Non-minimal Coupling Research Articles

Dynamical system analysis for scalar field potential in teleparallel gravity

AbstractIn this paper, we have presented a power law cosmological model and its dynamical system analysis in $$f(T,\phi )$$ f ( T , ϕ ) gravity, where T is the torsion scalar and $$\phi $$ ϕ is the canonical scalar field. The two well-motivated forms of the non-minimal coupling function $$F(\phi )$$ F ( ϕ ) , the exponential form and the power law form, with exponential scalar field potential, are investigated. The dynamical system analysis is performed by establishing the dimensionless dynamical variables, and the critical points were obtained. The evolution of standard density parameters is analysed for each case. The behaviour of the equation of state (EoS) and deceleration parameter agree with the result of recent cosmological observations. The model parameters are constrained using the existence and the stability conditions of the critical points describing different epochs of the evolution of the Universe.

Nonminimal coupling holographic superconductors

We explore a holographic superconductor model in which a real scalar field is nonminimally coupled to a gauge field. We consider several types of the nonminimal coupling function h(ψ) including exponential, hyperbolic (cosh), power-law, and fractional forms. We investigate the influences of the nonminimal coupling parameter α on condensation, critical temperature, and conductivity. We can categorize our results in two groups. In the first group, conductor/superconductor phase transition is easier to occur for larger values of α, while in the second group stronger effects of the nonminimal coupling makes the formation of scalar hair harder. Although the real and imaginary parts of conductivity are impressed by different forms of h(ψ), they follow some universal behaviors such as connecting with each other through Kramers–Kronig relation in ω → 0 limit or the appearance of gap frequency at low temperatures around ωg ∼ 8 Tc, which shifts to larger values by increasing the strength of α. Among all forms of h(ψ) we observe that h(ψ) = 1 + αψ2 gives us better information in wide range of nonminimal coupling constant and temperature. Choosing the best form of h(ψ), we construct a family of solutions for holographic conductor/superconductor phase transitions to discover the effect of the hyperscaling violation when the gauge and scalar fields are nonminimally coupled. we find that the critical temperature increases for higher effects of hyperscaling violation θ and nonminimal coupling constant α. By increasing these two parameters, we obtain lower values of condensation which means that conductor/superconductor phase transition will acquire easier. Furthermore, we understand that the hyperscaling violation affects the conductivity σ of the holographic superconductors and changes the expected relation in the gap frequency. Some universal behaviors like infinite DC conductivity are observed. In addition, we consider a five-dimensional Gauss–Bonnet (GB) black hole with a flat horizon. We find out that the critical temperature decreases for larger values of GB coupling constant, λ, or smaller values of nonminimal coupling constant, α, which means that the condensation is harder to form. Moreover, we study the electrical conductivity in the holographic setup. We observe that the gap frequency shifts to larger values for stronger λ, and becomes flat by increasing α.

Linearized second law for higher curvature gravity and nonminimally coupled vector fields

Expanding the work of Wall [], we show that black holes obey a second law for linear perturbations to bifurcate Killing horizons, in any covariant higher curvature gravity coupled to scalar and vector fields. The vector fields do not need to be gauged, and (like the scalars) can have arbitrary nonminimal couplings to the metric. The increasing entropy has a natural expression in covariant phase space language, which makes it manifestly invariant under Jacobson-Kang-Myers ambiguities. An explicit entropy formula is given for f(Riemann) gravity coupled to vectors, where at most one derivative acts on each vector. Besides the previously known curvature terms, there are three extra terms involving differentiating the Lagrangian by the symmetric vector derivative (which therefore vanish for gauge fields). Published by the American Physical Society 2024

