Scalar Field Potential Research Articles

Barrow holographic phantom

In the present work, we consider the recently proposed non-interacting Barrow holographic dark energy (Int. J. Geom. Methods Mod. Phys. 18(01) (2021) 2150014, doi:10.1142/S0219887821500146) with Hubble horizon as IR cutoff in a flat FLRW universe. We examine the evolutionary behavior of deceleration parameter and equation of state parameter for the different Barrow exponent [Formula: see text], and observe suitable behavior in the model. We choose [Formula: see text] in the non-interacting Barrow holographic dark energy which is explained by a phantom scalar field, then we exhibit the phantomic narration of the Barrow holographic dark energy with [Formula: see text] and reconstruct the potential of the phantom scalar field.

Variational symmetries and superintegrability in multifield cosmology

We consider a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker background space with an ideal gas and a multifield Lagrangian consisting of two minimally coupled scalar fields which evolve in a field space of constant curvature. For this cosmological model we classify the potential function for the scalar fields such that variational point symmetries exist. The corresponding conservation laws are calculated. Finally, analytic solutions are presented for specific functional forms of the scalar field potential in which the cosmological field equations are characterized as a Liouville integrable system by point symmetries. The free parameters of the cosmological model are constrained in order to describe analytic solutions for an inflationary epoch. Finally, stability properties of exact closed-form solutions are investigated. These solutions are scaling solutions with important physical properties for the cosmological model.

A Real Scalar Field Unifying the Early Inflation and the Late Accelerating Expansion of the Universe through a Quadratic Equation of State: The Vacuumon

In a previous paper we introduced a cosmological model describing the early inflation, the intermediate decelerated expansion, and the late accelerating expansion of the universe in terms of a single barotropic fluid characterized by a quadratic equation of state. We obtained a scalar field representation of this fluid and determined the potential V(ϕ) connecting the inflaton potential in the early universe to the quintessence potential in the late universe. This scalar field has later been called the ‘vacuumon’ by other authors, in the context of the Running Vacuum model. In this paper, we study how the scalar field potential is modified by the presence of other cosmic components such as stiff matter, black-body radiation, baryonic matter, and dark matter. We also determine the mass m and the self-interaction constant λ of the scalar field given by the second and fourth derivatives of the potential at its extrema. We find that its mass is imaginary in the early universe with a modulus of the order of the Planck mass MP=(ℏc/G)1/2=1.22×1019GeV/c2 and real in the late universe with a value of the order of the cosmon mass mΛ=(Λℏ2/c4)1/2=2.08×10−33eV/c2 predicted by string theory. Although our model is able to describe the evolution of the homogeneous background for all times, it cannot account for the spectrum of fluctuations in the early universe. Indeed, by applying the Hamilton–Jacobi formalism to our model of early inflation, we find that the Hubble hierarchy parameters and the spectral indices lead to severe discrepancies with the observations. This suggests that the vacuumon potential is just an effective classical potential that cannot be directly used to compute the fluctuations in the early universe. A fully quantum field theory may be required to achieve that goal. Finally, we discuss the connection between our model based on a quadratic equation of state and the Running Vacuum model which assumes a variation of the cosmological constant with the Hubble parameter.

Geodesic stability and quasinormal modes of non-commutative Schwarzschild black hole employing Lyapunov exponent

We study the dynamics of test particle and stability of circular geodesics in the gravitational field of a non-commutative geometry-inspired Schwarzschild black hole spacetime. The coordinate time Lyapunov exponent ( $$\lambda _{c}$$ ) is crucial to investigate the stability of equatorial circular geodesics of massive and massless test particles. The stability or instability of circular orbits is discussed by analyzing the variation of Lyapunov exponent with radius of these orbits for different values of non-commutative parameter ( $$\alpha $$ ). In the case of null circular orbits, the instability exponent is calculated and presented to discuss the instability of null circular orbits. Further, by relating parameters corresponding to null circular geodesics (i.e., angular frequency and Lyapunov exponent), the quasinormal modes for a massless scalar field perturbation in the eikonal approximation are evaluated and also visualized by relating the real and imaginary parts. The nature of scalar field potential, by varying the non-commutative parameter ( $$\alpha $$ ) and angular momentum of perturbation (l), is also observed and discussed.

Asymptotic observables and the swampland

We show that constraints on scalar field potentials and towers of light massive states in asymptotic limits of scalar field space (as posited by the de Sitter Conjecture and the Swampland Distance Conjecture, respectively) are correlated with the prospects for defining asymptotic observables in expanding FRW cosmologies. The observations of a "census taker" in an eternally inflating cosmology are further related to the question of whether certain domain walls satisfy a version of the Weak Gravity Conjecture. This suggests that answers to fundamental questions about asymptotic observables in cosmology could help shed light on the Swampland program, and vice versa.

