Extrapolating the Standard Model Higgs potential at high energies, we study the barrier between the electroweak and Planck scale minima. The barrier arises by taking the central values of the relevant experimental inputs, that is the strong coupling constant and the top quark and Higgs masses. We then extend the Standard Model by including a non-minimal coupling to gravity, and explore the phenomenology of the Higgs inflation model. We point out that even configurations that would be metastable in the Standard Model, become viable for inflation if the non-minimal coupling is large enough to flatten the Higgs potential at field values below the barrier; we find that the required value of the non-minimal coupling is smaller than the one needed for the conventional Higgs inflation scenario (which relies on a stable Standard Model Higgs potential, without any barrier); in addition, values of the top mass which are slightly larger than those required in the conventional scenario are allowed.
We study the stability of the electroweak vacuum in low-scale inflation models whose Hubble parameter is much smaller than the instability scale of the Higgs potential. In general, couplings between the inflaton and Higgs are present, and hence we study effects of these couplings during and after inflation. We derive constraints on the couplings between the inflaton and Higgs by requiring that they do not lead to catastrophic electroweak vacuum decay, in particular, via resonant production of the Higgs particles.
Ferrara University（费拉拉大学）；INFN Sez. Ferrara, Dept. of Physics and Earth Science（意大利国家核物理研究所费拉拉分部，地球科学与物理系）；Institut de Física d’Altes Energies (IFAE)（高能物理研究所）；The Barcelona Institute of Science and Technology (BIST)（巴塞罗那科学技术研究所）
The inert scalar doublet model of dark matter can be valid up to the Planck scale. We briefly review the bounds on the model in such a scenario and identify parameter spaces that lead to absolute stability and metastability of the electroweak vacuum.
We study several aspects of electroweak vacuum metastability when an extra gauge singlet scalar, a viable candidate for a dark matter particle, is added to the standard model of particle physics, which is assumed to be valid up to the Planck scale. Phase diagrams are drawn for different parameter spaces, and based on that, we graphically demonstrate how the confidence level, at which stability of electroweak vacuum is excluded, depends on such new physics parameters.
We consider the possibility that the gauge hierarchy is a byproduct of the metastability of the electroweak vacuum, i.e., that whatever mechanism is responsible for the latter also sets the running Higgs mass to a value smaller than its natural value by many orders of magnitude. This perspective is motivated by the early-time framework for eternal inflation put forth recently, which favors vacua that are relatively short-lived, but applies more generally to any theoretical approach predicting that our vacuum should be metastable. We find that the metastability of the electroweak vacuum, togeth…
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…
We analyse effective potential around the electroweak (EW) scale in the Standard Model extended with a heavy scalar doublet. We show that the additional scalars can have a strong impact on vacuum stability. Although the additional heavy scalars may improve the behaviour of running Higgs self-coupling at large field values, we prove that they can destabilise the vacuum due to EW-scale effects. A new EW symmetry conserving minimum of the effective potential can appear rendering the electroweak symmetry breaking minimum meta- or unstable. However, for the case of the inert doublet model (IDM) wit…
The current central experimental values of the parameters of the Standard Model give rise to a striking conclusion: metastability of the electroweak vacuum is favoured over absolute stability. A metastable vacuum for the Higgs boson implies that it is possible, and in fact inevitable, that a vacuum decay takes place with catastrophic consequences for the Universe. The metastability of the Higgs vacuum is especially significant for cosmology, because there are many mechanisms that could have triggered the decay of the electroweak vacuum in the early Universe. We present a comprehensive review o…
Current measurements of Standard Model parameters suggest that the electroweak vacuum is metastable. This metastability has important cosmological implications, because large fluctuations in the Higgs field could trigger vacuum decay in the early universe. For the false vacuum to survive, interactions which stabilize the Higgs during inflation -- e.g., inflaton-Higgs interactions or non-minimal couplings to gravity -- are typically necessary. However, the post-inflationary preheating dynamics of these same interactions could also trigger vacuum decay, thereby recreating the problem we sought t…
