Nonminimal Interaction Research Articles

Classes of holographic Mott gaps

The fermion gaps are classified into order gap or Mott gap depending on the presence/absence of the order parameter. We construct the holographic model of the Mott gap using the field that is supported by the density only without introducing any order parameter. We then classify the Mott gap, depending on the shape of the gap in the density of states and whether the Fermi surface is touching the valence bond or not, into three classes: i) Symmetric gap, ii) Asymmetric gap with isolated Fermi sea. iii) Asymmetric gap with Fermi sea touching the valence band. Finally, we identify possible non-minimal gauge interactions that produce a flatband without symmetry breaking.

Magnetic Bianchi-I cosmology in the Horndeski theory

In this paper, we study the evolution of Bianchi-I spacetimes within the framework of the Horndeski theory with [Formula: see text]. The spacetimes are filled a global unidirectional electromagnetic field interacting with a scalar field. We consider the minimal interaction and the non-minimal interaction by the law [Formula: see text]. The Horndeski theory allows anisotropy to grow over time, so the question arises of regulating the anisotropic level in this theory. Using the designer method, we build models in which the anisotropic level tends to a small value as the Universe expands. One of the results is a model with a anisotropic bounce.

The rise and fall of the Standard-Model Higgs: electroweak vacuum stability during kination

In this paper we investigate the vacuum stability of the non-minimally coupled Standard-Model Higgs during a phase of kinetic domination following the end of inflation. The non-minimal coupling to curvature stabilises the Higgs fluctuations during inflation while driving them towards the instability scale during kination, when they can classically overcome the potential barrier separating the false electroweak vacuum from the true one at super-Planckian field values. Avoiding the instability of the Standard-Model vacuum sets an upper bound on the inflationary scale that depends both on the strength of the non-minimal interaction and on the top quark Yukawa coupling. Classical vacuum stability is guaranteed if the gravitationally-produced energy density is smaller than the height of barrier in the effective potential. Interestingly enough, thanks to the explosive particle production in the tachyonic phase, the Higgs itself can be also appointed to the role of reheaton field responsible for the onset of the hot Big Bang era, setting an additional lower bound on the inflationary scale Hinf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{H}}_{\ extrm{inf}} $$\\end{document} ≳ 105.5 GeV. Overall, these constraints favour lower masses for the top quark, in agreement with the current measurements of the top quark pole mass. We perform our analysis semi-analytically in terms of the one-loop and three-loop running of the Standard-Model Higgs self-coupling and make use of lattice-based parametric formulas for studying the (re)heating phase derived in arXiv:2307.03774. For a specific choice of mt = 171.3 GeV we perform also an extensive numerical scanning of the parameter space via classical lattice simulations, identifying stable/unstable regions and supporting the previous analytical arguments. For this fiducial value, the heating of the Universe is achieved at temperatures in the range 10−2–109 GeV.

Rescuing gravitational-reheating in chaotic inflation

We show, within the single-field inflationary paradigm, that a linear non-minimal interaction ξ M P ϕ R between the inflaton field ϕ and the Ricci scalar R can result in successful inflation that concludes with an efficient heating of the Universe via perturbative decays of the inflaton, aided entirely by gravity. Considering the inflaton field to oscillate in a quadratic potential, we find that 𝒪(10-1) ≲ 𝒪 ≲ 𝒪(102) is required to satisfy the observational bounds from Cosmic Microwave Background (CMB) and Big Bang Nucleosynthesis (BBN). Interestingly, the upper bound on the non-minimal coupling guarantees a tensor-to-scalar ratio r ≳ 10-4, within the range of current and future planned experiments. We also discuss implications of dark matter production, along with the potential generation of the matter-antimatter asymmetry resulting from inflaton decay, through the same gravity portal.

Conformal and Non-Minimal Couplings in Fractional Cosmology

Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered “anomalous”. It is often used when traditional integer derivatives models fail to represent cases where the power law is observed accurately. Fractional calculus must reflect non-local, frequency- and history-dependent properties of power-law phenomena. This tool has various important applications, such as fractional mass conservation, electrochemical analysis, groundwater flow problems, and fractional spatiotemporal diffusion equations. It can also be used in cosmology to explain late-time cosmic acceleration without the need for dark energy. We review some models using fractional differential equations. We look at the Einstein–Hilbert action, which is based on a fractional derivative action, and add a scalar field, ϕ, to create a non-minimal interaction theory with the coupling, ξRϕ2, between gravity and the scalar field, where ξ is the interaction constant. By employing various mathematical approaches, we can offer precise schemes to find analytical and numerical approximations of the solutions. Moreover, we comprehensively study the modified cosmological equations and analyze the solution space using the theory of dynamical systems and asymptotic expansion methods. This enables us to provide a qualitative description of cosmologies with a scalar field based on fractional calculus formalism.

