Self-interaction Potential Research Articles

Covariant formulation of refracted gravity

We propose a covariant formulation of refracted gravity (RG), which is a classical theory of gravity based on the introduction of gravitational permittivity – a monotonic function of the local mass density – in the standard Poisson equation. Gravitational permittivity mimics dark matter phenomenology. The covariant formulation of RG (CRG) that we propose belongs to the class of scalar-tensor theories, where the scalar fieldφhas a self-interaction potential 𝒱(φ) = − Ξφ, with Ξ being a normalization constant. We show that the scalar field is twice the gravitational permittivity in the weak-field limit. Far from a spherical source of densityρs(r), the transition between the Newtonian and the RG regime appears below the acceleration scaleaΞ = (2Ξ − 8πGρ/φ)1/2, withρ = ρs + ρbgandρbgbeing an isotropic and homogeneous background. In the limit 2Ξ ≫ 8πGρ/φ, we obtainaΞ ∼ 10−10m s−2. This acceleration is comparable to the accelerationa0originally introduced in MOdified Newtonian Dynamics (MOND). From CRG, we also derived the modified Friedmann equations for an expanding, homogeneous, and isotropic universe. We find that the same scalar fieldφthat mimics dark matter also drives the accelerated expansion of the Universe. From the stress-energy tensor ofφ, we derived the equation of state of a redshift-dependent effective dark energywDE = pDE/ρDE. Current observational constraints onwDEand distance modulus data of type Ia supernovae suggest that Ξ has a comparable value to the cosmological constant Λ in the standard model. Since Ξ also plays the same role of Λ, CRG suggests a natural explanation of the known relationa0 ∼ Λ1/2. CRG thus appears to describe both the dynamics of cosmic structure and the expanding Universe with a single scalar field, and it falls within the family of models that unify the two dark sectors, highlighting a possible deep connection between phenomena currently attributed to dark matter and dark energy separately.

Cosmology of a Chaplygin Gas Model Under f(T) Gravity and Evolution of Primordial Perturbations

This paper reports a detailed study of generalized Chaplygin gas (GCG) with power law form of scale factor and truncated form of the scale factor using binomial expansion in both interacting and non-interacting scenarios along with its cosmological consequences, studied in terms of equation of state (EoS) parameter. In the non-interacting scenario, the EoS parameter behaves as quintessence in both forms of the scale factor. In the interacting scenario, the EoS parameter behaves as phantom and for the truncated form of the scale factor, it violates the constraints of the positive parameter α. The cosmological implementation of GCG interacting with pressureless dark matter is investigated in the framework of f(T) modified gravity, where T is the torsion scalar in teleparallelism. The interaction term is directly proportional to the GCG density with positive coupling constant. In f(T) gravity, the EoS is behaving like phantom. The stability of the reconstructed model is investigated and it is found to be stable against small gravitational perturbations, i.e., the squared speed of sound is non-negative and an increasing function of cosmic time t. We have observed that our reconstructed f(T) model satisfies one of the sufficient conditions of a realistic reconstructed model and it is consistent with the CMB constraints and primordial nucleosynthesis. Cosmology of primordial perturbations has also been analyzed and the self-interacting potential has been found to be an increasing function of cosmic time t.

Constraining resonant dark matter self-interactions with strong gravitational lenses

We devise a method to constrain self-interacting dark matter (SIDM) from observations of quadruply imaged quasars, and apply it to five self-interaction potentials with a long-range dark force. We consider several SIDM models with an attractive potential that allows for the formation of quasibound states, giving rise to resonant features in the cross section localized at particular velocities below $50\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. We propose these resonances, which amplify or suppress the cross section amplitude by over an order of magnitude, accelerate or delay the onset of core collapse in low-mass dark matter halos, and derive constraints on the timescale for core collapse for the five interaction potentials we consider. Our data strongly disfavors scenarios in which a majority of halos core collapse, with the strongest constraints obtained for cross section strengths exceeding $100\text{ }\text{ }{\mathrm{cm}}^{2}\text{ }{\mathrm{g}}^{\ensuremath{-}1}$ at relative velocities below $30\text{ }\text{ }\mathrm{km}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. This work opens a new avenue to explore the vast landscape of possible SIDM theories.

