Non-minimal Coupling Parameter Research Articles

Estimating power-law exponents from observations in electromagnetic non-minimal Maxwell-Gauss-Bonnet coupling cosmology

We discuss a generalized non-minimal Maxwell-Gauss-Bonnet power-law cosmological model characterized by the presence of electromagnetic field and variable cosmological and gravitational constant. We analyze the late-time dynamics characterized by power-law solutions. The model is constrained with local gravitational acceleration measurements, the SH0ES project which estimate the Hubble parameter, Planck TT, TE, EE + low E +lensing +SNe+ BAO data which estimate the EoS parameter and data coming from distant supernovae type Ia, the Hubble function H(z) measurements and information coming from the Alcock-Paczynski test which estimate the numerical range of the non-minimal coupling parameter. By adopting a variable cosmological and gravitational constants, it was found that the universe is acceleratedly expanding with time and dominated by dark/phantom energy and an electromagnetic field comparable to the cosmological lambda. The variations of the gravitational constant time agree with several phenomenological theories including the entropic and holographic principle. The final fate of an asymptotically static universe was found also to be a plausible scenario in the model discussed.

Non-minimal unimodular inflation

We study an extension of the unimodular cosmological inflation in the context of the non-minimal coupling of a generic scalar field with gravitational sector. We consider the non-minimal coupling of the scalar field and gravity as the only source of energy–momentum tensor in this setup. Without introducing new particles other than those already existing in electroweak theory, the generic scalar field’s non-minimal coupling is responsible for the generation of the seeds of perturbations for structure formation and the observed Cosmic Microwave Background anisotropies in this scenario. We calculate inflation parameters in both the Jordan and Einstein frames, and then we study primordial spectral indices for slow-roll parameters in Einstein’s frame at the first and second orders. The numerical results of this model are consistent with the Planck2018 and BICEP/Keck joint data sets in some subspaces of the model parameters space. By considering a sufficient amount of inflation, we estimate the strength of the non-minimal coupling parameter, ξ, to find appropriate new constraints on the values of this parameter. By comparing the numerical values of the inflation observables in two frames and also with observation, we comment on the issue of frames in this framework.

Cosmological solutions of chameleon scalar field model

We investigate cosmological solutions of the chameleon model with a non-minimal coupling between the matter and the scalar field through a conformal factor with gravitational strength. By considering the spatially flat FLRW metric and the matter density as a non-relativistic perfect fluid, we focus on the matter-dominated phase and the late-time accelerated-phase of the universe. In this regard, we manipulate and scrutinize the related field equations for the density parameters of the matter and the scalar fields with respect to the e-folding. Since the scalar field fluctuations depend on the background and the field equations become highly non-linear, we probe and derive the governing equations in the context of various cases of the relation between the kinetic and potential energies of the chameleon scalar field, or indeed, for some specific cases of the scalar field equation of state parameter. Thereupon, we schematically plot those density parameters for two different values of the chameleon non-minimal coupling parameter, and discuss the results. In the both considered phases, we specify that, when the kinetic energy of the chameleon scalar field is much less than its potential energy (i.e., when the scalar field equation of state parameter is ≃-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\simeq - 1 $$\\end{document}), the behavior of the chameleon model is similar to the ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda CDM$$\\end{document} model. Such compatibility suggests that the chameleon model is phenomenologically viable and can be tested with the observational data.

Inflationary Cosmology with a scalar-curvature mixing term [formula omitted

We use the PLANCK 2018 and the WMAP data to constraint inflation models driven by a scalar field ϕ in the presence of the non-minimal scalar-curvature mixing term 12ξRϕ2. We consider four distinct scalar field potentials ϕpe−λϕ,(1−ϕp)e−λϕ,(1−λϕ)p and αϕ21+αϕ2 to study inflation in the non-minimal gravity theory. We calculate the potential slow-roll parameters, predict the scalar spectral index ns, tensor-to-scalar ratio r, leading and higher order non-Gaussianity parameters (fNL,τNL and gNL) and the amplitude of the scalar spectrum As in the parameter space (λ,p,α) of the potentials corresponding to different values of the non-minimal coupling parameter ξ. We have compared our results with the ones existing in the literature, and this indicates the present status of non-minimal inflation after the release of the PLANCK 2018 data.

