Higgs-like Potential Research Articles

Gravitating Scalarons with Inverted Higgs Potential

Previously, a class of regular and asymptotically flat gravitating scalar solitons (scalarons) has been constructed in the Einstein–Klein–Gordon (EKG) theory by adopting a phantom field with Higgs-like potential where the kinetic term has the wrong sign and the scalaron possesses the negative Arnowitt–Deser–Misner (ADM) mass as a consequence. In this paper, we demonstrate that the use of the phantom field can be avoided by inverting the Higgs-like potential in the EKG system when the kinetic term has a proper sign, such that the corresponding gravitating scalaron can possess the positive ADM mass. We systematically study the basic properties of the gravitating scalaron, such as the ADM mass, the energy conditions, the geodesics of test particles, etc. Moreover, we find that it can be smoothly connected to the counterpart hairy black hole solutions from our recent work in the small horizon limit.

Entangled states as a probe of early universe history: a Higgs case study

I explore whether distinguishing features of phase transitions and/or the inflationary energy scale can be imprinted on cosmological observables due to entanglement during inflation, given a spectator scalar field with a Higgs-like potential. As a consequence of this analysis, I also present results that illustrate the variety of features a Higgs-like spectator can imprint on the primordial power spectrum due to entanglement, as well as how easy it might be to distinguish such spectra from other similar scalar field results at the level of CMB residuals. I utilize the technical framework for dynamically generated entangled states developed in [1,2] to obtain my results.

Shrouded black holes in Einstein-Gauss-Bonnet gravity

We study black holes in a modified gravity scenario involving a scalar field quadratically coupled to the Gauss-Bonnet invariant. The scalar is assumed to be in a spontaneously broken phase at spatial infinity due to a bare Higgs-like potential. For a proper choice of sign, the non-minimal coupling to gravity leads to symmetry restoration near the black hole horizon, prompting the development of the scalar wall in its vicinity. The wall thickness depends on the bare mass of the scalar and can be much smaller than the Schwarzschild radius. In a weakly coupled regime, the quadratic coupling to the Gauss-Bonnet invariant effectively becomes linear, and no walls are formed. We find approximate analytical solutions for the scalar field in the test field regime, and obtain numerically static black hole solutions within this setup. We discuss cosmological implications of the model and show that it is fully consistent with the existence of an inflationary stage, unlike the spontaneous scalarization scenario assuming the opposite sign of the non-minimal coupling to gravity. Our model predicts the speed of gravitational waves to be extremely close to unity, - in a comfortable agreement with the observation of the GW170817 event and its electromagnetic counterpart.

Particle creation inspired warm inflation according to Planck 2018

In the present work, Chaplygin warm inflationary model is reformulated by assuming the universe as an open thermodynamic system which contains an interacting two component fluid. The scalar field decay and the particle creation due to energy transfer is the key feature of this model providing a baseline for the warm inflationary scenario. In the background of a spatially flat, isotropic and homogeneous universe, we obtain set of equations describing the evolution of dynamical variables by combining the formalism of irreversible thermodynamics and gravitational field equations. Regarding particle creation, the stress–energy tensor is redefined in order to include explicitly creation pressure term. For analyzing the role of inflationary scalar field potential, we take into account a constant potential and a Higgs-like potential. For each potential, the set of dynamical equations is numerically solved and its graphical analysis indicates that particle production gives rise to an accelerated universe during inflationary era, and then expanding universe starts decelerating showing that inflation has a graceful exit. Moreover, we determine the slow-roll and perturbed parameters with the inclusion of Higgs type potential. The graphical behavior of tensor–scalar ratio and scalar spectral is studied, and it is found that the models are in well agreement with Planck 2018 data in weak as well as in strong regimes.

Quantum Higgs inflation

The Higgs field is an attractive candidate for the inflaton because it is an observationally confirmed fundamental scalar field. Importantly, it can be modeled by the most general renormalizable scalar potential. However, if the classical Higgs potential is used in models of inflation, it is ruled out by detailed observations of the cosmic microwave background. Here, a new application of non-adiabatic quantum dynamics to cosmological models is shown to lead to a multi-field Higgs-like potential, consistent with observations of a slightly red-tilted power spectrum and a small tensor-to-scalar ratio, without requiring non-standard ingredients. These methods naturally lead to novel effects in the beginning of inflation, circumventing common fine-tuning issues by an application of uncertainty relations to estimate the initial quantum fluctuations in the early universe. Moreover, inflation ends smoothly as a consequence of the derived multi-field interactions.