Quadratic energy–momentum squared gravity: Constraints from big bang nucleosynthesis

In this work, we extend the standard cosmological model within the quadratic energy–momentum squared gravity (qEMSG) framework, introducing a nonminimal interaction between the usual material field (Tμν) and its accompanying partner field (qEMSF, TμνqEMSF), defined by f(T2)=αT2 with T2=TμνTμν. Adopting an analytical approach within the qEMSG framework, we present a comprehensive exploration of Big Bang Nucleosynthesis (BBN) dynamics. Our analysis selects the radiation-dominated universe solution compatible with the standard cosmological model limit as α→0 and reveals that qEMSF interaction model can modify the radiation energy density’s evolution, potentially altering neutron–proton interconversion rates and consequently affecting 4He abundance in various ways. By explicitly defining modifications to the predicted primordial 4He mass fraction, Yp, we establish the most stringent cosmological constraints on the parameter α based on recent measurements of Yp: (−8.81≤α≤8.14)×10−27eV−4 (68% CL) from Aver et al.’s primordial 4He abundance measurements, aligning with α=0. Additionally, (3.48≤α≤4.43)×10−27eV−4 (68% CL) from Fields et al.’s estimates, utilizing the Planck-CMB estimated baryon density within the standard cosmological model framework, diverges from α=0, thereby lending support to the qEMSF interaction model. The study also highlights the bidirectional nature of energy–momentum/entropy transfer in qEMSF interaction model, depending on the sign of α. The implications of qEMSF in the presence of additional relativistic relics are also explored, showcasing the model’s potential to accommodate deviations from standard cosmology and the Standard Model of particle physics.

Cubic action for spinning black holes from massive higher-spin gauge symmetry

Scattering of two Kerr Black Holes emitting gravitational waves can be captured by an effective theory of a massive higher-spin field interacting with the gravitational field. While other compact objects should activate a multitude of non-minimal interactions it is the black holes that should be captured by the simplest minimal interaction. Implementing massive higher-spin symmetry via a string-inspired BRST approach we construct an action that reproduces the correct cubic amplitude of Arkani-Hamed-Huang-Huang. The same is achieved for the root-Kerr theory, i.e. for the minimal electromagnetic interaction of a massive higher-spin field.

Evolution of an interacting fermion–antifermion pair in the near-horizon of the BTZ black hole

In this study, we investigate the evolution of a composite system comprising a fermion–antifermion pair engaged in Cornell-type non-minimal interaction in the near-horizon region of a BTZ black hole. Our exploration involves the derivation of an exact solution for the covariant two-body Dirac equation, derived from quantum electrodynamics through the action principle. To commence our analysis, we formulate the relevant equation, resulting in a 4×4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\ imes 4$$\\end{document} dimensional matrix equation that governs the relative motion of the fermion–antifermion pair. Notably, we demonstrate that this matrix equation results in an exactly solvable wave equation, enabling us to determine the relativistic frequency modes for this spinless static composite system. Our findings unveil a temporal decay in these modes, with the decay time explicitly dependent on both the inter-particle interaction and the spacetime parameters. Our comprehensive examination extends to a detailed analysis of the system’s evolution, shedding light on the influence of inter-particle interaction on the evolution of a fermion–antifermion pair in the near-horizon region of the BTZ black hole.

Model-independent reconstruction of the interacting dark energy kernel: Binned and Gaussian process

Abstract The cosmological dark sector remains an enigma, offering numerous possibilities for exploration. One particularly intriguing option is the (non-minimal) interaction scenario between dark matter and dark energy. In this paper, to investigate this scenario, we have implemented Binned and Gaussian model-independent reconstructions for the interaction kernel alongside the equation of state; while using data from BAOs, Pantheon+ and Cosmic Chronometers. In addition to the reconstruction process, we conducted a model selection to analyze how our methodology performed against the standard ΛCDM model. The results revealed a slight indication, of at least 1σ confidence level, for some oscillatory dynamics in the interaction kernel and, as a by-product, also in the DE and DM. A consequence of this outcome is the possibility of a sign change in the direction of the energy transfer between DE and DM and a possible transition from a negative DE energy density in early-times to a positive one at late-times. While our reconstructions provided a better fit to the data compared to the standard model, the Bayesian Evidence showed an intrinsic penalization due to the extra degrees of freedom. Nevertheless these reconstructions could be used as a basis for other physical models with lower complexity but similar behavior.