Hybrid metric-Palatini Higgs inflation

We propose an extension of the Higgs inflation to the hybrid metric-Palatini gravity, where we introduce non-minimal couplings between Higgs and both the metric-type and the Palatini-type Ricci scalars. We study the inflationary phenomenology of our model and find that slow-roll inflation can be realized in the large-field regime, giving the observationally favored predictions. In particular, the scalar spectral index exhibits an attractor behavior to n s ∼ 0.964, while the tensor-to-scalar ratio can take an arbitrary value depending on the non-minimal coupling parameters, with the metric-Higgs limit r ∼ 10-3 being the maximum. We also investigate the unitarity property of our model. As the ultraviolet (UV) cutoff as a low-energy effective field theory (EFT) of this model is significantly lower than the Planck scale due to a strong curvature of field-space, we consider a possible candidate of UV-extended theories with an additional scalar field introduced so as to flatten the field-space in five-dimension. While the field-space can be flatten completely and this approach can lead to a weakly-coupled EFT, we gain an implication that Planck-scale EFT can be only realized in the limit of metric-Higgs inflation. We also discuss generalizations of the model up to mass-dimension four.

On the non-minimal coupling of magnetic fields with gravity in Schwarzschild spacetime

In this work we study the effects of non-minimal coupling between electromagnetism and gravity, which are motivated by quantum effects such as vacuum polarization. We investigate the modification of both asymptotically dipole and uniform magnetic fields around a Schwarzschild black hole that come as the result of non-minimal coupling. While in both cases the magnetic field gets enhanced or suppressed with respect to the case of minimal coupling, depending on the sign of non-minimal coupling parameter, in the case of a background uniform magnetic field the direction of the magnetic field also alters in the vicinity of the black hole horizon. We have discussed the possible astrophysical and cosmological sources for which the vacuum polarization may be at play, while also discussing the observational effects, in particular the possibility of synchrotron radiation from the vicinity of a black hole. We conclude that such observations could be used to constrain the value of the non-minimal coupling parameter.

Anti-de Sitter neutron stars in the theory of gravity with nonminimal derivative coupling

We consider neutron star configurations in the scalar-tensor theory of gravity with the coupling between the kinetic term of a scalar field and the Einstein tensor (such the model is a subclass of Horndeski gravity). Neutron stars in this model were studied earlier for the special case with a vanishing “bare” cosmological constant, Λ0 = 0, and a vanishing standard kinetic term, α = 0. This special case is of interest because it admits so-called stealth configuration, i.e. vacuum configuration with nontrivial scalar field and the Schwarzschild metric. However, generally one has Λ0 ≠ 0 and α ≠ 0 and in this case a vacuum configuration is represented as an asymptotically anti-de Sitter (AdS) black hole solution with the nontrivial scalar field. We construct neutron star configurations in this general case and show that resulting diagrams describing the relation between mass and radius of the star essentially differ from those obtained in GR or the particular model with α = Λ0 = 0. Instead, the mass-radius diagrams are similar to those obtained for so-called bare strange stars when a star radius decreases monotonically with decreasing mass. We show also that neutron stars in the theory of gravity with nonminimal derivative coupling are more compact comparing to those in GR or the particular model with α = Λ0 = 0 and suggest a way to estimate possible values of the parameter of nonminimal coupling ℓ. At last, using the Regge-Wheeler method, we discuss briefly the stability of obtained neutron star configurations.

Magnetogenesis in Higgs-Starobinsky inflation

In the framework of mixed Higgs-Starobinsky inflation, we consider the generation of Abelian gauge fields due to their nonminimal coupling to gravity (in two different formulations of gravity -- metric and Palatini). We couple the gauge-field invariants $F_{\mu\nu}F^{\mu\nu}$ and $F_{\mu\nu}\tilde{F}^{\mu\nu}$ to an integer power of the scalar curvature $R^n$ in Jordan frame and, treating these interactions perturbatively, switch to the Einstein frame where they lead to effective kinetic and axial couplings between gauge fields and inflaton. We determine the power spectra, energy densities, correlation length, and helicality of the generated gauge fields for different values of the nonminimal coupling constants and parameter $n$. We analytically estimate the spectral index $n_{B}$ of the magnetic power spectrum and show that for $n>1$ it is possible to get the scale-invariant or even red-tilted spectrum for a wide range of modes that implies larger correlation length of the generated fields. On the other hand, the magnitude of these fields typically decreases in time becoming very small in the end of inflation. Thus, it is difficult to obtain both large magnitude and correlation length of the gauge field in the frame of this model.