Intermediate inflation in a generalized non-minimal derivative coupling model

In this work, we consider intermediate inflation in the context of the generalized non-minimal derivative coupling (GNMDC) model. In the GNMDC model, inflation is driven by a canonical scalar field that is coupled not only to gravity but also to the derivative of the scalar field. The model introduces new dynamics and features during the inflationary epoch. We find inflationary solutions with a power law scalar field for the power law coupling function. Additionally, we determine the inflaton potential that generates intermediate expansion of the scale factor. We also discuss the background equations in the high friction limit and derive constraints on the parameters of our model. Furthermore, we investigate the cosmological perturbations in the slow roll approximation within the GNMDC model, and we calculate the scalar and tensor spectral index and the tensor-to-scalar ratio during intermediate inflation. We compare the results of this model with observational data that can be used to test the model using cosmic microwave background radiation data. Overall, we establish conditions for the inflaton potential that ensure the continuation of accelerated expansion during slow roll inflation. We numerically analyze the power spectrum and spectral index for scalar and tensor modes in intermediate inflation in the high friction limit, and we use Planck 2018 data to obtain constraints on the parameters of the model. We demonstrate that intermediate inflation in the GNMDC model is successful in evaluation and explanation of background and perturbation quantities using observational data.

Circular motion and QPOs near black holes in Kalb–Ramond gravity

General relativity (GR) theory modifications include different scalar, vector, and tensor fields with non-minimal gravitational coupling. Kalb–Ramond (KR) gravity is a modified theory formulated based on the presence of the bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BHs) using observational data. In the present work, we aimed to test KR gravity through theoretical studies of epicyclic frequencies of particle oscillations using quasi-periodic oscillation (QPO) frequency data from microquasars. First, we derive equations of motion and analyze the effective potential for circular orbits. Also, we studied the energy and angular momentum of particles corresponding to circular orbits. In addition, we analyze the stability of circular orbits. It is shown that the radius of the innermost stable circular orbits is inversely proportional to the KR parameter. We are also interested in how the energy and angular momentum of test particles at ISCO behave around the KR BHs. We found that the Keplerian frequency for the test particles in KR gravity is the same as that in GR. Finally, we study the QPOs by applying epicyclic oscillations in the relativistic precession (RP), warped disc (WD), and epicyclic resonance (ER) models. We also analyze QPO orbits in the resonance cases of upper and lower frequencies 3:2, 4:3, and 5:4 in the QPO as mentioned above models. We obtain constraints on the KR gravity parameter and BH mass using a Monte Carlo Markov Chain simulation in the multidimensional parameter space for the microquasars GRO J1655-40 & XTE J1550-564, M82 X-1, and Sgr A*.

Gravitational production of completely dark photons with nonminimal couplings to gravity

Dark photons are a theorized massive spin-1 particle which can be produced via various mechanisms, including cosmological gravitational particle production (GPP) in the early universe. In this work, we extend previous results for GPP of dark photons to include nonminimal couplings to gravity. We find that nonminimal couplings can induce a ghost instability or lead to runaway particle production at high momentum and discuss the constraints on the parameter space such that the theory is free of instabilities. Within the instability-free regime we numerically calculate the particle production and find that the inclusion of nonminimal couplings can lead to an enhancement of the particle number. As a result, GPP of nonminimally coupled dark photons can open the parameter space for production of a cosmological relevant relic density (constituting all or part of the dark matter) as compared to the minimally-coupled theory. These results are independent of the choice of inflation model, which we demonstrate by repeating the analysis for a class of rapid-turn multi-field inflation models.

Primordial black holes in non-minimal Gauss–Bonnet inflation in light of the PTA data

Here, we investigate the formation of primordial black holes (PBHs) in non-minimal coupling Gauss–Bonnet inflationary model in the presence of power-law potentials. We employ a two part coupling function to enhance primordial curvatures at small scales as well as satisfy Planck measurements at the CMB scale. Moreover, our model satisfies the swampland criteria. We find PBHs with different mass scales and demonstrate that PBHs with masses around O(10-14)M⊙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(10^{-14})M_{\\odot }$$\\end{document} can account for almost all of the dark matter in the universe. In addition, we investigate the implications of the reheating stage and show that the PBHs in our model are generated during the radiation-dominated era. Furthermore, we investigate the production of scalar-induced gravitational waves (GWs). More interestingly enough is that, for the specific cases Dn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_\ extrm{n}$$\\end{document} in our model, the GWs can be considered as a source of PTA signal. Also, we conclude that the GWs energy density parameter at the nano-Hz regime can be parameterized as ΩGW0(f)∼f5-γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _\\mathrm{GW_0} (f) \\sim f^{5-\\gamma }$$\\end{document}, where the obtained γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} is consistent with the PTA Observations.