We make an attempt to identify regions in a Type II Two-Higgs Doublet Model, which correspond to a metastable electroweak vacuum with lifetime larger than the age of the universe. We analyse scenarios which retain perturbative unitarity up to Grand unification and Planck scales. Each point in the parameter space is restricted using Data from the Large Hadron Collider (LHC) as well as flavor and precision electroweak constraints. We find that substantial regions of the parameter space are thus identified as corresponding to metastability, which compliment the allowed regions for absolute stabil…
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…
It is known that the present electroweak vacuum is likely to be metastable and it may lead to a serious instability during/after inflation. We propose a simple solution to the problem of vacuum instability during/after inflation. If there is a moduli field which has Planck-suppressed interactions with the standard model fields, the Higgs quartic coupling in the early universe naturally takes a different value from the present one. A slight change of the quartic coupling in the early universe makes the Higgs potential absolutely stable and hence we are free from the vacuum instability during/af…
Five fundamental problems - neutrino oscillations, baryogenesis, dark matter, inflation, strong CP problem - are solved at one stroke in "SM-A-S-H" (Standard Model-Axion-Seesaw-Higgs portal inflation) model by Andreas Ringwald et. al. The Standard Model (SM) particle content was extended by three right-handed SM-singlet neutrinos $N_i$, a vector-like color triplet quark $Q$, a complex SM-singlet scalar field $σ$ that stabilises the Higgs potential, all of them being charged under a global lepton number (hyper-charge) and Peccei-Quinn (PQ) $U(1)$ symmetry. We found numerically that SMASH model …
If the Higgs mass m_H is as low as suggested by present experimental information, the Standard Model ground state might not be absolutely stable. We present a detailed analysis of the lower bounds on m_H imposed by the requirement that the electroweak vacuum be sufficiently long-lived. We perform a complete one-loop calculation of the tunnelling probability at zero temperature, and we improve it by means of two-loop renormalization-group equations. We find that, for m_H=115 GeV, the Higgs potential develops an instability below the Planck scale for m_t>(166\pm 2) GeV, but the electroweak vacuu…
We study the stability of the electroweak vacuum during and after the Starobinsky inflation, assuming the existence of the non-minimal Higgs coupling to the Ricci scalar. In the Starobinsky inflation, there exists $R^2$ term (with $R$ being the Ricci scalar), which modifies the evolution equation of the Higgs field. We consider the case that the non-minimal coupling is sizable so that the quantum fluctuation of the Higgs field is suppressed and that the Higgs amplitude is settled near the origin during the inflation. In such a case, the Higgs amplitude may be amplified in the preheating epoch …
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…
In this work, we investigate the possibility to realize inflation and strong first order electroweak phase transitions(SFOEWPT) together with the relic density explanation. We studied the usual Higgs-portal real singlet dark matter model and the global U(1) breaking complex singlet model with the pseudoscalar being dark matter candidate. We focus on higher dark matter parameter regions due to the lower dark matter masses region are almost excluded by the current direct detection experiments except that of the so-called ${\it Higgs~ funnel ~regime}$ with $m_{DM}\sim m_h/2$. In both models, the …
Particle phase transitions in the early universe including electroweak and grand unification ones are well-studied subjects. We point out that there are new possible particle phase transitions around inflation. Those new inflationary particle phase transitions, if of the first order, may yield low-frequency gravitational waves (GWs) due to bubble dynamics, leaving imprints on the cosmic microwave background (CMB). In contrast to the nearly scale-invariant primordial GWs caused by vacuum fluctuation, these bubble-generated GWs are classical and have scale dependent B-mode spectra. If decoupled …
In this work, we revisit the non-minimally coupled Higgs Inflation scenario and investigate its observational viability in light of the current Cosmic Microwave Background, Baryon Acoustic Oscillation and type Ia Supernovae data. We explore the effects of the Coleman-Weinberg approximation to the Higgs potential in the primordial universe, connecting the predictions for the Lagrangian parameters at inflationary scales to the electroweak observables through Renormalization Group methods at two-loop order. As the main result, we find that observations on the electroweak scale are in disagreement…
It is shown that dark energy can be obtained from the interplay of the Higgs boson and the inflaton. A key element is the realization that electroweak symmetry breaking can trigger a second phase of rolling of the inflaton, which, when provided with the appropriate couplings between the fields, can be sufficiently slow to source accelerated expansion in the late time Universe. The observed dark energy density is obtained without fine-tuning of parameters or initial conditions due to an intricate conspiracy of numbers related to inflation, gravity and electroweak physics.