Lattice simulations of non-minimally coupled scalar fields in the Jordan frame

The presence of scalar fields with non-minimal gravitational interactions of the form \xi |\phi|^2 Rξ|ϕ|2R may have important implications for the physics of the early universe. We propose a procedure to solve the dynamics of non-minimally coupled scalar fields directly in the Jordan frame, where the non-minimal couplings are maintained explicitly. Our algorithm can be applied to lattice simulations that include minimally coupled fields and an arbitrary number of non-minimally coupled scalars, with the expansion of the universe sourced by all fields present. This includes situations when the dynamics become fully inhomogeneous, fully non-linear (due to e.g. backreaction or mode rescattering effects), and/or when the expansion of the universe is dominated by non-minimally coupled species. As an example, we study geometric preheating with a non-minimally coupled scalar spectator field when the inflaton oscillates following the end of inflation.

Renormalization group for nonminimal ϕ2R couplings and gravitational contact interactions

Theories of scalars and gravity, with an Einstein-Hilbert term and nonminimal interactions, ${M}^{2}R/2\ensuremath{-}\ensuremath{\alpha}{\ensuremath{\phi}}^{2}R/12$, have graviton exchange-induced contact interactions. These modify the renormalization group, leading to a discrepancy between the conventional calculations in the Jordan frame that ignore this effect (and are found to be incorrect), and the Einstein frame in which $\ensuremath{\alpha}$ does not exist. Thus, the calculation of quantum effects in the Jordan and Einstein frames does not generally commute with the transition from the Jordan to the Einstein frame. In the Einstein frame, though $\ensuremath{\alpha}$ is absent, for small steps in scale $\ensuremath{\delta}\ensuremath{\mu}/\ensuremath{\mu}$ infinitesimal contact terms $\ensuremath{\sim}\ensuremath{\delta}\ensuremath{\alpha}$ are induced, that are then absorbed back into other couplings by the contact terms. This modifies the $\ensuremath{\beta}$-functions in the Einstein frame. We show how correct results can be obtained in a simple model by including this effect.

Spin 2 Particle with Anomalous Magnetic Moment in Riemann Space−Time: A Massless Case with the Gauge Symmetry

The most of studies in the theory of spin 2 field were performed with the use of the 2-nd order equations. The spin 2 particle theory proposed by F.I. Fedorov is based on the first order equations requires a 30-component set of tensors. Besides, by him and coauthors was elaborated a more general theory, which is based on 50-component set of tensors. In the present paper, we consider this more general theory in presence of arbitrary electromagnetic fields and Riemannian space-time backgrounds. First we study the 50-component theory for a massive particle. In this case, there arises the non-minimal interaction with the curved space-time background through the Ricci and Riemann tensors. It is important that the theory under consideration allows for a new massless limit for the spin 2 field. This fact is of special interest, because the conventional Pauli - Fierz theory for the massless field does not possess gauge symmetry in the curved space-time, in particular, in models with the vanishing Ricci tensor. We show that the generalized theory possesses such a gauge symmetry in all space-time models for which the Ricci tensor vanishes.

Schwarzschild quasi-normal modes of non-minimally coupled vector fields

We study perturbations of massive and massless vector fields on a Schwarzschild black-hole background, including a non-minimal coupling between the vector field and the curvature. The coupling is given by the Horndeski vector-tensor operator, which we show to be unique, also when the field is massive, provided that the vector has a vanishing background value.We determine the quasi-normal mode spectrum of the vector field, focusing on the fundamental mode of monopolar and dipolar perturbations of both even and odd parity, as a function of the mass of the field and the coupling constant controlling the non-minimal interaction. In the massless case, we also provide results for the first two overtones, showing in particular that the isospectrality between even and odd modes is broken by the non-minimal gravitational coupling.We also consider solutions to the mode equations corresponding to quasi-bound states and static configurations. Our results for quasi-bound states provide strong evidence for the stability of the spectrum, indicating the impossibility of a vectorization mechanism within our set-up. For static solutions, we analytically and numerically derive results for the electromagnetic susceptibilities (the spin-1 analogs of the tidal Love numbers), which we show to be non-zero in the presence of the non-minimal coupling.

Evolution of holographic Fermi surface from non-minimal couplings

We study a holographic toy model by considering a probe fermion of finite charge density in an anisotropic background. By computing the fermionic spectral function numerically, we observed that the system exhibits some interesting behaviours in the nature of the Fermi surface (FS) and its evolution when tuning the controlling parameters. We introduced non-minimal interaction terms in the action for holographic fermions along with a complex scalar field but neglecting the backreaction of the fermions field on the background. Suppression in the spectral weight and deformation of FS is observed, which are reminiscent of the results seen in various condensed matter experiments in real materials.