Observational constraints on α-attractor inflationary models with a Higgs-like potential

We investigate the observational viability of a class of α-attractors inflationary models in light of the most recent Cosmic Microwave Background (CMB) and Large-Scale Structure (LSS) data. By considering a double-well potential we perform a slow-roll analysis to study the behavior of this class of models, which is a continuous interpolation between the chaotic inflation for large values of α and the universal attractor, i.e., ns=1−2/N and r=α12/N2 for small α, where ns is the scalar spectral index, r is the tensor-to-scalar ratio, and N is the e-fold number. In order to explore the parameter space of the model, we also perform a MCMC analysis and find α=7.56±5.15 (1σ).

Ricci Linear Weyl/Maxwell Mutual Sourcing

We elevate the field theoretical similarities between Maxwell and Weyl vector fields into a full local scale/gauge invariant Weyl/Maxwell mutual sourcing theory. In its preliminary form, and exclusively in four dimensions, the associated Lagrangian is dynamical scalar field free, hosts no fermion matter fields, and Holdom kinetic mixing is switched off. The mutual sourcing term is then necessarily spacetime curvature (not just metric) dependent, and inevitably Ricci linear, suggesting that a non-vanishing spacetime curvature can in principle induce an electromagnetic current. In its mature form, however, the Weyl/Maxwell mutual sourcing idea serendipitously constitutes a novel variant of the gravitational Weyl-Dirac (incorporating Brans-Dicke) theory. Counter intuitively, and again exclusively in four dimensions, the optional quartic scalar potential gets consistently replaced by a Higgs-like potential, such that the co-divergence of the Maxwell vector field resembles a conformal vacuum expectation value.

Composite Nambu–Jona-Lasinio inflation near infrared fixed point of the Hořava-Lifshitz theory

In this work, we first propose a cosmological scenario inherently based on the effective Nambu–Jona-Lasio (NJL) model near the infrared (IR) limit of the Hořava-Lifshitz (HL) theory. Having used the one-loop correction, we employ the NJL framework in the ultraviolet (UV) limit of the HL theory, with critical exponent z=3, to demonstrate in the IR limit that the symmetry of the potential at the critical coupling value is broken at z=1. We also derive the effective Higgs-like potential in the low energy regimes. Here the symmetry of the effective potential will be broken near z=1 at a certain value of the critical coupling. In our scenario, the scalar channel of the NJL model plays the role of a composite inflaton. We find that the Lorentz invariance (LI) appears at the IR regime of the HL theory and employ the standard inflationary (slow-roll) paradigm as a probe of physics at very high energy. We compute inflationary parameters and compare them with recent Planck 2015 data. Interestingly, we discover that the predictions of the model are in perfect agreement with the Planck analysis. Our salient feature is that we used inflation to quantify the IR and UV fixed points of underlying theory. We discover that the IR fixed point of HL gravity is compatible with the grand unified energy scale; whilst the UV fixed point is the Planck energy scale.

Neutron star structure in the presence of nonminimally coupled scalar fields

We study the structure of neutron stars in scalar-tensor theories for the nonminimal coupling of the form $(1+\kappa \xi \phi^{2})\cal R$. We solve the hydrostatic equilibrium equations for two different types of scalar field potentials and three different equations of state representative of different degrees of stiffness. We obtain the mass-radius relations of the configurations and determine the allowed ranges for the term $\xi\phi^2$ at the center of the star and spatial infinity based on the measured maximum value of the mass for neutron stars and the recent constraints on the radius coming from gravitational wave observations. Thus we manage to limit the deviation of the model from general relativity. We examine the possible constraints on the parameters of the model and compare the obtained restrictions with the ones inferred from other cosmological probes that give the allowed ranges for the coupling constant only. In the case of the Higgs-like potential, we also find that the central value for the scalar field cannot be chosen arbitrarily but it depends on the vacuum expectation value of the field. Finally, we discuss the effect of the scalar field potential on the mass and the radius of the star by comparing the results obtained for the cases considered here.

Cosmic acceleration and de Sitter expansion in hybrid mass varying neutrino model

A nonminimally coupled hybrid dark energy model is introduced. The dark energy evolution is triggered by mass varying neutrinos. Quintessence evolution begins from an initial point, with an insignificant dark energy density, and arrives at a final de Sitter attractor. While initially, for a Higgs-like potential, the non-minimal coupling keeps the system in a state with negligible dark energy density, finally the second quintessence conducts the evolution to a stable fixed point. These evolutions occur through successive Z2 symmetry breakings.

Maximal extensions and singularities in inflationary spacetimes

Extendibility of inflationary spacetimes with flat spatial geometry is investigated. We find that the past boundary of an inflationary spacetime becomes a so-called parallely propagated curvature singularity if the ratio diverges at the boundary, where and a represent the time derivative of the Hubble parameter and the scale factor, respectively. On the other hand, if the ratio converges, then the past boundary is regular and continuously extendible. We also develop a method to judge the continuous (C0) extendibility of spacetime in the case of slow-roll inflation driven by a canonical scalar field. As applications of this method, we find that Starobinsky inflation has a C0 parallely propagated curvature singularity, but a small field inflation model with a Higgs-like potential does not. We also find that an inflationary solution in a modified gravity theory with limited curvature invariants is free of such a singularity and is smoothly extendible.