Vector boson oscillator in the near-horizon of the BTZ black hole

We investigate the interaction of a generalized vector boson oscillator with the near-horizon geometry of the Bañados–Teitelboim–Zanelli (BTZ) black hole and try to determine the corresponding quasibound state frequencies. To do this, we seek an analytical solution of the relativistic vector boson equation, derived as an excited state of Zitterbewegung, with Cornell-type non-minimal coupling in the near-horizon geometry of the BTZ black hole. The vector boson equation includes a symmetric spinor of rank two and this allows to obtain an analytical solution of the corresponding equation. By imposing appropriate boundary conditions, we show that it is possible to arrive at a relativistic frequency (ω) expression in the form of . Our results show that real () and damped () oscillations depend on the parameters of the background geometry, coefficients of the non-minimal coupling and strength of the oscillator. This allows us to analyse the effects of both non-minimal coupling and spacetime parameters on the evolution of the considered vector field. We discuss the results in details and see also that the background is stable under the perturbation field in question.

Exact scalar (quasi-)normal modes of black holes and solitons in gauged SUGRA

In this paper we identify a new family of black holes and solitons that lead to the exact integration of scalar probes, even in the presence of a non-minimal coupling with the Ricci scalar which has a non-trivial profile. The backgrounds are planar and spherical black holes as well as solitons of SU (2) × SU (2) mathcal{N} = 4 gauged supergravity in four dimensions. On these geometries, we compute the spectrum of (quasi-)normal modes for the non-minimally coupled scalar field. We find that the equation for the radial dependence can be integrated in terms of hypergeometric functions leading to an exact expression for the frequencies. The solutions do not asymptote to a constant curvature spacetime, nevertheless the asymptotic region acquires an extra conformal Killing vector. For the black hole, the scalar probe is purely ingoing at the horizon, and requiring that the solutions lead to an extremum of the action principle we impose a Dirichlet boundary condition at infinity. Surprisingly, the quasinormal modes do not depend on the radius of the black hole, therefore this family of geometries can be interpreted as isospectral in what regards to the wave operator non-minimally coupled to the Ricci scalar. We find both purely damped modes, as well as exponentially growing unstable modes depending on the values of the non-minimal coupling parameter. For the solitons we show that the same integrability property is achieved separately in a non-supersymmetric solutions as well as for the supersymmetric one. Imposing regularity at the origin and a well defined extremum for the action principle we obtain the spectra that can also lead to purely oscillatory modes as well as to unstable scalar probes, depending on the values of the non-minimal coupling.

Non-minimally coupled massive scalar field configurations supported by charged reflecting shells: Analytic treatment in the weak coupling regime

The physical and mathematical properties of bound-state matter configurations which are made of massive scalar fields with a non-trivial (non-minimal) coupling to the electromagnetic field of a central charged reflecting shell of radius Rs are studied analytically. In particular, we explicitly prove that the Klein-Gordon wave equation for the composed charged-reflecting-shell-nonminimally-coupled-linearized-massive-scalar-field system is amenable to an analytical treatment in the dimensionless weak coupling regime (or equivalently, in the dimensionless small-mass regime) μαQ≪1 (here μ,Q, and α are respectively the proper mass of the non-minimally coupled scalar field, the electric charge of the spherically symmetric supporting shell, and the non-minimal coupling parameter of the composed Maxwell-scalar theory). We derive a remarkably compact resonance formula {μ(α,Q,Rs;n)}n=1n=∞ for the allowed masses of the supported spatially regular scalar fields in the composed charged-shell-nonminimally-coupled-massive-scalar-field bound-state configurations.