Singularities in Inflationary Cosmological Models

Due to the accelerated expansion of the universe, the possibilities for the formation of singularities has changed from the classical Big Bang and Big Crunch singularities to include a number of new scenarios. In recent papers it has been shown that such singularities may appear in inflationary cosmological models with a fractional power scalar field potential. In this paper we enlarge the analysis of singularities in scalar field cosmological models by the use of generalised power expansions of their Hubble scalars and their scalar fields in order to describe all possible models leading to a singularity, finding other possible cases. Unless a negative scalar field potential is considered, all singularities are weak and of type IV.

Lorentzian vacuum transitions for anisotropic universes

The vacuum transition probabilities for anisotropic universes in the presence of a scalar field potential in the Wentzel-Kramers-Brillouin approximation are studied. We follow the work by Cespedes et al. [Phys. Rev. D 104, 026013 (2021)], which discuss these transitions in the isotropic context using the Wheeler-DeWitt equation, the Lorentzian Hamiltonian approach and the thin wall limit. First, we propose a general procedure to adapt their formalism to compute the decay rates for any superspace model. Then we apply it to compute the transition probabilities of an Friedmann-Lemaitre-Robertson-Walker (FLRW) metric with both positive and zero curvature, reproducing in this way one of the results obtained at Cespedes et al. We then proceed to apply the formalism to three anisotropic metrics, namely, Kantowski-Sachs, Bianchi III and biaxial Bianchi IX to compute the rate decays for these three cases. In the process we find that this method involves some conditions which relates the effective number of independent degrees of freedom resulting on all probabilities being described with only two independent variables. For the Bianchi III metric, we find that a general effect of anisotropy is to decrease the transition probability as the degree of anisotropy is increased, having as the isotropic limit the flat FLRW result.

Primordial perturbations in kinetically dominated regimes of general relativity and hybrid quantum cosmology

Scalar fields with an energy density dominated by its kinetic part may have played a relevant role in the very early stages of the Universe. Compared to the standard inflationary paradigm, they may lead to modifications in observable quantities, e.g. the anisotropies found in the cosmic microwave background. Kinetically dominated regimes arise in classical fast-roll scenarios as well as in quantum bouncing cosmologies. For instance, kinetic dominance is typical in interesting preinflationary phases of Loop Quantum Cosmology. In this work, we analyze the leading-order effects that the presence of a scalar field potential causes on the primordial cosmological perturbations in these kinetically dominated epochs. These effects can be grouped in two sets, namely, those that affect the effective mass of the perturbations and those that affect the choice of their vacuum state. The effective mass is modified directly by terms that include the potential, but also indirectly by the change in the background dynamics and the relation between the parameterization of these dynamics and the conformal time, usually employed to describe the evolution of the perturbations. On the other hand, away from de Sitter inflation, the Bunch-Davies state is no longer the most natural vacuum at all scales. Recent proposals suggest to modify it by carrying out certain Hamiltonian diagonalization with a suitable asymptotic behavior at large wavenumber scales. Both this diagonalization condition and the imposed asymptotic behavior depend on the effective mass of the perturbations, and therefore the selected vacuum state varies in the presence of the scalar field potential.

Einstein-æther scalar–tensor cosmology

We propose an Einstein-æther scalar–tensor cosmological model. In particular, in the scalar–tensor Action Integral, we introduce the æther field with æther coefficients to be functions of the scalar field. This cosmological model extends previous studies on Lorentz-violating theories. For a spatially flat Friedmann–Lemaître–Robertson–Walker background space, we write the field equations which are of second order with dynamical variables the scale factor and the scalar field. The physical evolution of the field equations depends upon three unknown functions which are related to the scalar–tensor coupling function, the scalar field potential, and the æther coefficient functions. We investigate the existence of analytic solutions for the field equations and the integrability properties according to the existence of linear in the momentum conservation laws. We define a new set of variables in which the dynamical evolution depends only upon the scalar field potential. Furthermore, the asymptotic behavior and the cosmological history are investigated where we find that the theory provides inflationary eras similar to that of scalar–tensor theory but with Lorentz-violating terms provided by the æther field. Finally, in the new variables, we found that the field equations are integrable due to the existence of nonlocal conservation laws for arbitrary functional forms of the three free functions.

Emergence of extended Newtonian gravity from thermodynamics

Discovery of a novel thermodynamic aspect of nonrelativistic gravity is reported. Here, initially, an unspecified scalar field potential is considered and treated not as an externally applied field but as a thermodynamic variable on an equal footing with the fluid variables. It is shown that the second law of thermodynamics imposes a stringent constraint on the field, and, quite remarkably, the allowable field turns out to be only of gravity. The resulting field equation for the gravitational potential derived from the analysis of the entropy production rate contains a dissipative term due to irreversibility. It is found that the system relaxes to the conventional theory of Newtonian gravity up to a certain spatial scale, whereas on the larger scale there emerges non-Newtonian gravity described by a nonlinear field equation containing a single coefficient. A comment is made on an estimation of the coefficient that has its origin in the thermodynamic property of the system.