(Un)balanced Holographic Superconductors with Electric and Spin Motive Force Coupling

We study holographic phase transitions in (2+1) dimensions that possess interacting phases which result from a direct coupling between the two U(1) gauge fields. This can be interpreted as a non-minimal interaction between the electric and spin motive forces of the dual model. We first present a new analytical solution of the Einstein-Maxwell equations that describes a black hole with charge non-equivalent to the sum of the asymptotic charges of the two U(1) gauge fields and briefly discuss formation of uncharged scalar hair on this solution. We then study the formation of charged scalar hair on an uncharged black hole background and discuss the dual description of balanced as well as unbalanced superconductors.

Dynamics of a fermion with dipole moments in external wave fields

We discuss the motion of a massive fermion spin 1/2 particle in external wave field configurations when the Pauli type non-minimal interaction of the gauge field strengths with particle’s dipole moments is taken into account. The exact solution of the relativistic Dirac-Pauli equation is presented for the case of the plane electromagnetic wave.

Relation between parity-even and parity-odd CFT correlation functions in three dimensions

In this paper we relate the parity-odd part of two and three point correlation functions in theories with exactly conserved or weakly broken higher spin symmetries to the parity-even part which can be computed from free theories. We also comment on higher point functions.The well known connection of CFT correlation functions with de-Sitter amplitudes in one higher dimension implies a relation between parity-even and parity-odd amplitudes calculated using non-minimal interactions such as {mathcal{W}}^3 and {mathcal{W}}^2tilde{mathcal{W}} . In the flat-space limit this implies a relation between parity-even and parity-odd parts of flat-space scattering amplitudes.

Interaction of the generalized Duffin–Kemmer–Petiau equation with a non-minimal coupling under the cosmic rainbow gravity

In this study, we survey the generalized Duffin–Kemmer–Petiau oscillator containing a non-minimal coupling interaction in the context of rainbow gravity in the presence of the cosmic topological defects in space-time. In this regard, we intend to investigate relativistic quantum dynamics of a spin-0 particle under the modification of the dispersion relation according to the Katanaev–Volovich geometric approach. Thus, based on the geometric model, we study the aforementioned bosonic system under the modified background by a few rainbow functions. In this way, by using an analytical method, we acquire energy eigenvalues and corresponding wave functions to each scenario. Regardless of rainbow gravity function selection, the energy eigenvalue can present symmetric, anti-symmetric, and symmetry breaking characteristics. Besides, one can see that the deficit angular parameter plays an important role in the solutions.

Generalized proof of the linearized second law in general quadric corrected Einstein-Maxwell gravity

Although the entropy of black holes in any diffeomorphism invariant theory of gravity can be expressed as the Wald entropy, the issue of whether the entropy always obeys the second law of black hole thermodynamics remains open. Since the nonminimal coupling interaction between gravity and the electromagnetic field in the general quadric corrected Einstein-Maxwell gravity can sufficiently influence the expression of the Wald entropy, we check whether the Wald entropy of black holes in the quadric corrected gravity still satisfies the second law. A quasistationary accreting process of black holes is first considered, which describes that black holes are perturbed by matter fields and eventually settle down to a stationary state. Two assumptions that the matter fields should obey the null energy condition and that a regular bifurcation surface exists on the background spacetime are further proposed. According to the two assumptions and the Raychaudhuri equation, we demonstrate that the Wald entropy monotonically increases along the future event horizon under the linear order approximation of the perturbation. This result indicates that the Wald entropy of black holes in the quadric corrected gravity strictly obeys the linearized second law of thermodynamics.

Massless polarized particle and Faraday rotation of light in the Schwarzschild spacetime

We present the manifestly covariant Lagrangian of a massless polarized particle that implies all dynamic and algebraic equations as the conditions of extreme of this variational problem. The model allows for minimal interaction with a gravitational field, leading to the equations, coinciding with Maxwell equations in the geometrical optics approximation. The model allows also a wide class of nonminimal interactions, which suggests an alternative way to study the electromagnetic radiation beyond the leading order of geometrical optics. As a specific example, we construct a curvature-dependent interaction in Schwarzschild spacetime, predicting the Faraday rotation of polarization plane, linearly dependent on the wave frequency. As a result, the Schwarzschild spacetime generates a kind of angular rainbow of light: waves of different frequencies, initially linearly polarized in one direction, acquire different orientations of their polarization planes when propagated along the same ray.