General dynamical properties of cosmological models with nonminimal kinetic coupling

We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as η Gμνϕ,μϕ,ν, where η is an arbitrary coupling parameter, and the scalar potential V(ϕ) which assumed to be as general as possible. With an appropriate dimensionless parametrization we represent the field equations as an autonomous dynamical system which contains ultimately only one arbitrary function χ (x)= 8 π | η | V(x/√8 π) with x=√8 πϕ. Then, assuming the rather general properties of χ(x), we analyze stationary points and their stability, as well as all possible asymptotical regimes of the dynamical system. It has been shown that for a broad class of χ(x) there exist attractors representing three accelerated regimes of the Universe evolution, including de Sitter expansion (or late-time inflation), the Little Rip scenario, and the Big Rip scenario. As the specific examples, we consider a power-law potential V(ϕ)=M4(ϕ/ϕ0)σ, Higgs-like potential V(ϕ)=λ/4(ϕ2−ϕ02)2, and exponential potential V(ϕ)=M4 e−ϕ/ϕ0.

Possible evolution of a bouncing universe in cosmological models with non-minimally coupled scalar fields

We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaître-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced gravity term with a negative coupled constant, and even polynomial potentials of the scalar field. Bounce solutions with non-monotonic Hubble parameters have been obtained and analyzed. The case when the scalar field has the conformal coupling and the Higgs-like potential with an opposite sign is studied in detail. In this model the evolution of the Hubble parameter of the bounce solution essentially depends on the sign of the cosmological constant.

Reconstruction of f ( T ) $f(T)$ -gravity in the absence of matter

We derive an exact $f(T)$ gravity in the absence of ordinary matter in Friedmann-Robertson-Walker (FRW) universe, where $T$ is the teleparallel torsion scalar. We show that vanishing of the energy-momentum tensor $\mathcal{T}^{\mu \nu}$ of matter does not imply vanishing of the teleparallel torsion scalar, in contrast to general relativity, where the Ricci scalar vanishes. The theory provides an exponential (inflationary) scale factor independent of the choice of the sectional curvature. In addition, the obtained $f(T)$ acts just like cosmological constant in the flat space model. Nevertheless, it is dynamical in non-flat models. In particular, the open universe provides a decaying pattern of the $f(T)$ contributing directly to solve the fine-tuning problem of the cosmological constant. The equation of state (EoS) of the torsion vacuum fluid has been studied in positive and negative Hubble regimes. We study the case when the torsion is made of a scalar field (tlaplon) which acts as torsion potential. This treatment enables to induce a tlaplon field sensitive to the symmetry of the spacetime in addition to the reconstruction of its effective potential from the $f(T)$ theory. The theory provides six different versions of inflationary models. The real solutions are mainly quadratic, the complex solutions, remarkably, provide Higgs-like potential.

Cosmology with nonminimal kinetic coupling and a Higgs-like potential

We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as κGμνϕ,μϕ,ν, and the Higgs-like potential . Using the dynamical system method, we analyze stationary points, their stability, and all possible asymptotical regimes of the model under consideration. We show that the Higgs field with the kinetic coupling provides an existence of accelerated regimes of the Universe evolution. There are three possible cosmological scenarios with acceleration: (i) The late-time de Sitter epoch when the Hubble parameter tends to the constant value, as t → ∞, while the scalar field tends to zero, 0ϕ(t)→ , so that the Higgs potential reaches its local maximum . (ii) The Big Rip when H(t)∼(t*−t)−1 → ∞ and ϕ(t)∼(t*−t)−2 → ∞ as t → t*. (iii) The Little Rip when H(t)∼ t1/2 → ∞ and ϕ(t)∼ t1/4 → ∞ as t → ∞. Also, we derive modified slow-roll conditions for the Higgs field and demonstrate that they lead to the Little Rip scenario.

Equation-of-state parameter for reheating

Constraints to the parameters of inflation models are often derived assuming some plausible range for the number--e.g., $N_k=46$ to $N_k=60$--of $e$-folds of inflation that occurred between the time that our current observable Universe exited the horizon and the end of inflation. However, that number is, for any specific inflaton potential, related to an effective equation-of-state parameter $w_{\mathrm{re}}$ and temperature $T_{\mathrm{re}}$, for reheating. Although the physics of reheating is highly uncertain, there is a finite range of reasonable values for $w_{\mathrm{re}}$. Here we show that by restricting $w_{\mathrm{re}}$ to this range, more stringent constraints to inflation-model parameters can be derived than those obtained from the usual procedure. To do so, we focus in this work in particular on natural inflation and inflation with a Higgs-like potential, and on power law models as limiting cases of those. As one example, we show that the lower limit to the tensor-to-scalar ratio $r$, derived from current measurements of the scalar spectral index, is about 20%-25% higher (depending on the model) with this procedure than with the usual approach.