Exact solutions and constraints on the dark energy model in FRW Universe

The inflationary epoch and the late time acceleration of the expansion rate of universe can be explained by assuming a gravitationally coupled scalar field. In this article, we propose a new method of finding exact solutions in the background of flat Friedmann-Robertson-Walker (FRW) cosmological models by considering both scalar field and matter where the scalar field potential is a function of the scale factor. Our method provides analytical expressions for equation of state parameter of scalar field, deceleration parameter and Hubble parameter. This method can be applied to various other forms of scalar field potential, to the early radiation dominated epoch and very early scalar field dominated inflationary dynamics. Since the method produces exact analytical expression for $H(a)$ (i.e., H(z) as well), we then constrain the model with currents data sets, which includes-Baryon Acoustic Oscillations, Hubble parameter data and Type 1a Supernova data (Pantheon Dataset). As an extension of the method, we also consider the inverse problem of reconstructing scalar field potential energy by assuming any general analytical expression of scalar field equation of state parameter as a function of scale factor.

Singularities in Static Spherically Symmetric Configurations of General Relativity with Strongly Nonlinear Scalar Fields

There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly nonlinear scalar field, which allow the appearance of singularities of a new type (“spherical singularities”) outside the center of curvature coordinates. As the example, we consider a scalar field potential ∼sinh(ϕ2n),n>2, which grows rapidly for large field values. The space-time is assumed to be asymptotically flat. We fulfill a numerical investigation of solutions with different n for different parameters, which define asymptotic properties at spatial infinity. Depending on the configuration parameters, we show that the distribution of the stable circular orbits of test bodies around the configuration is either similar to that in the case of the Schwarzschild solution (thus mimicking an ordinary black hole), or it contains additional rings of unstable orbits.

Reconstruction of the New Agegraphic Polytropic Gas Dark Energy Model in the Flat Friedmann Robertson Walker (FRW) Universe

In this paper, we study the Polytropic Gas Dark Energy model and New Agegraphic Dark Energy model in the flat Friedmann Robertson Walker (FRW) Universe and establish a correspondence between them for the scalar fields. This correspondence allows reconstructing the potential of the Polytropic Gas scalar fields and dynamics of the scalar fields according to the evolutions of the New Agegraphic Dark Energy, which describes the accelerated expansion of the Universe.

Particle creation inspired warm inflation according to Planck 2018

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

Evaluation of cosmological models in [formula omitted] gravity in different dark energy scenario

In the present paper, we search the existence of dark energy scalar field models within in f(R,T) gravity theory established by Harko et al. (Phys. Rev. D 84, 024020, 2011) in a flat FRW universe. The correspondence between scalar field models has been examined by employing the new generalized dynamical cosmological term Λ(t). In this regard, the best fit observational values of parameters from three distinct sets of data are applied. To decide the solution to field equations, a scale factor a=sinh(βt)1/n has been considered, where β&n are constants. Here, we employ the recent ensues (H0=69.2 and q0=−0.52) from (OHD+JLA) observation (Yu et al. (2018)). Through the numerical estimation and graphical assessing of various cosmological parameters, it has been experienced that findings are comparable with kinematics and physical properties of the universe and compatible with recent cosmological ensues. The dynamics and potentials of scalar fields are clarified in the FRW scenario in the present model. Potentials reconstruction is highly reasonable and shows a periodic establishment and in agreement with the latest observations.

Power-law [formula omitted] gravity corrected canonical scalar field inflation

The effective inflationary Lagrangian is a prominent challenge for theoretical cosmologists, since it may contain imprints of the quantum epoch. In view of the fact that higher order curvature terms might be present in the effective inflationary Lagrangian, in this work we introduce the theoretical framework of power-law f(R) gravity corrected canonical scalar field inflation, aiming to study the inflationary dynamics of this new framework. The main characteristic of this new theoretical framework is the dominance of a power-law f(R) gravity term ∼Rn, with 1<n<2, compared to the Einstein–Hilbert term ∼R. In effect, the field equations are controlled by the Rn term in contrast to the Einstein–Hilbert canonical scalar theory. We extract the slow-roll field equations and we calculate the slow-roll indices of the resulting theory which acquire quite elegant final form, when the slow-roll conditions hold true. Accordingly, we examine quantitatively the inflationary phenomenological implications of the theoretical framework we introduced, by choosing simple hybrid-like scalar field potentials. As we evince the resulting theory is in good agreement with the latest Planck data for a wide range of the free parameters of the model. Thus our theoretical framework makes possible to obtain viable inflationary theories, which otherwise would be non-viable, such as the simple power-law f(R) gravity model or the simple power-law scalar model.