Quasinormal modes of a massive scalar field nonminimally coupled to gravity in the spacetime of self-dual black hole

In this work, we investigate the quasinormal modes for a massive scalar field with a nonminimal coupling with gravity in the spacetime of a loop quantum black hole, known as the self-dual black hole. In this way, we have calculated the characteristic frequencies using the 3rd order WKB approach, where we can verify a strong dependence with the mass of scalar field, the parameter of nonminimal coupling with gravity, and parameters of the loop quantum gravity. From our results, we can check that the self-dual black hole is stable under the scalar perturbations when assuming small values for the parameters. Also, such results tell us that the quasinormal modes assume different values for the cases where the mass of field is null and the nonminimal coupling assumes xi =0 and xi =1/6, i.e., a possible breaking of the conformal invariance can be seen in the context of loop quantum black holes.

Chaotic inflation and reheating in generalized scalar-tensor gravity

In the present work, we study slow-roll inflation in scalar-tensor gravity theories in the presence of both the non-minimal coupling between the scalar field and curvature, and the Galileon self-interaction of the scalar field. Furthermore, we give predictions for the duration of reheating as well as for the reheating temperature after inflation. After working out the expressions for the power spectra of scalar and tensor perturbations in the case of a general non-minimal coupling function that depends solely on the scalar field and a general scalar potential, we focus on the special cases of the power-law coupling function and chaotic quadratic inflation. Thus, under the slow-roll approximation we confront the predictions of the model with the current PLANCK constraints on the spectral index n s and the tensor-to-scalar ratio r using the n s-r plane. We found that the combination of the non-minimal coupling and Galileon self-interaction effects allows us to obtain better results for r than in the case in which each effect is considered separately. Particularly, we obtained that the predictions of the model are in agreement with the current observational bounds on n s and r within the 95 % C.L region and also slightly inside the 68 % C.L region. Also, we investigate the oscillatory regime after the end of inflation by solving the full background equations, and then we determine the upper bound for the Galileon and non-minimal coupling parameters under the condition that the scalar field oscillates coherently during reheating. Finally, after approximating reheating by a constant equation of state, we derive the relations between the reheating duration, the temperature at the end of reheating, its equation of state, and the number of e-folds of inflation and then we relate them all to the inflationary observables.

Palatini Higgs inflation and the refined dS conjecture

The refined de Sitter derivative conjecture provides constraints to potentials that are low energy effective theories of quantum gravity. It can give direct bounds on inflationary scenarios and determine whether the theory is in the Landscape or the Swampland. Any infationary model can be checked by these conditions and non-minimally coupled scalar field theory is not an exception. We consider the Palatini Higgs inflation scenario taking the refined de Sitter derivative conjecture into account. According to the latest cosmological observations from Planck 2018, BICEP2+Keck and the bound of non-minimal coupling parameter {\xi}, we suggest that if the refined dS conjecture does indeed hold, then the Palatini Higgs inflation model cannot be the low energy effective theory of a consistent quantum gravity theory since the two parameters c1 and c2 are much smaller than order 1, which is inconsistent with the refined dS conjecture. Therefore we suggest that it is in the Swampland.

Primordial Black Holes Formation and Secondary Gravitational Waves in Nonminimal Derivative Coupling Inflation

Abstract We study the possibility of the primordial black holes (PBHs) formation with the aim of finding a considerable fraction of dark matter (DM), using the gravitationally enhanced friction mechanism which arises from a nonminimal derivative coupling between the scalar field and the gravity. Assuming the nonminimal coupling parameter as a special function of the scalar field and considering the potential of natural inflation, we find three parameter sets that produce a period of ultra slow-roll inflation. This leads to sufficiently large enhancement in the curvature power spectra to form PBHs. We show that under the gravitationally enhanced friction mechanism, PBHs with a mass around  10 − 12 M ⊙ can constitute around 96% of the total DM and so this class of PBHs can be taken as a great candidate for DM. We further study the secondary gravitational waves (GWs) in our setting and show that our model predicts the peak of the present fractional energy density as ΩGW0 ∼ 10−8 at different frequencies for all the three parameter sets. This value lies well inside the sensitivity region of some GWs detectors at some frequencies, and therefore the observational compatibility of our model can be appraised by the data from these detectors.