Gauged M-flation after BICEP2

In view of the recent BICEP2 results [arXiv:1403.3985] which may be attributed to the observation of B-modes polarization of the CMB with tensor-to-scalar ratio r=0.2−0.05+0.07, we revisit M-flation model. Gauged M-flation is a string theory motivated inflation model with Matrix valued scalar inflaton fields in the adjoint representation of a U(N) Yang–Mills theory. In continuation of our previous works, we show that for a class of M-flation models the action for these inflaton fields can be such that the “effective inflaton field” ϕ has a double-well Higgs-like potential, with minima at ϕ=0,μ. We focus on the ϕ>μ, symmetry-breaking region. We thoroughly examine predictions of the model for r in the 2σ region allowed for nS by the Planck experiment. As computed in [arXiv:0903.1481], for Ne=60 and nS=0.96 we find r≃0.2, which sits in the sweet spot of BICEP2 region for r. We find that with increasing μ arbitrarily, nS cannot go beyond ≃0.9670, the scalar spectral index for the quadratic chaotic potential. As nS varies in the 2σ range which is allowed by Planck and could be reached by the model, r varies in the range [0.13,0.26]. Future cosmological experiments, like the CMBPOL, that confines nS with σ(nS)=0.0029 can constrain the model further. Also, in this region of potential, for nS=0.9603, we find that the largest isocurvature mode, which is uncorrelated with curvature perturbations, has a power spectrum with the amplitude of order 10−11 at the end of inflation. We also discuss the range of predictions of r in the hilltop region, ϕ<μ.

Soliton configurations in generalized Mie electrodynamics

The generalization of the Mie electrodynamics within the scope of the effective 8-spinor field model is suggested, with the Lagrangian including Higgs-like potential and higher degrees of the invariant AµAµ. Using special Brioschi 8-spinor identity, we show that the model includes the Skyrme and the Faddeev models as particular cases. We investigate the large-distance asymptotic of static solutions and estimate the electromagnetic contribution to the energy of the localized charged configuration.

Realistic Inflation Models and Primordial Gravity Waves

We consider a variety of realistic inflationary potentials and discuss their predictions for the tensor to scalar ratio r, a canonical measure of gravity waves generated during inflation. For a Standard Model gauge singlet inflaton with a Higgs-like potential, for example, we find that r ≳ 0.02, which may be observed by the Planck satellite. We also identify supersymmetric hybrid inflation models where r can be as high as 0.03, again within the reach of Planck. The scalar spectral index in these models lies within the WMAP one sigma bounds.

Astrophysical effects of scalar dark matter miniclusters

We model the formation, evolution and astrophysical effects of dark compact Scalar Miniclusters (``ScaMs''). These objects arise when a scalar field, with an axion-like or Higgs-like potential, undergoes a second-order phase transition below the QCD scale. Such a scalar field may couple too weakly to the standard model to be detectable directly through particle interactions, but may still be detectable by gravitational effects, such as lensing and baryon accretion by large, gravitationally bound miniclusters. The masses of these objects are shown to be constrained by the $\mathrm{Ly}\ensuremath{\alpha}$ power spectrum to be less than $\ensuremath{\sim}{10}^{4}{M}_{\ensuremath{\bigodot}}$, but they may be as light as classical axion miniclusters, of the order of ${10}^{\ensuremath{-}12}{M}_{\ensuremath{\bigodot}}$. We simulate the formation and nonlinear gravitational collapse of these objects around matter-radiation equality using an $N$-body code, estimate their gravitational lensing properties, and assess the feasibility of studying them using current and future lensing experiments. Future MACHO-type variability surveys of many background sources can reveal either high-amplification, strong-lensing events, or measure density profiles directly via weak-lensing variability, depending on ScaM parameters and survey depth. However, ScaMs, due to their low internal densities, are unlikely to be responsible for apparent MACHO events already detected in the Galactic halo. As a result, in the entire window between ${10}^{\ensuremath{-}7}{M}_{\ensuremath{\bigodot}}$ and ${10}^{2}{M}_{\ensuremath{\bigodot}}$ covered by the galactic scale lensing experiments, ScaMs may in fact compose all the dark matter. A simple estimate is made of parameters that would give rise to early structure formation; in principle, early stellar collapse could be triggered by ScaMs as early as recombination, and significantly affect cosmic reionization.