Towards testing the general bounce cosmology with the CMB B-mode auto-bispectrum

It has been shown that a three-point correlation function of tensor perturbations from a bounce model in general relativity with a minimally-coupled scalar field is highly suppressed, and the resultant three-point function of cosmic microwave background (CMB) B-mode polarizations is too small to be detected by CMB experiments. On the other hand, bounce models in a more general class with a non-minimal derivative coupling between a scalar field and gravity can predict the three-point correlation function of the tensor perturbations without any suppression, the amplitude of which is allowed to be much larger than that in general relativity. In this paper, we evaluate the three-point function of the B-mode polarizations from the general bounce cosmology with the non-minimal coupling and show that a signal-to-noise ratio of the B-mode auto-bispectrum in the general class can reach unity for ℓ max=100 in the full-sky case, with and without the lensing B-mode added to cosmic variance. Considering additionally the LiteBIRD experimental noise, we obtain a SNR smaller than unity.

Teleparallel gravity and quintessence: The role of nonminimal boundary couplings

In this paper, we have outlined the development of an autonomous dynamical system within a general scalar-tensor gravity framework. This framework encompasses the overall structure of the non-minimally coupled scalar field functions for both the torsion scalar (T) and the boundary term (B). We have examined three well-motivated forms of potential functions and constrained the model parameters through dynamical system analysis. This analysis has played a crucial role in identifying cosmologically viable models. We have analysed the behaviour of dynamical parameters such as equation-of-state parameters, as well all the standard density parameters for radiation, matter, and dark energy to assess their compatibility with current observational data. The phase space diagrams are presented to support the stability conditions of the corresponding critical points. The Universe is apparent in its late-time cosmic acceleration phase via the dark energy-dominated critical points. Additionally, we compare our findings with the most prevailing ΛCDM model. The outcomes are further inspected using the cosmological data sets of Supernovae Ia and the Hubble rate H(z).

The motion of twisted particles in a stellar gravitational field

Abstract In this work, we explore the motion of a twisted particle possessing intrinsic orbital angular momentum (OAM) as it traverses a weak stellar gravitational field, which we approximate using a polytropic model. We disregard the spin characteristic of the twisted particle, modeling it as a massless complex twisted scalar wave packet to simplify its interaction with gravitational fields. Building on this simplification, we determine the trajectory of this twisted particle by using the center of its energy density and investigate the gravitational birefringence induced by its OAM. In a weak field approximation, we find the gravitational birefringence-OAM relationship parallels that with spin, as described by the Mathisson-Papapetrou-Dixon equations. This indicates that the gravitational birefringence induced by OAM can potentially exceed that induced by spin by several orders of magnitude, significantly enhancing its detectability. To broaden our analysis, we introduce a nonminimal coupling term, $\lambda R|\phi|^2$, into the Lagrangian, resulting in the modified expression $\mathcal{L}=-\frac{1}{2}\nabla _\rho\phi\nabla^\rho\phi^*-\frac{1}{2}\lambda R|\phi|^2$. This adjustment is necessitated by the quantization of the scalar field in curved spacetime. We then explore the effects of this term on the motion of the twisted particle. Our findings show that the trajectory of the twisted particle under nonminimal coupling ($\lambda\neq 0$) differs from that in the minimal coupling scenario ($\lambda=0$). Specifically, for a positive nonminimal coupling constant $\lambda$, the trajectory of the twisted particle is expected to deviate away from the stellar center, compared to the minimal coupling scenario.

Impact of charge and non-minimal fluid-geometry coupling on anisotropic interiors

This paper explores the interior configuration of various charged anisotropic compact models within the framework of f(R,T,RληTλη) gravity. The chosen model in this theory is represented by R+γRληTλη , where γ is a real-valued parameter. We adopt a static spherical metric to describe the interior of compact strange stars and derive the corresponding field equations. The solution to these equations is then obtained using the Finch-Skea metric and a linear equation of state. Taking the radius and mass of the compact star model 4U 1820-30 as a case study, we investigate the impact of charge and modified corrections on its internal distribution. The stability of the resulting model is also determined within a specific range of γ. Additionally, we determine the values of the model parameter through the vanishing radial pressure constraint, aligning with the experimental data of eight different stars. Our findings indicate that the resulting model adheres to the conditions necessary for physically relevant interiors, particularly in the case of lower charge.