Symmetry restoration in the vicinity of neutron stars with a nonminimal coupling

We propose a new model of scalarized neutron stars (NSs) realized by a self-interacting scalar field ϕ nonminimally coupled to the Ricci scalar R of the form F(ϕ)R. The scalar field has a self-interacting potential and sits at its vacuum expectation value ϕv far away from the source. Inside the NS, the dominance of a positive nonminimal coupling over a negative mass squared of the potential leads to a symmetry restoration with the central field value ϕc close to 0. This allows the existence of scalarized NS solutions connecting ϕv with ϕc whose difference is significant, whereas the field is located in the vicinity of ϕ=ϕv for weak gravitational stars. The Arnowitt-Deser-Misner mass and radius of NSs as well as the gravitational force around the NS surface can receive sizable corrections from the scalar hair, while satisfying local gravity constraints in the Solar system. Unlike the original scenario of spontaneous scalarization induced by a negative nonminimal coupling, the catastrophic instability of cosmological solutions can be avoided. We also study the cosmological dynamics from the inflationary epoch to today and show that the scalar field ϕ finally approaches the asymptotic value ϕv without spoiling a successful cosmological evolution. After ϕ starts to oscillate about the potential minimum, the same field can also be the source for cold dark matter.

Inspiral gravitational waveforms from compact binary systems in Horndeski gravity

In a subclass of Horndeski theories with the speed of gravity equivalent to that of light, we study gravitational radiation emitted during the inspiral phase of compact binary systems. We compute the waveform of scalar perturbations under a post-Newtonian expansion of energy-momentum tensors of pointlike particles that depend on a scalar field. This scalar mode not only gives rise to breathing and longitudinal polarizations of gravitational waves, but it is also responsible for scalar gravitational radiation in addition to energy loss associated with transverse and traceless tensor polarizations. We calculate the Fourier-transformed gravitational waveform of two tensor polarizations under a stationary phase approximation and show that the resulting waveform reduces to the one in a parametrized post-Einsteinian (ppE) formalism. The ppE parameters are directly related to a scalar charge in the Einstein frame, whose existence is crucial to allow the deviation from general relativity (GR). We apply our general framework to several concrete theories and show that a new theory of spontaneous scalarization with a higher-order scalar kinetic term leaves interesting deviations from GR that can be probed by the observations of gravitational waves emitted from neutron star--black hole binaries. If the scalar mass exceeds the order of typical orbital frequencies $\ensuremath{\omega}\ensuremath{\simeq}{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{eV}$, which is the case for a recently proposed scalarized neutron star with a self-interacting potential, the gravitational waveform practically reduces to that in GR.

Late time cosmology in f(R,{{mathcal {G}}}) gravity with exponential interactions

Cosmological models with f(R) modified gravity are significant to investigate the present and late-time behavior of the Universe. The dynamics of the Universe is studied in the framework of f(R)= R + gamma R^2- lambda left( frac{R}{3m_s^2} right) ^{delta } gravity (gamma , lambda , delta are arbitrary constants) with a coupled Gauss–Bonnet (GB) term in the gravitational action and estimate the constraints on the model parameters as well as the late time behavior of the Universe. In this case, the coupled Gauss–Bonnet term is coupled with a free scalar field in the presence of interacting fluid. In addition, we investigate the same for a different form of gravity f(R)=R, where the coupled GB term is coupled with a scalar field in a self-interacting potential.

Fermionic tachyons as a source of dark energy

We investigate a model for the universe based on the self-interacting fermionic tachyon field. We have shown that by devising a self-interaction potential of a proper form, the fermionic tachyon field is capable of producing an accelerating expansion. At late times, this potential tends to a constant value; this behavior is consistent with the cosmological constant. In this way, the introduced fermionic tachyon field can be interpreted as the source of dark energy.

Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology

The Hamiltonian constraint of scalar-tensor theories (STTs) in the Jordan frame is quantised using three quantisation prescriptions in loop quantum cosmology, from which we obtain three different effective Hamiltonian constraints. The corresponding effective equations of motion derived from these effective Hamiltonian constraints turn out to be drastically different. The implications of each set of effective equations of motion are discussed in detail. In the latter half of this paper, as a concrete example, we study the effective dynamics of a specific model of STTs with the non-minimal coupling function and self-interacting quartic potential. Using numerical results, we find different features for different effective dynamics. Moreover, it is also found that the spacetime singularity is absent and the cosmological bounce exists in each effective dynamics of this model.

