Inverse Power Law Potential Research Articles

General study of chameleon fifth force in gravity space experiments

This article investigates the profile of the scalar field of a scalar-tensor theory subject to the chameleon mechanism in the context of gravity space missions like the MICROSCOPE experiment. It analyses the experimental situations for models with an inverse power law potential that can in principle induce a fifth force inside the satellite, hence either be detected or constrained. As the mass of the scalar field depends on the local matter density, the screening of the scalar field depends crucially on both the parameters of the theory (potential and non-minimal coupling to matter) and on the geometry of the satellite. We calculate the profile of the scalar field in 1-, 2- and 3-dimensional satellite configurations without relying on the thick or thin shell approximations for the scalar field. In particular we consider the typical geometry with nested cylinders which is close to the MICROSCOPE design. In this case we evaluate the corresponding fifth force on a test body inside the satellite. This analysis clarifies previous claims on the detectability of the chameleon force by space-borne experiments.

Early dark energy constraints on growing neutrino quintessence cosmologies

We investigate cosmological models in which dynamical dark energy consists of a scalar field whose present-day value is controlled by a coupling to the neutrino sector. The behaviour of the scalar field depends on three functions: a kinetic function, the scalar field potential, and the scalar field-neutrino coupling function. We present an analytic treatment of the background evolution during radiation- and matter-domination for exponential and inverse power law potentials, and find a relaxation of constraints compared to previous work on the amount of early dark energy in the exponential case. We then carry out a numerical analysis of the background cosmology for both types of potential and various illustrative choices of the kinetic and coupling functions. By applying bounds from Planck on the amount of early dark energy, we are able to constrain the magnitude of the kinetic function at early times.

Topological extension of the isomorph theory based on the Shannon entropy.

Isomorph theory is one of the promising theories for understanding the quasiuniversal relationship between thermodynamic, dynamic, and structural characteristics. Based on the hidden scale invariance of the inverse power law potentials, it rationalizes the excess entropy scaling law of dynamic properties. This work aims to show that this basic idea of isomorph theory can be extended by examining the microstructural features of the system. Using the topological framework in conjunction with the entropy calculation algorithm, we demonstrate that Voronoi entropy, a measure of the topological diversity of single atoms, provides a scaling law for the transport properties of soft-sphere fluids, which is comparable to the frequently used excess entropy scaling. By examining the relationship between the Voronoi entropy and the solidlike fraction of simple fluids, we suggest that the Frenkel line, a rigid-nonrigid crossover line, be a topological isomorphic line at which the scaling relation qualitatively changes.

Cosmic acceleration in the Randall-Sundrum II brane world

In this paper, we implement the dynamical system tools to study the dynamics of a self-interacting scalar field for suitable interactions of dark energy and dark matter in the Randall-Sundrum II brane scenario. Here we investigate three distinct forms of interaction strength namely, $I_{\phi}=\alpha\dot{\rho_{\phi}}$ , $I_{m1}=\delta \dot{\phi} \rho_{m}$ and $I_{m2}=\frac{\sigma\dot{\phi}^{2} \rho_{m}}{H}$ . We consider a homogeneous and isotropic Friedmann-Robertson-Walker brane model. The transformation equations are simplified to an autonomous system of ordinary differential equations by a suitable change of variables and hence a dynamical system analysis is performed for the respective interacting models in RS II brane cosmology. During the dynamical system analysis, we use the linear stability theory to study the stability of hyperbolic points, but these linearization techniques fail for non-hyperbolic points. So we apply the center manifold theory to determine the stability of non-hyperbolic points. For these specific interaction strengths, the 3D and 4D dynamical system analysis infers the existence of late-time attractors. These attractors are found for constant potential and inverse power law potential. The presence of these attractors results in late-time cosmic acceleration.

Semiclassical Limit to the Vlasov Equation with Inverse Power Law Potentials

We consider mixed quasi-free states describing $N$ fermions in the mean-field limit. In this regime, the time evolution is governed by the nonlinear Hartree equation. In the large $N$ limit, we study the convergence towards the classical Vlasov equation. Under integrability and regularity assumptions on the initial state, we prove strong convergence in trace and Hilbert-Schmidt norm and provide explicit bounds on the convergence rate for a class of singular potentials of the form $V(x)=|x|^{-\alpha}$, for $\alpha\in(0,1/2)$.

