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.     

Cosmic strings in a space–time with positive cosmological constant

We study Abelian strings in a fixed de Sitter background. We find that the gauge and Higgs fields extend smoothly across the cosmological horizon and that the string solutions have oscillating scalar fields outside the cosmological horizon for all currently accepted values of the cosmological constant. If the gauge to Higgs boson mass ratio is small enough, the gauge field function has a power-like behaviour, while it is oscillating outside the cosmological horizon if Higgs and gauge boson mass are comparable. Moreover, we observe that Abelian strings exist only up to a maximal value of the cosmological constant and that two branches of solutions exist that meet at this maximal value. We also construct radially excited solutions that only exist for non-vanishing values of the cosmological constant and are thus a novel feature as compared to flat space–time. Considering the effect of the de Sitter string on the space–time, we observe that the deficit angle increases with increasing cosmological constant. Lensed objects would thus be separated by a larger angle as compared to asymptotically flat space–time.     

Higgs boson cosmology

The discovery of the Standard Model Higgs boson opens up a range of speculative cosmological scenarios, from the formation of structure in the early universe immediately after the big bang, to relics from the electroweak phase transition one nanosecond after the big bang, on to the end of the present-day universe through vacuum decay. Higgs physics is wide ranging, and gives an impetus to go beyond the Standard Models of particle physics and cosmology to explore the physics of ultra-high energies and quantum gravity.     

Radiatively generated maximal mixing scenario for the Higgs boson mass and the least fine-tuned minimal supersymmetric standard model

We argue that given the experimental constraints on the Higgs boson mass the least fine-tuned parameter space of the minimal supersymmetric standard model is with negative top-squark masses squared at the grand unification scale. While the top-squark mass squared is typically driven to positive values at the weak scale, the contribution to the Higgs boson mass squared parameter from the running can be arbitrarily small, which reduces the fine-tuning of electroweak symmetry breaking. At the same time the top-squark mixing is necessarily enhanced and the maximal mixing scenario for the Higgs boson mass can be generated radiatively even when starting with negligible mixing at the unification scale. This highly alleviates constraints on possible models for supersymmetry breaking in which fine-tuning is absent.     

Renormalization-group analysis of the cosmological constraint on the Higgs scalar mass

The standard Model Higgs scalar boson minimally coupled to gravity does not take part in the inflation of the early universe if its mass exceeds a threshold value, which is m _H ^min = 142 GeV in the tree approximation for the potential of the scalar. Two-loop corrections modify this estimate, which becomes m _H ^min = 150 ± 3 GeV. Therefore, higher order corrections of perturbation theory have quite a controllable moderate character, but they are numerically important for experiments.     

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.     

On the Higgs mass generation mechanism in the Standard Model

The mass-generation mechanism is the most urgent problem of modern particle physics. The discovery and study of the Higgs boson with the Large Hadron Collider at CERN are the highest priority steps to solve the problem. In this paper, the Standard Model Higgs mechanism of elementary particle mass generation is reviewed with pedagogical details. The discussion of the Higgs quadric self-coupling λ parameter and the bounds to the Higgs boson mass are presented. In particular, the unitarity, triviality, and stability constraints on the Higgs boson mass are discussed. The generation of a finite value for the λ parameter due to quantum corrections via effective potential is illustrated. Some simple predictions for the top quark and the Higgs boson masses are given when both the top Yukawa coupling and the Higgs self-coupling λ are equal to 1. The text was submitted by the authors in English.     

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.     

Inflation at the TeV scale with a PNGB curvaton

We investigate a particular type of curvaton mechanism, under which inflation can occur at Hubble scale of order 1 TeV. The curvaton is a pseudo Nambu–Goldstone boson, whose order parameter increases after a phase transition during inflation, triggered by the gradual decrease of the Hubble scale. The mechanism is studied in the context of modular inflation, where the inflaton is a string axion. We show that the mechanism is successful for natural values of the model parameters, provided the phase transition occurs much earlier than the time when the cosmological scales exit the horizon. Also, it turns our that the radial mode for our curvaton must be a flaton field.     

The Common Origin of the Cosmological Constant and the Higgs Mechanism

The author’s 1997 cosmological model predicted a Dark Energy driven accelerating universe with a small cosmological constant. This was observed the very next year in a study of Type Ia supernovae. Following this work, we now deduce a value of the cosmological constant consistent with observation, and indeed the earlier work. We also argue that these considerations are also at the root of the Higgs Mechanism.     

Studying invisible axion models at high temperature

During the thermal evolution of the universe, symmetry of the vacuum state in the presence of quantum fields should have changed at various stages. A possible indication of this effect on the DFSZ invisible axion model of the Peccei-Quinn CP conserving mechanism is presented here. To start with, the background theory of this mechanism in the cosmic evolution has been fully reviewed, as well as the leading cosmological arguments setting limits on the mass and coupling of such a particle. The CP conserving lagrangian of the invisible axion model also includes instanton gauge field configurations. In our opinion, these configurations could behave non trivially while decreasing the temperature as a consequence of the vacuum symmetry modifications. The interplay between symmetry modifications and cosmic evolution may thus lead to yet unclear effects. In fact, the model considered here is really quite a baby version of the real world, so that only preliminary indications and bare consistency arguments have been done from it. Nevertheless, the underlying idea, a possible neutral Higgs fields approximate resonance condition, seems to survive even in more sophisticated models.     