Black bounces, wormholes, and partly phantom scalar fields

Simpson and Visser recently proposed a phenomenological way to avoid some kinds of space-time singularities by replacing a parameter whose zero value corresponds to a singularity (say, $r$) with the manifestly nonzero expression $r(u) = \sqrt{u^2 + b^2}$, where $u$ is a new coordinate, and $b =$ \const $>0$. This trick, generically leading to a regular minimum of $r$ beyond a black hole horizon (called a "black bounce"), may hopefully mimic some expected results of quantum gravity, and was previously applied to regularize the Schwarzschild, Reissner-Nordstr\"om, Kerr and some other metrics. In this paper it is applied to regularize the Fisher solution with a massless canonical scalar field in general relativity (resulting in a traversable wormhole) and a family of static, spherically symmetric dilatonic black holes (resulting in regular black holes and wormholes). These new regular metrics represent exact solutions of general relativity with a sum of stress-energy tensors of a scalar field with a nonzero self-interaction potential and a magnetic field in the framework of nonlinear electrodynamics with a Lagrangian function $L(F)$, $F = F_{\mu\nu} F^{\mu\nu}$. A novel feature in the present study is that the scalar fields involved have "trapped ghost" properties, that is, are phantom in a strong-field region and canonical outside it, with a smooth transition between the regions. It is also shown that any static, spherically symmetric metric can be obtained as an exact solution to the Einstein equations with the stress-energy tensor of the above field combination.

Erratum: Analytical scalar field solutions on Lifshitz spacetimes [Phys. Rev. D 105 , 016001 (2022)

In this work, we investigate the existence of analytic solutions of static scalar fields on Lifshitz spacetimes. We evade Derrick's theorem on curved spacetimes by breaking general covariance and use first-order formalism to obtain solutions with finite energy related to the time-translational invariance of the background geometry along with the energy-momentum tensor of the model. We show that such solutions exist and are stable in systems where the Lifshitz background geometry is fixed and the self-interaction potential of the scalar field explicitly depends on the radial coordinate present in the metric.

Energy conditions in a modified Brans-Dicke theory

We consider a modified version of Brans-Dicke theory (MBDT) in four dimensions (4D) obtained by applying the induced matter method of Wesson to a 5D generalized Brans-Dicke theory. In 5D the model consists of pure vacuum, with no self-interacting potential, except for a scalar field. Following Wesson’s protocol, we group geometric terms in the 5D Einstein tensor arising from the extra dimension, move them to the other side of the generalized field equations, and identify them as the energy-momentum of the induced matter in 4D. Thus the extra dimension in 5D leads naturally to an effective matter field in 4D. Constraining the 5D geometry to be a generalization of the anisotropic Bianchi type I universe model first studied by Kasner, we derive the induced energy-momentum in MBDT and apply it to the investigation of energy conditions. The specified induced energy-momentum of that MBDT model consists of the energy density and directional pressure which indicate the anisotropy of the universe. We discuss the energy conditions and their bounds in the MBDT with such an induced imperfect fluid, with an eye toward a realistic model of the present-day universe, and consider the large-scale behavior of that spatially homogeneous and anisotropic model. We discuss how the energy conditions would be satisfied or violated in the context of MBDT, with the aim of providing a feasible description of the universe in the current era.

Accelerated Universe from Modified Chaplygin Gas and Tachyonic Fluid

A cosmological model with an exotic fluid is investigated. We show that the equation of state of this “modified Chaplygin” gas can describe the current accelerated expansion of the universe. We then reexpress it as FRW cosmological model containing a scalar field ϕ and find its self-interacting potential. Moreover motivated by recent works on tachyon field theory, a map for this exotic fluid as a normal scalar field ϕ with Lagrangian Lϕ=ϕ˙22−U(ϕ) to the tachyonic field T with Lagrangian LT=−V(T)1−T˙2 is obtained.

