supersymmetric model, the perturbations are O(10⁻⁴) is the Yukawa interactions are O(10⁻⁶μ/m_p) where μ is the magnitude of the Higgs vacuum expectation value driving the inflation. It is therefore easier to have small fluctuations if inflation occurs close to the Planck epoch.     

Unifying darko-lepto-genesis with scalar triplet inflation

We present a scalar triplet extension of the standard model to unify the origin of inflation with neutrino mass, asymmetric dark matter and leptogenesis. In presence of non-minimal couplings to gravity the scalar triplet, mixed with the standard model Higgs, plays the role of inflaton in the early Universe, while its decay to SM Higgs, lepton and dark matter simultaneously generate an asymmetry in the visible and dark matter sectors. On the other hand, in the low energy effective theory the induced vacuum expectation value of the triplet gives sub-eV Majorana masses to active neutrinos. We investigate the model parameter space leading to successful inflation as well as the observed dark matter to baryon abundance. Assuming the standard model like Higgs mass to be at 125–126 GeV, we found that the mass scale of the scalar triplet to be ?O(10⁹) GeV$?O({10}^9)\text{GeV}$ and its trilinear coupling to doublet Higgs is ?0.09 so that it not only evades the possibility of having a metastable vacuum in the standard model, but also lead to a rich phenomenological consequences as stated above. Moreover, we found that the scalar triplet inflation strongly constrains the quartic couplings, while allowing for a wide range of Yukawa couplings which generate the CP asymmetries in the visible and dark matter sectors.     

Metric Expansion from Microscopic Dynamics in an Inhomogeneous Universe

Theories with ingredients like the Higgs mechanism, gravitons, and inflatonfields rejuvenate the idea that relativistic kinematics is dynamicallyemergent. Eternal inflation treats the Hubble constant H as depending onlocation. Microscopic dynamics implies that H is over much smaller lengthsthan pocket universes to be understood as a local space reproduction rate.We illustrate this via discussing that even exponential inflation inTeV-gravity is slow on the relevant time scale. In our on small scalesinhomogeneous cosmos, a reproduction rate H depends on position. We therefore discuss Einstein-Strauss vacuoles and a Lindquist-Wheeler like lattice to connect the local rate properly with the scaling of an expanding cosmos. Consistency allows H to locally depend on Weyl curvature similar to vacuum polarization. We derive a proportionality constant known from Kepler's third law and discuss the implications for the finiteness of the cosmological constant.     

Higgs mass and inflation

We show that the standard-model Higgs boson mass mh is correlated with the spectral index of density perturbation ns in the inflation scenario with the inflaton being identified with the B-L Higgs boson. The Higgs boson mass ranges from mh?120 GeV to 140 GeV for ns?0.95-0.96. In particular, as ns approaches to 0.96, the Higgs mass is predicted to be in the range of 125 GeV to 140 GeV in the case of relatively light gauginos, and 120 GeV to 135 GeV in the case where all SUSY particle masses are of the same order. This will be tested soon by the LHC experiment and the Planck satellite. The relation is due to the PeV-scale supersymmetry required by the inflationary dynamics. We also comment on the cosmological implications of our scenario such as non-thermal leptogenesis and dark matter.