Recent analysis shows that if the 125-126 GeV LHC resonance turns out to be the Standard Model Higgs boson, the electroweak vacuum would be a metastable state at 98% C.L. In this paper we argue that, during inflation, the electroweak vacuum can actually be very short-lived, contrary to the conclusion that follows from the flat spacetime analysis. Namely, in the case of a pure Higgs potential the electroweak vacuum decays via the Hawking-Moss transition, which has no flat spacetime analogue. As a result, the Higgs vacuum is unstable, unless the rate of inflation is low enough: $H_{\rm inf}\less…
Our electroweak vacuum may be metastable in light of the current experimental data of the Higgs/top quark mass. If this is really the case, high-scale inflation models require a stabilization mechanism of our vacuum during inflation. A possible candidate is the Higgs-inflaton/-curvature coupling because it induces an additional mass term to the Higgs during the slow roll regime. However, after the inflation, the additional mass term oscillates, and it can potentially destabilize our electroweak vacuum via production of large Higgs fluctuations during the inflaton oscillation era. In this paper…
We investigate a scale-invariant $B-L$ scenario where the Standard Model (SM) is supplemented with a dark scalar $ϕ$ which has gauge \& Yukawa interactions, with the couplings $g_{BL}$ and $y$, respectively, leading to radiative plateau inflation at scale $ϕ=M$ in the ultraviolet (UV), while dynamically generating the Electroweak and Seesaw scales \textit{á lá} Coleman-Weinberg in the infrared (IR). This is particularly achieved by implementing threshold corrections at an energy scale $μ_T$ arising due to the presence of vector-like fermions. We show that implementing the inflationary observab…
We study Coleman-De Luccia tunneling of the Standard Model Higgs field during inflation in the case when the electroweak vacuum is metastable. We verify that the tunneling rate is exponentially suppressed. The main contribution to the suppression is the same as in flat space-time. We analytically estimate the corrections due to the expansion of the universe and an effective mass term in the Higgs potential that can be present at inflation.
Measurements of the Higgs boson and top quark masses indicate that the Standard Model Higgs potential becomes unstable around $Λ_I \sim 10^{11}$ GeV. This instability is cosmologically relevant since quantum fluctuations during inflation can easily destabilize the electroweak vacuum if the Hubble parameter during inflation is larger than $Λ_I$ (as preferred by the recent BICEP2 measurement). We perform a careful study of the evolution of the Higgs field during inflation, obtaining different results from those currently in the literature. We consider both tunneling via a Coleman-de Luccia or Ha…
We consider the most minimal scale invariant extension of the standard model that allows for successful radiative electroweak symmetry breaking and inflation. The framework involves an extra scalar singlet, that plays the rôle of the inflaton, and is compatibile with current experimental bounds owing to the non-minimal coupling of the latter to gravity. This inflationary scenario predicts a very low tensor-to-scalar ratio $r \approx 10^{-3}$, typical of Higgs-inflation models, but in contrast yields a scalar spectral index $n_s \simeq 0.97$ which departs from the Starobinsky limit. We briefly …
We consider the effect of a period of inflation with a high energy density upon the stability of the Higgs potential in the early universe. The recent measurement of a large tensor-to-scalar ratio, $r_T \sim 0.16$, by the BICEP-2 experiment possibly implies that the energy density during inflation was very high, comparable with the GUT scale. Given that the standard model Higgs potential is known to develop an instability at $Λ\sim 10^{10}$ GeV this means that the resulting large quantum fluctuations of the Higgs field could destabilize the vacuum during inflation, even if the Higgs field star…
We propose a modification to the standard hybrid inflation model \cite{Linde:1993cn}, that connects a successful hybrid inflation scenario to the standard model Higgs sector, via the electroweak vacuum stability. The proposed model results in an effective inflation potential of a hilltop-type, with both the trans-Planckian and sub-Planckian inflation regimes consistent with the recent Planck/BICEP combined results. Reheating via the inflation sector decays to right-handed neutrinos is considered. An upper bound on the reheating temperature $T_{\rm R} \lsim 2\times 10^{11}~(1\times 10^{13})$ Ge…
We analyze the stability of the electroweak vacuum in neutrino mass models containing right handed neutrinos or fermionic isotriplets. In addition to considering absolute stability, we place limits on the Yukawa couplings of new fermions based on metastability and thermal stability in the early Universe. Our results reveal that the upper limits on the neutrino Yukawa couplings can change significantly when the top quark mass is allowed to vary within the experimental range of uncertainty in its determination.
We present a simple model for slow-rollover inflation where the vacuum energy that drives inflation is of the order of $G_F^{-2}$; unlike most models, the conversion of vacuum energy to radiation (``reheating'') is moderately efficient. The scalar field responsible for inflation is a standard-model singlet, develops a vacuum expectation value of the order of $4\times 10^6\GeV$, has a mass of order $1\GeV$, and can play a role in electroweak phenomena.