REVERSE-ENGINEERED DBI-ESSENCE FIELD IN THE RAINBOW GRAVITY

The current astrophysical data sets have implied that our universe has recently entered in an accelerated expansion phase. In literature, it is commonly thought that the late-time speedy enlargement behaviour is caused by mysterious dark contents (dark matter, dark energy and dark radiation) that cannot be observed directly. Although Einstein's General Theory of Relativity has provided very successful theoretical explanations and predictions, it cannot explain the aforementioned unusual nature of the cosmos. This situation has led scientists to try to create a new theoretical model for the nature of dark contents. The cosmological constant, scalar fields, unified energy densities, additional dimension idea and modified gravity theories are among the prominent point of views. In this research, mainly, the reverse-engineering method is taken into account in the rainbow gravity formalism for the DBI-essence scalar field dark energy model. As it is known, scalar field models can be introduced with the help of some fundamental physics theories, but these theories do not provide a direct way to write explicitly the self-interaction potentials that we encounter in scalar field models. Therefore, the reverse-engineering method used in this research takes significant role while writing the self-interaction potential of a scalar field model.

Non-asymptotically flat Einstein-Scalar black hole

Exact solutions in general relativity and other theories in physics are important. One of such theories is the Einstein-Scalar theory. We present an exact class of solutions in the Einstein-Scalar theory with a specific nonlinear self-interacting potential. The potential admits a local minimum and a local maximum in general configuration. The solutions include AdS and dS black hole and non-black hole spacetimes. The scalar field is regular on and outside the horizon and asymptotically vanishes when We also study the thermal stability of the black hole solution and it is shown that the black hole is thermally stable for a certain interval of the radius of the horizon.

Non-minimal coupled warm inflation with quantum-corrected self-interacting inflaton potential

In this work, we investigate the non-minimally coupled scenario in the context of warm inflation with quantum-corrected self-interacting potential. We transform the potential in the Jordan frame to the Einstein frame and consider a dissipation parameter of the form Gamma = C_{T}T with C_T being a coupling parameter. We focus on the strong regime of which the interaction between inflaton and radiation fluid has been taken into account. We compute inflationary observables and constrain the parameters of our model using current Planck 2018 data. With the sizeable number of e-folds and proper choices of parameters, we discover that allowed values of C_T lie in the range 0.014lesssim C_{T}lesssim 0.020 in which the predictions are in good agreement with the latest Planck 2018 results at the 2,sigma confident level.

Spherical black holes with minimally coupled scalar cloud/hair in Einstein–Born–Infeld gravity

Previous studies showed that, in the presence of a simple and well-motivated self-interaction scalar potential, asymptotically flat and spherical black holes can carry minimally coupled and charged scalar cloud/hair in Einstein–Maxwell gravity. We extend these studies to Einstein–Born–Infeld gravity to consider the effect of nonlinearity of the electromagnetic field. Series of spherical cloudy/hairy black hole solutions are constructed numerically. Results show that increasing the Born–Infeld coupling constant b will make the domain of existence of the solution shrink or even disappear when b is large enough. This implies that, competing with the gravitation, nonlinearity of the electromagnetic field will make the formation of scalar cloud/hair harder or even impossible.

Exploring the electronic and optical anisotropy of quasi-one-dimensional ternary chalcogenide CrSbSe3: a DFT study

The anisotropy of the electronic and optical properties of the quasi-one-dimensional ternary transition metal chalcogenide CrSbSe3 is investigated using density functional theory (DFT) including the on-site Coulomb self-interaction potential (DFT + U) and spin-orbit interaction. The compound is an indirect bandgap semiconductor with bandgap of 0.58 eV. Effective masses and charge recombination rates along different directions show appreciable anisotropy, indicating the possibility of sensor applications. CrSbSe3 exhibits satisfactorily high carrier mobility and charge recombination rates along all directions, making it suitable for solar and photovoltaic applications. The Se-p and Cr-d orbitals contribute to the DOS in the valence band, while DOS contribution to the conduction band bottom comes mainly from Sb-p and Cr-d orbitals. Simulated XPS and HAXPES show that for soft x-rays, the peak in the low binding energy is due to the electron emission from Se-p and Cr-d orbitals while the peak in the high binding energy is due to the electron emission from Cr-d and Se-s orbitals. For hard x-rays, the relative intensity of the low binding energy peak decreases in comparison to the high binding energy peak, indicating enhanced electron emission from Se-s orbitals at higher energy x-rays. CrSbSe3 possesses large anisotropy in optical parameters such as refractive index, optical absorption, reflectivity, optical conductivity and optical extinction. The birefringence and dichroism are large in the IR, visible and near UV regions, with a giant birefringence equal to 0.56 at 650 nm and dichroism equal to 0.57 at 550 nm. The electron energy loss function is anisotropic for high energetic electrons, while for electrons below 4 eV it is isotropic. CrSbSe3 is an ideal material for photovoltaic, sensor and other optoelectronic applications as it possesses a bandgap of 0.58 eV, large optical anisotropy, high values of dielectric constant, refractive index, absorption coefficient and extinction coefficient.