Accurate and efficient computation of the Boltzmann equation for Couette flow: Influence of intermolecular potentials on Knudsen layer function and viscous slip coefficient

The Couette flow is one of the fundamental problems of rarefied gas dynamics, which has been investigated extensively based on the linearized Boltzmann equation (LBE) of hard-sphere molecules and simplified kinetic model equations. However, how the different intermolecular potentials affect the viscous slip coefficient and the structure of Knudsen layer remains unclear. Here, a novel synthetic iteration scheme (SIS) is developed for the LBE to find solutions of Couette flow accurately and efficiently: the velocity distribution function is first solved by the conventional iterative scheme, then it is modified such that in each iteration i) the flow velocity is guided by an ordinary differential equation that is asymptotic-preserving at the Navier–Stokes limit and ii) the shear stress is equal to the average shear stress. Based on the Bhatnagar–Gross–Krook model, the SIS is assessed to be efficient and accurate. Then we investigate the Knudsen layer function for gases interacting through the inverse power-law, shielded Coulomb, and Lennard-Jones potentials, subject to diffuse-specular and Cercignani–Lampis gas-surface boundary conditions. When the tangential momentum accommodation coefficient (TMAC) is not larger than one, the Knudsen layer function is strongly affected by the potential, where its value and width increase with the effective viscosity index of gas molecules. Moreover, the Knudsen layer function exhibits similarities among different values of TMAC when the intermolecular potential is fixed. For Cercignani–Lampis boundary condition with TMAC larger than one, both the viscous slip coefficient and Knudsen layer function are affected by the intermolecular potential, especially when the “backward” scattering limit is approached. With the asymptotic theory by Jiang and Luo (2016) [14] for the singular behavior of the velocity gradient in the vicinity of solid surfaces, we find that the whole Knudsen layer function can be well fitted by the power series ∑n=02∑m=02cn,mxn(xln⁡x)m, where x is the distance to the solid surface. Finally, the experimental data of the Knudsen layer profile are explained by the LBE solution with proper values of the viscosity index and TMAC.

Observational Constraints on the Chaplygin Gas with Inverse Power Law Potential in Braneworld Inflation

We study Chaplygin gas as a candidate for inflation in the context of braneworld inflationary model. We investigate this model in the framework of the Randall–Sundrum type II, considering a original and generalized Chaplygin gas. We use inverse power law potential to examine the behavior of some inflationary spectrum parameters such as the spectral index ns, the ratio r and the running of the scalar spectral index dns/dlnk, our results are in agreement with recent observational data for a particular choice of e-folding number N and parameters space of the model.

Perfect fluid solutions of Brans–Dicke and [formula omitted] cosmology

Brans–Dicke cosmology with an (inverse) power-law potential is revisited in the light of modern quintessence and inflation models. A simple ansatz relating scale factor and scalar field recovers most of the known solutions and generates new ones. A phase space interpretation of the ansatz is provided and these universes are mapped into solutions of f(R) cosmology.

Effective equilibrium states in mixtures of active particles driven by colored noise.

We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the particles are driven by colored noises with exponential correlation functions whose intensities and correlation times vary from species to species. By extending Fox's theory to many components, we derive by functional calculus an approximate Fokker-Planck equation for the configurational distribution function of the system. After illustrating the predicted distribution in the solvable case of two particles interacting via a harmonic potential, we consider systems of particles repelling through inverse power-law potentials. We compare the analytic predictions to computer simulations for such soft-repulsive interactions in one dimension and show that at linear order in the persistence times the theory is satisfactory. This work provides the toolbox to qualitatively describe many-body phenomena, such as demixing and depletion, by means of effective pair potentials.

Constraints on Dynamical Dark Energy with Precision Cosmological Data

We present a Dark Energy (DE) model based on a scalar field with an inverse power law potential (IPL) V(∅)=M4+n∅−n. We consider three different models n=1/2, n=3/4 and n=1 and we vary the value of M and the initial amount of energy density Ω∅ at the scale factor ac. We obtain a time dependent equation of state (EoS) , with w∅=1/3 at early times for a scale factor ac with a steep transition to w∅=1 at , , , lasting a long period of time and a subsequent descent w∅=-1 to for to finally grow to w∅= -0.906, w∅=-0.932, w∅=-0.924 for n=1/2, n=3/4 and n=1 respectively. The values of M and Ω∅(ac) are M(eV)= 4.63,127.31,2465.46 and Ω∅(ac)=0.038,0.148,0.227 for n= 1/2, n= 3/4 and n=1 respectively. We show the differences in the evolution of H, the CMB and Matter power spectra, and the redshift space distortion (RSD)parameter. Precision cosmological data allow us to test the dynamics of Dark Energy and we obtain in all three cases a reduction of compared to ∧CDM with and an equivalent fit for CMB and SNIa data.

Quantum correlations in one-dimensional Wigner molecules

We studied one-dimensional systems formed by N identical particles confined in a harmonic trap and subject to an inverse power-law interaction potential ~ |x|−d. The correlation properties of a Wigner molecule with the lowest energy are investigated in terms of their dependence on the number N and the power d, including the limit as d → 0. There are N-particle Wigner molecules with properties such that their correlations are mainly manifested in the N lowest natural orbitals. The values of the control parameters of the system at which such states appear are identified. The properties of Wigner molecules formed in the limit as d approaches infinity are also revealed.Graphical abstract

Highly excited bound-state resonances of short-range inverse power-law potentials

We study analytically the radial Schrödinger equation with long-range attractive potentials whose asymptotic behaviors are dominated by inverse power-law tails of the form V(r)=-beta _n r^{-n} with n>2. In particular, assuming that the effective radial potential is characterized by a short-range infinitely repulsive core of radius R, we derive a compact analytical formula for the threshold energy E^{text {max}}_l=E^{text {max}}_l(n,beta _n,R), which characterizes the most weakly bound-state resonance (the most excited energy level) of the quantum system.