We study inflation and cosmological electroweak phase transitions utilizing the Standard model augmented by $N$ scalars respecting a global $O(N)$ symmetry. We observe that the representation of the global symmetry is restricted by the inflationary observables and the condition of a strongly first order electroweak phase transition. Theoretical constraints including the stability, perturbativity and unitarity are used to bound the model parameter space. The Electroweak precision observables and Higgs precisions limit the representation of the symmetry. We evaluate the possibility to simultaneo…
We consider inflation within a model framework where the Higgs boson arises as a pseudo-Goldstone boson associated with the breaking of a global symmetry at a scale significantly larger than the electroweak one. We show that in such a model the scalar self-couplings can be parametrically suppressed and, consequently, the non-minimal couplings to gravity can be of order one or less, while the inflationary predictions of the model remain compatible with the precision cosmological observations. Furthermore, in the model we study, the existence of the electroweak scale is entirely due to the infla…
The constraints imposed by the requirement that the scalar potential of supersymmetric theories does not have unbounded directions and charge or color breaking minima deeper than the usual electroweak breaking minimum (EWM) are significantly relaxed if one just allows for a metastable EWM but with a sufficiently long lifetime. For this to be acceptable one needs however to explain how the vacuum state reaches this metastable configuration in the first place. We discuss the implications for this issue of the inflaton induced scalar masses, of the supersymmetry breaking effects generated during …
Within the Standard Model, the current Higgs and top quark data favor metastability of the electroweak vacuum, although the uncertainties are still significant. The true vacuum is many orders of magnitude deeper than ours and the barrier separating the two is tiny compared to the depth of the well. This raises a cosmological question: how did the Higgs field get trapped in the shallow minimum and why did it stay there during inflation? The Higgs initial conditions before inflation must be fine--tuned to about one part in 10^8 in order for the Higgs field to end up in the right vacuum. In this …
The Next-to-Minimal Supersymmetric Standard Model (NMSSM) can incorporate inflation, where a combination of the Higgs-doublet fields plays the role of the inflaton. At the high scale, the Higgs doublets are non-minimally coupled to supergravity; this coupling appears as an additional contribution to the $μ$ term in the low-energy effective superpotential and potentially changes physics at the electroweak scale. In a recent publication, we investigate the extended parameter space of this model with respect to collider phenomenology at the electroweak scale, and discuss scenarios which are poten…
We construct a phenomenological model of electroweak-scale inflation that is in accordance with recent cosmic microwave background observations by WMAP, while setting the stage for a zero-temperature electroweak transition as assumed in recent models of baryogenesis. We find that the scalar spectral index especially poses tight constraints for low-scale inflation models. The inflaton-Higgs coupling leads to substantial mixing of the scalar degrees of freedom. Two types of scalar particles emerge with decay widths similar to that of the Standard Model Higgs particle.
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.
We study a singlet scalar extension of the Standard Model. The singlet scalar is coupled non-minimally to gravity and assumed to drive inflation, and also couple sufficiently strongly with the SM Higgs field in order to provide for a strong first order electroweak phase transition. Requiring the model to describe inflation successfully, be compatible with the LHC data, and yield a strong first order electroweak phase transition, we identify the regions of the parameter space where the model is viable. We also include a singlet fermion with scalar coupling to the singlet scalar to probe the sen…
We propose a model for combining the Standard Model (SM) with gravity. It relies on a non-minimal coupling of the Higgs field to the Ricci scalar and on the Palatini formulation of gravity. Without introducing any new degrees of freedom in addition to those of the SM and the graviton, this scenario achieves two goals. First, it generates the electroweak symmetry breaking by a non-perturbative gravitational effect. In this way, it does not only address the hierarchy problem but opens up the possibility to calculate the Higgs mass. Second, the model incorporates inflation at energies below the o…
We revisit the compatibility between the chaotic inflation, which provides a natural solution to the initial condition problem, and the metastable electroweak vacuum, which is suggested by the results of LHC and the current mass measurements of top quark and Higgs boson. It is known that the chaotic inflation poses a threat to the stability of the electroweak vacuum because it easily generates large Higgs fluctuations during inflation or preheating and triggers the catastrophic vacuum decay. In this paper, we propose a simple cosmological solution in which the vacuum is stabilized during chaot…
We show that the Standard Model vacuum can be stabilized if all particle propagators are non-minimally coupled to gravity. This is due to a Higgs-background dependent redefinition of the Standard Model fields: in terms of canonical variables and in the large Higgs field limit, the quantum fluctuations of the redefined fields are suppressed by the Higgs background. Thus, in this regime, quantum corrections to the tree-level electroweak potential are negligible. Finally, we show that in this framework the Higgs boson can be responsible for inflation. Due to a numerical coincidence that originate…
Our current measurements of the Standard Model parameters imply that the Higgs field resides in a metastable electroweak vacuum, where the vacuum can decay to a lower ground state, with cataclysmic repercussions for our Universe. According to our observations, no such event has happened in the observable universe, in spite of the various energetic processes that could have triggered it. This work serves as an overview of a method that uses the metastability of the false vacuum during cosmological inflation to provide constraints on the Higgs curvature coupling $ξ$. Considering also the effects…
Current Higgs boson and top quark data favor metastability of our vacuum which raises questions as to why the Universe has chosen an energetically disfavored state and remained there during inflation. In this Letter, we point out that these problems can be solved by a Higgs-inflaton coupling which appears in realistic models of inflation. Since an inflaton must couple to the Standard Model particles either directly or indirectly, such a coupling is generated radiatively, even if absent at tree level. As a result, the dynamics of the Higgs field can change dramatically.