Energy-Momentum Squared Gravity: A Brief Overview

In this work, we present a review of Energy-Momentum Squared Gravity (EMSG)—more specifically, f(R,TμνTμν) gravity, where R represents the Ricci scalar and Tμν denotes the energy-momentum tensor. The inclusion of quadratic contributions from the energy-momentum components has intriguing cosmological implications, particularly during the Universe’s early epochs. These effects dominate under high-energy conditions, enabling EMSG to potentially address unresolved issues in General Relativity (GR), such as the initial singularity and aspects of big-bang nucleosynthesis in certain models. The theory’s explicit non-minimal coupling between matter and geometry leads to the non-conservation of the energy-momentum tensor, which prompts the investigation of cosmological scenarios through the framework of irreversible thermodynamics of open systems. By employing this formalism, we interpret the energy-balance equations within EMSG from a thermodynamic perspective, viewing them as descriptions of irreversible matter creation processes. Since EMSG converges to GR in a vacuum and differences emerge only in the presence of an energy-momentum distribution, these distinctions become significant in high-curvature regions. Therefore, deviations from GR are expected to be pronounced in the dense cores of compact objects. This review delves into these facets of EMSG, highlighting its potential to shed light on some of the fundamental questions in modern cosmology and gravitational theory.

Energy extraction and Keplerian fundamental frequencies in the Kalb–Ramond gravity

The nonminimal coupling of the nonzero vacuum expectation value of the self-interacting antisymmetric Kalb–Ramond field with gravity leads to a power-law hairy BH having a parameter s, which encompasses the Reissner-Nordström black hole (s=1). It is obtained the axially symmetric counterpart of this hairy solution, namely, the rotating Kalb–Ramond black hole, which encompasses, as special cases, Kerr (s=0) and Kerr–Newman (s=1) black holes. With rotating Kalb–Ramond black hole metric, we study its horizon structure and motion of the test particles in the near of the equatorial plane and we determine radial motion equations which governing t and ϕ. We also explore thatthe black hole mass increasing when falling many of mass-less particles are relative to the black hole mass. We consider how the Kalb–Ramond parameters depend on increasing its mass. Furthermore, we analyze the Keplerian frequency, as well as the vertical and horizontal oscillations of basic frequencies, using a graph-based approach. The frequency charts are contingent upon the Kalb–Ramond parameters s and Γ. By consulting certain sources, ones can investigate the distinctions between KR gravity and other models.

A thermodynamic study of (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf {(2+1)}}$$\\end{document}-dimensional analytic charged hairy black holes with Born–Infeld electrodynamics

This work presents analytical black hole solutions for a coupled Einstein–Born–Infeld–Scalar gravity system in AdS spacetime with two different non-minimal coupling functions f(z). For both solutions, we establish the regularity of the scalar field and curvature scalars outside the horizon. For one of the considered coupling cases, thermodynamic analysis in the canonical ensemble reveals stability across all temperatures, while the other case exhibits the Hawking/Page phase transition between the stable large phase of the black hole and thermal-AdS. We investigate the effect of the scalar hair parameter and black hole charge on the phase transition temperature and observe that the critical values of the scalar hair and the charge parameters constrain the feasibility of Hawking/Page phase transition.

Runaway Gravitational Production of Dark Photons.

We demonstrate that gravitational particle production of a massive, Abelian, vector (Proca) field during inflation in the presence of nonminimal coupling to gravity may suffer from an instability which leads to runaway production of high-momentum modes. This is untenable unless there is some mechanism to regulate the runaway. We discuss the parameter space of the particle mass and nonminimal couplings where such a runaway occurs and possible ways to tame the runaway. We find that there is no obvious way to resolve the runaway in a UV completion or with kinetic mixing to the standard model.