Mass gap for a monopole interacting with different nonlinear spinor fields

We study the properties of the mass gap for monopole solutions in SU(2) Yang-Mills theory with a source of the non-Abelian gauge field in the form of a spinor field described by the nonlinear Dirac equation. Different types of nonlinearities parameterized by the parameter λ are under consideration. It is shown that for the range of values of this parameter studied in the present paper the value of the mass gap depends monotonically on this parameter, and the position of the mass gap does not practically depend on λ. In the present paper we study the dependence of the size of a mass gap, its position, etc., on the value of a parameter describing the nonlinear self-interaction potential of the spinor field. By the term a position of the mass gap, we mean the value of the frequency E, for which the energy spectrum has a minimum. It is of interest to note that the position of the mass gap E,  does not practically depend on the nonlinearity parameter λ. One can assume that in fact this is the case, and deviations from this value are related to errors in numerical calculations. It is of interest that the position of the mass gap does not practically depend on the value of the nonlinearity parameter, at least in the range of values of the spinor field nonlinearity parameter considered here.

Compact stars in the Einstein dark energy model

We investigate the properties of high density compact objects in a vector type theory, inspired by Einstein's 1919 theory of elementary particles, in which Einstein assumed that elementary particles are held together by gravitational as well as electromagnetic type forces. From a modern perspective, Einstein's theory can be interpreted as a vector type model, with the gravitational action constructed as a linear combination of the Ricci scalar, of the trace of the matter energy-momentum tensor, and of a massive self-interacting vector type field. To obtain the properties of stellar models we consider the field equations for a static, spherically symmetric system, and we investigate numerically their solutions for different equations of state of quark and neutron matter, by assuming that the self-interaction potential of the vector field either vanishes or is quadratic in the vector field potential. We consider quark stars described by the MIT bag model equation of state and in the Color Flavor Locked phase, as well as compact stars consisting of a Bose-Einstein Condensate of neutron matter, with neutrons forming Cooper pairs. Constant density stars, representing a generalization of the Interior Schwarzschild solution of general relativity, are also analyzed. Also, we consider the Douchin-Haensel (SLy) equation of state. The numerical solutions are explicitly obtained in both standard general relativity, and the Einstein dark energy model and an in depth comparison between the astrophysical predictions of these two theories are performed. As a general conclusion of our study, we find that for all the considered equations of state a much larger variety of stellar structures can be obtained in the Einstein dark energy model, including classes of stars that are more massive than their general relativistic counterparts.

Dynamical universality for random matrices

We establish an invariance principle corresponding to the universality of random matrices. More precisely, we prove the dynamical universality of random matrices in the sense that, if the random point fields mu ^N of N-particle systems describing the eigenvalues of random matrices or log-gases with general self-interaction potentials V converge to some random point field mu , then the associated natural mu ^N -reversible diffusions represented by solutions of stochastic differential equations (SDEs) converge to some mu -reversible diffusion given by the solution of an infinite-dimensional SDE (ISDE). Our results are general theorems that can be applied to various random point fields related to random matrices such as sine, Airy, Bessel, and Ginibre random point fields. In general, the representations of finite-dimensional SDEs describing N-particle systems are very complicated. Nevertheless, the limit ISDE has a simple and universal representation that depends on a class of random matrices appearing in the bulk, and at the soft- and at hard-edge positions. Thus, we prove that ISDEs such as the infinite-dimensional Dyson model and the Airy, Bessel, and Ginibre interacting Brownian motions are universal dynamical objects.