Regular nonminimal magnetic black hole as a source of quasiperiodic oscillations

We study the properties of the spacetime around a regular nonminimal magnetic black hole (BH) together with the dynamics of the neutral, magnetized, and magnetically charged particles in its vicinity. The dependence of the values of curvature invariants and the outer event horizon corresponding to the extreme charge of the BH from the coupling parameter are studied in detail. Our study of the test particle motion shows that the innermost stable circular orbit (ISCO) radius decreases with the increase of the magnetic charge of the nonminimal regular magnetic BH. We show that the increase of the ISCO radius with the increase of the coupling parameter is due to the decrease of the extreme value of the BH charge. In particular, when the coupling parameter $q\ensuremath{\rightarrow}\ensuremath{\infty}$ the ISCO radius tends to the value ${r}_{\mathrm{ISCO}}=4.5M$. The effect of the magnetic charge parameter on ISCO radius can mimic the effect due to the spin parameter of the rotating Kerr BH, and the mimicking values of the spin parameter decreases with the increase of the coupling parameter. We also explore the possible mimicking of the parameters through the observations of twin-peak quasiperiodic oscillations (QPOs). Our analysis shows that the Reissner-Nordstr\"om (RN) charge can mimic the spin parameter of the Kerr BH up to $a/M\ensuremath{\simeq}0.51$ provided that there is the same relation between the upper and lower frequencies of the twin-peak QPOs. On the other hand, the nonminimal regular magnetic BH coupling parameter may mimic the spin parameter up to $a/M\ensuremath{\simeq}0.215$ in the relativistic precession model.

The spin-one DKP equation with a nonminimal vector interaction in the presence of minimal uncertainty in momentum

In this work, we consider the relativistic Duffin–Kemmer–Petiau equation for spin-one particles with a nonminimal vector interaction in the presence of minimal uncertainty in momentum. By using the position space representation, we exactly determine the bound-states spectrum and the corresponding eigenfunctions. We discuss the effects of the deformation and nonminimal vector coupling parameters on the energy spectrum analytically and numerically.

Gravitational waves from inflation with antisymmetric tensor field

We build upon the past studies of inflation with rank-2 antisymmetric tensor field, including here the tensor perturbations to metric. We perform a comprehensive analysis of the background dynamics of our model in the presence of non-minimal coupling curvature terms R and Rμ ν. We find appropriate conditions on the nonminimal coupling parameters to satisfy the constraint of speed of propagation of gravitational waves. Including the tensor perturbations, the model is found to be free from ghost instabilities with minimal constraints on the parameters. We also study the evolution of gravitational waves, calculate the power spectrum and the tensor spectral index.

Non-minimal M-flation

We show how in a matrix inflationary model in which there is a non-minimal coupling between the matrix inflatons and gravity — hence dubbed Non-M-flation — some of the disadvantages of the minimal model can be avoided. In particular, the number of D3 branes can be reduced substantially to underset{sim }{<}mathcal{O}(100) , which can alleviate the “potential” backreaction problem of large number of D3 branes on the background geometry. This is achieved by values of non-minimal coupling of order few hundred, which is much smaller than that of Higgs Inflation. The prediction of the model in the symmetry breaking part of the potential, which is a local attractor and can support eternal inflation, is compatible with the latest PLANCK results. In contrast to the minimal model, the spectator fields can partially or completely reheat the universe, depending on the symmetry-breaking vacuum expectation value and the non-minimal coupling parameter. We also comment on how the presence of gauge species keep the UV cutoff at around the Planck scale in the Einstein frame and, in contrast to the Higgs inflation, the problem of field displacements beyond the cutoff does not occur.

Charged reflecting shells supporting non-minimally coupled massless scalar field configurations

We study analytically the physical and mathematical properties of spatially regular massless scalar field configurations which are non-minimally coupled to the electromagnetic field of a spherically symmetric charged reflecting shell. In particular, the Klein–Gordon wave equation for the composed charged-reflecting-shell-nonminimally-coupled-linearized-massless-scalar-field system is solved analytically. Interestingly, we explicitly prove that the discrete resonance spectrum {R_{text {s}}(Q,alpha ,l;n)}^{n=infty }_{n=1} of charged shell radii that can support the non-minimally coupled massless scalar fields can be expressed in a remarkably compact form in terms of the characteristic zeros of the Bessel function (here Q, alpha , and l are respectively the electric charge of the central supporting shell, the dimensionless non-minimal coupling parameter of the Maxwell-scalar theory, and the angular harmonic index of the supported scalar configuration).