Consistent actions for massive particles interacting with electromagnetism and gravity

Consistent interactions with electromagnetism and gravity for mass m particles of any spin are obtained. This is done by finding interactions which preserve the covariantized massive gauge symmetry present in recently constructed massive particle actions. This gauge principle is sufficient for finding consistent completions of minimal as well as non-minimal couplings of any type. For spins s ≥ 3/2, consistency requires infinitely many interaction terms in the action, including arbitrarily high order derivatives of electromagnetic and gravitational curvatures, with correspondingly high powers of 1/m. These interactions may be formally resummed and expressed in terms of non-local operators. Finally, although the interactions appear non-local, evidence is presented for the existence of a field redefinition which makes the interacting action local. This work provides the first explicit realization of an exactly gauge invariant formulation of massive particles interacting with electromagnetism and gravity.

Embedding the ΛCDM framework in non-minimal f(Q) gravity with matter-coupling

In exploring the dynamics of the Universe, modified gravity theories offer an alternative explanation for dark energy. Although the ΛCDM model has served as a foundational description for understanding the Universe, it also has its limitations. Our primary objective in this study is to overcome these shortcomings and reconstruct the ΛCDM Universe. We aim to achieve this by embedding the ΛCDM scenario within a modified gravity framework. Here, the investigation is conducted within the framework of novel non-minimal coupling of f(Q) gravity. A generic non-minimal form is considered, expressed in terms of two arbitrary functions f1(Q) and f2(Q). Analytic solutions are derived to mimic the ΛCDM paradigm. Finally, through cosmographic analysis, the models are validated against observational results.

Cosmological constraints on the background dynamics of a two-field nonsingular bounce model

In this study, we consider a nonsingular two-field bounce scenario with non-minimal kinetic coupling between two scalar fields. We derive constraints on the model parameters from the finiteness of the physical quantities at the classical level and from the relation between the late-time accelerated expansion and particle production up to the bounce phase. We then determine the allowed parameter space for the model.

Electric Penrose, circular orbits and collisions of charged particles near charged black holes in Kalb–Ramond gravity

General relativity (GR) is a well-tested theory of gravity in strong and weak field regimes. Many modifications to this theory were obtained, including different scalar, vector, and tensor fields to the GR with non-minimal coupling to gravity. Kalb–Ramond (KR) gravity is also a modified theory formulated in the presence of a bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BH). In this work, we study the circular motion of charged particles and explore energetic processes around charged BHs in KR theory. First, we investigated the event horizon radius and analyzed horizon-no horizon regions in the BH charge and KR parameter space. Considering the Coulomb interaction, we derive and analyze the effective potential for charged particles around a charged KR BH. We investigate charged particles’ angular momentum and energy corresponding to circular orbits. We also investigate how the KR non-minimal coupling parameter affects the radius of the innermost stable circular orbits, the corresponding energy, and the angular momentum. We also investigated the electric Penrose process and charged-particle collisions near the KR BH. The presence of the nonzero KR parameter results in a decrease in the energy efficiency of the Penrose process. Also obtained is that the KR parameter’s positive (negative) values cause a decrease (increase) in the center of mass energy of colliding particles near the BH horizon.

Constant-roll inflation with non-minimally derivative coupling

We investigate the constant-roll inflation with non-minimally kinetic coupling to the Einstein tensor. With the slow-roll parameter ηϕ=−ϕ̈/(Hϕ̇) being a constant, we calculate the power spectra for scalar and tensor perturbations, and derive the expressions for the scalar spectral tilt n s , the tensor spectral tilt n T , and the tensor-to-scalar ratio r. We find that the expressions for n s are different with different ordering of taking the derivative of the scalar power spectrum with respect to the scale k and the horizon crossing condition c s k = aH in the constant-roll inflation, the consistency relation r = − 8n T does not hold if ∣η ϕ ∣ is not small, and the duality of the tensor-to-scalar ratio between the slow-roll inflation and ultra-slow-roll inflation does not exist in inflationary models with non-minimally derivative coupling. The result offers a fresh perspective on the understanding of the inflationary models with non-minimally derivative coupling and is helpful for the production of scalar induced gravitational waves in the framework of ultra-slow-roll inflation with non-minimally derivative coupling.