In a previous paper, the standard model was generalized to include an electroweak axion which carries baryon plus lepton number, $B+L$. It was shown that such a model naturally gives the observed value of the dark energy, if the scale of explicit baryon number violation was chosen to be of the order of the Planck mass. In this paper, we consider the effect of the modulus of the axion field. Such a field must condense in order to generate the standard Goldstone boson associated with the phase of the axion field. This condensation breaks baryon number. We argue that this modulus might be associa…
We point out that the successful generation of the electroweak scale via gravitational instanton configurations in certain scalar-tensor theories can be viewed as the aftermath of a simple requirement: the existence of a quadratic pole with a sufficiently small residue in the Einstein-frame kinetic term for the Higgs field. In some cases, the inflationary dynamics may also be controlled by this residue and therefore related to the Fermi-to-Planck mass ratio, up to possible uncertainties associated with the instanton regularization. We present here a unified framework for this hierarchy generat…
In this work, we investigated the electroweak vacuum instability during or after inflation. In the inflationary Universe, i.e., de Sitter space, the vacuum field fluctuations $\left< {δϕ}^{ 2 } \right>$ enlarge in proportion to the Hubble scale $H^{2}$. Therefore, the large inflationary vacuum fluctuations of the Higgs field $\left< {δϕ}^{ 2 } \right>$ are potentially catastrophic to trigger the vacuum transition to the negative-energy Planck-scale vacuum state and cause an immediate collapse of the Universe. However, the vacuum field fluctuations $\left< {δϕ}^{ 2 } \right>$, i.e., the vacuum …
We study whether the hinted 750 GeV resonance at the LHC can be a Coleman-Weinberg inflaton which is non-minimally coupled to gravity. Since the inflaton must couple to new charged and coloured states to reproduce the LHC diphoton signature, the same interaction can generate its effective potential and trigger the electroweak symmetry breaking via the portal coupling to the Higgs boson. This inflationary scenario predicts a lower bound on the tensor-to-scalar ratio of $r\gtrsim 0.006$, where the minimal value corresponds to the measured spectral index $n_s\simeq0.97$. However, we find that the…
The concept of Higgs inflation can be elegantly incorporated in the Next-to-Minimal Supersymmetric Standard Model (NMSSM). A linear combination of the two Higgs-doublet fields plays the role of the inflaton which is non-minimally coupled to gravity. This non-minimal coupling appears in the low-energy effective superpotential and changes the phenomenology at the electroweak scale. While the field content of the inflation-inspired model is the same as in the NMSSM, there is another contribution to the $μ$ term in addition to the vacuum expectation value of the singlet. We explore this extended 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…
Current cosmological data favour inflationary models non-minimally coupled to gravity. In this work we study the implications of the metastability of the electroweak vacuum in this framework. We consider an inflaton field with a non-minimal coupling to Ricci curvature and a portal coupling between the Higgs field and the inflaton and find that the ratio of the two couplings is severely constrained from stability during inflation and reheating dynamics, with constraints becoming more severe for weaker non-minimal coupling as during inflation Higgs fluctuations are amplified by inflationary expa…
We study F-term hybrid inflation in a novel supersymmetric extension of the SM with a subdominant Fayet-Iliopoulos D-term. We call this particular form of inflation, in short, F_D-term hybrid inflation. The proposed model ties the mu-parameter of the MSSM to an SO(3)-symmetric Majorana mass m_N, through the vacuum expectation value of the inflaton field. The late decays of the ultraheavy particles associated with the extra U(1) gauge group, which are abundantly produced during the preheating epoch, could lower the reheat temperature even up to 1 TeV, thereby avoiding the gravitino overproducti…
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…