Scalar lumps with a horizon

We study a self-interacting scalar field theory coupled to gravity and are interested in spherically symmetric solutions with a regular origin surrounded by a horizon. For a scalar potential containing a barrier, and using the most general spherically symmetric ansatz, we show that in addition to the known static, oscillating solutions discussed earlier in the literature there exist new classes of solutions which appear in the strong field case. For these solutions the spatial sphere shrinks either beyond the horizon, implying a collapsing universe outside of the cosmological horizon, or it shrinks already inside of the horizon, implying the existence of a black hole surrounding the scalar lump in all directions. Crucial for the existence of all such solutions is the presence of a scalar field potential with a barrier that satisfies the swampland conjectures.

Dimensional reduction and (Anti) de Sitter bounds

Dimensional reduction has proven to be a surprisingly powerful tool for delineating the boundary between the string landscape and the swampland. Bounds from the Weak Gravity Conjecture and the Repulsive Force Conjecture, for instance, are exactly preserved under dimensional reduction. Motivated by its success in these cases, we apply a similar dimensional reduction analysis to bounds on the gradient of the scalar field potential V and the mass scale m of a tower of light particles in terms of the cosmological constant Λ, which ideally may pin down ambiguous O(1) constants appearing in the de Sitter Conjecture and the (Anti) de Sitter Distance Conjecture, respectively. We find that this analysis distinguishes the bounds left|nabla Vright|/Vge sqrt{4/left(d-2right)} , m ≲ |Λ|1/2, and m ≲ |Λ|1/d in d-dimensional Planck units. The first of these bounds is equivalent to the strong energy condition in Einstein-dilaton gravity and precludes accelerated expansion of the universe. It is almost certainly violated in our universe, though it may apply in asymptotic limits of scalar field space. The second bound cannot be satisfied in our universe, though it is saturated in supersymmetric AdS vacua with well-understood uplifts to 10d/11d supergravity. The third bound likely has a limited range of validity in quantum gravity as well, so it may or may not apply to our universe. However, if it does apply, it suggests a possible relation between the cosmological constant and the neutrino mass, which (by the see-saw mechanism) may further provide a relation between the cosmological constant problem and the hierarchy problem. We also work out the conditions for eternal inflation in general spacetime dimensions, and we comment on the behavior of these conditions under dimensional reduction.

Stability analysis of geodesics and quasinormal modes of a dual stringy black hole via Lyapunov exponents

We investigate the stability of both timelike as well as null circular geodesics in the vicinity of a dual (3+1) dimensional stringy black hole (BH) spacetime by using an excellent tool so-called Lyapunov exponent. The proper time (\(\tau \)) Lyapunov exponent (\(\lambda _{p}\)) and coordinate time (t) Lyapunov exponent (\(\lambda _{c}\)) are explicitly derived to analyze the stability of equatorial circular geodesics for the stringy BH spacetime with electric charge parameter (\(\alpha \)) and magnetic charge parameter (Q). By computing these exponents for both the cases of BH spacetime, it is observed that the coordinate time Lyapunov exponent of magnetically charged stringy BH for both timelike and null geodesics are independent of magnetic charge parameter (Q). The variation of the ratio of Lyapunov exponents with radius of timelike circular orbits (\(r_{0}/M\)) for both the cases of stringy BH are presented. The behavior of instability exponent for null circular geodesics with respect to charge parameters (\(\alpha \) and Q) are also observed for both the cases of BH. Further, by establishing a relation between quasinormal modes (QNMs) and parameters related to null circular geodesics (like angular frequency and Lyapunov exponent), we deduced the QNMs (or QNM frequencies) for a massless scalar field perturbation around both the cases of stringy BH spacetime in the eikonal limit. The variation of scalar field potential with charge parameters and angular momentum of perturbation (l) are visually presented and discussed accordingly.

Constant-roll inflation driven by q-de Sitter

We have studied constant-roll inflation using the q-de Sitter scale factor. Both the cold and warm inflation have been considered, and the scalar potential and inflaton field have been determined. Also tensor to scalar ratio and the spectral index are obtained. In the cold inflation case, the perturbations have been investigated using Mukhanov–Sasaki equation, and the results determined for the spectral index and tensor to scalar ration are consistent with observations. In the warm inflation two cases of constant damping ([Formula: see text]) and the field dependent damping ([Formula: see text]) have been studied. In both cases the power spectrum and the tensor to scalar ratio are determined as a function of the inflaton field. It has been shown that in both cases the spectral index is independent of the inflaton field. In the case of constant damping the obtained value for the spectral index is inconsistent with observations but for the case of field dependent damping the parameter [Formula: see text] can be chosen such that the value obtained for all the physical quantities including the spectral index be consistent with present cosmological observations.