Search for a lighter Higgs boson in the Next-to-Minimal Supersymmetric Standard Model

Following the discovery of the Higgs boson with a mass of approximately 125 Ge V at the LHC, many studies have been performed from both the theoretical and experimental viewpoints to search for a new Higgs Boson that is lighter than 125 Ge V. We explore the possibility of constraining a lighter neutral scalar Higgs boson h_1 and a lighter pseudo-scalar Higgs boson a_1 in the Next-to-Minimal Supersymmetric Standard Model by restricting the next-to-lightest scalar Higgs boson h_2 to be the one observed at the LHC after applying the phenomenological constraints and those from experimental measurements. Such lighter particles are not yet completely excluded by the latest results of the search for a lighter Higgs boson in the diphoton decay channel from LHC data. Our results show that some new constraints on the Next-to-Minimal Supersymmetric Standard Model could be obtained for a lighter scalar Higgs boson at the LHC if such a search is performed by experimental collaborations and more data. The potentials of discovery for other interesting decay channels of such a lighter neutral scalar or pseudo-scalar particle are also discussed.     

Implication on Two Higgs Doublet Models from the Latest b→sγ Measurement and Top Discovery

With the fresh experimental bounds of b→sγ issued by CLEO and the value of the topquark mass by CDF and DO, the constraints on the two Higgs doublet models (2HDM) are re-examined. In the examination an effective Lagrangian is used, which contains all of the energy scale evolution not only from the W boson mass to the bottom-quark mass but also from the top-quark mass to W boson mass for the QCD corrections. As a result, it is implied that the constraint on the mass of the charged Higgs boson emerging in the concerned models turns to be more stringent than that achieved by the earlier analyses.     

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 inflaton as dark matter

Within the framework of an explicit dynamical model, in which we calculate the radiatively-corrected, tree-level potential that sets up inflation, we show that the inflaton can be a significant part of dark matter today. We exhibit potentials with both a maximum and a minimum. Using the calculated position of the potential minimum, and an estimate for fluctuations of the inflaton field in the early universe, we calculate a contribution to the matter energy density of in the present universe, from cold inflatons with mass of about . We show that the inflaton might decay in a specific way, and we calculate a possible lifetime that is several orders of magnitude greater than the present age of the universe. Inflaton decay is related to an interaction which, together with a spontaneous breakdown of CP invariance at a cosmological energy scale, can give rise to a neutrino-antineutrino asymmetry just prior to the time of electroweak symmetry breaking. Received: 26 November 1997 / Revised version: 8 December 1997 / Published online: 24 March 1998     

The probable fate of the Standard Model

Extrapolating the Standard Model to high scales using the renormalisation group, three possibilities arise, depending on the mass of the Higgs boson: if the Higgs mass is large enough the Higgs self-coupling may blow up, entailing some new non-perturbative dynamics; if the Higgs mass is small the effective potential of the Standard Model may reveal an instability; or the Standard Model may survive all the way to the Planck scale for an intermediate range of Higgs masses. This latter case does not necessarily require stability at all times, but includes the possibility of a metastable vacuum which has not yet decayed. We evaluate the relative likelihoods of these possibilities, on the basis of a global fit to the Standard Model made using the Gfitter package. This uses the information about the Higgs mass available directly from Higgs searches at LEP and now the Tevatron, and indirectly from precision electroweak data. We find that the ‘blow-up’ scenario is disfavoured at the 99% confidence level (96% without the Tevatron exclusion), whereas the ‘survival’ and possible ‘metastable’ scenarios remain plausible. A future measurement of the mass of the Higgs boson could reveal the fate of the Standard Model.     

Precision Higgs physics at the CEPC

The discovery of the Higgs boson with its mass around 125 GeV by the ATLAS and CMS Collaborations marked the beginning of a new era in high energy physics.The Higgs boson will be the subject of extensive studies of the ongoing LHC program.At the same time,lepton collider based Higgs factories have been proposed as a possible next step beyond the LHC,with its main goal to precisely measure the properties of the Higgs boson and probe potential new physics associated with the Higgs boson.The Circular Electron Positron Collider(CEPC)is one of such proposed Higgs factories.The CEPC is an e~+e~- circular collider proposed by and to be hosted in China.Located in a tunnel of approximately 100 km in circumference,it will operate at a center-of-mass energy of 240 GeV as the Higgs factory.In this paper,we present the first estimates on the precision of the Higgs boson property measurements achievable at the CEPC and discuss implications of these measurements.     

Higgs boson properties in the Standard Model and its supersymmetric extensions

We review the realization of the Brout–Englert–Higgs mechanism in the electroweak theory and describe the experimental and theoretical constraints on the mass of the single Higgs boson expected in the minimal Standard Model. We also discuss the couplings of this Higgs boson and its possible decay modes as functions of its unknown mass. We then review the structure of the Higgs sector in the minimal supersymmetric extension of the Standard Model (MSSM), noting the importance of loop corrections to the masses of its five physical Higgs bosons. Finally, we discuss some non-minimal models. To cite this article: J. Ellis et al., C. R. Physique 8 (2007).