Extended phase space analysis of interacting dark energy models in loop quantum cosmology

The present work deals with the dynamical system investigation of interacting dark energy models (quintessence and phantom) in the framework of Loop Quantum Cosmology by taking into account a broad class of self-interacting scalar field potentials. The main reason for studying potentials beyond the exponential type is to obtain additional critical points which can yield more interesting cosmological solutions. The stability of critical points and the asymptotic behavior of the phase space are analyzed using dynamical system tools and numerical techniques. We study two class of interacting dark energy models and consider two specific potentials as examples: the hyperbolic potential and the inverse power-law potential. We found a rich and interesting phenomenology including the avoidance of big rip singularities due to loop quantum effects, smooth and non-linear transitions from matter domination to dark energy domination and finite periods of phantom domination with dynamical crossing of the phantom barrier.

New inhomogeneous universes in scalar-tensor and f(R) gravity

A new family of spherically symmetric inhomogeneous solutions of Brans-Dicke gravity is generated using the Fonarev solution of general relativity as a seed and a map from the Einstein to the Jordan conformal frame. The Brans-Dicke scalar field self-interacts with a power-law or inverse power-law potential in the Jordan frame. This 4-parameter family of geometries, which is dynamical and asymptotically Friedmann-Lemaitre-Robertson-Walker, contains as special cases two previously known classes of solutions and solves also the field equations of $f(R)=R^n$ gravity

Tachyon with an inverse power-law potential in a braneworld cosmology

We study a tachyon cosmological model based on the dynamics of a 3-brane in the bulk of the second Randall–Sundrum model extended to more general warp functions. A well known prototype of such a generalization is the bulk with a selfinteracting scalar field. As a consequence of a generalized bulk geometry the cosmology on the observer brane is modified by the scale dependent four-dimensional gravitational constant. In particular, we study a power law warp factor which generates an inverse power-law potential of the tachyon field φ. We find a critical power ncr that divides two subclasses with distinct asymptotic behaviors: a dust universe for and a quasi de Sitter universe for .

Resurrecting the exponential and inverse power-law potentials in non-canonical inflation

We study inflation within the framework of non-canonical scalar field. In this scenario, we obtain the inflationary observables such as the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index as well as the equilateral non-Gaussianity parameter. Then, we apply these results for the exponential and inverse power-law potentials. Our investigation shows that although the predictions of these potentials in the standard canonical inflation are completely ruled out by the Planck 2015 observations, their results in non-canonical scenario can lie inside the allowed regions of the Planck 2015 data. We also find that in non-canonical inflation, the predictions of the aforementioned potentials for the running of the scalar spectral index and the equilateral non-Gaussianity parameter are in well agreement with the Planck 2015 results. Furthermore, we show that in the context of non-canonical inflation, the graceful exit problem of the exponential and inverse power-law potentials is resolved.

Tachyon inflation with steep potentials

Within the framework of tachyon inflation, we consider different steep potentials and check their viability in light of the Planck 2015 data. We see that in this scenario, the inverse power-law potential $V(\phi)=V_{0}(\phi/\phi_{0})^{-n}$ with $n=2$ leads to the power-law inflation with the scale factor $a(t)\propto t^{q}$ where $q>1$, while with $n<2$, it gives rise to the intermediate inflation with the scale factor $a(t)\propto\exp\left(At^{f}\right)$ where $A>0$ and $0<f<1$. We find that, although the inverse power-law potential with $n\leq 2$ is completely ruled out by the Planck 2015 data, the result of this potential for $n>2$ can be compatible with the 95\% CL region of Planck 2015 TT, TE, EE+lowP data. We further conclude that the exponential potential $V(\phi)=V_{0}e^{-\phi/\phi_{0}}$, the inverse $\cosh$ potential $V(\phi)=V_{0}/\cosh(\phi/\phi_{0})$, and the mutated exponential potential $V(\phi)=V_{0}\left[1+(n-1)^{-(n-1)}(\phi/\phi_{0})^{n}\right]e^{-\phi/\phi_{0}}$ with $n=4$, can be consistent with the 95\% CL region of Planck 2015 TT, TE, EE+lowP data. Moreover, using the $r-n_s$ constraints on the model parameters, we also estimate the running of the scalar spectral index $dn_{s}/d\ln k$ and the local non-Gaussianity parameter $f_{{\rm NL}}^{{\rm local}}$. We find that the lower and upper bounds evaluated for these observables are compatible with the Planck 2015 results.

Dynamical properties of scaling solutions in teleparallel dark energy cosmologies with nonminimal coupling

The dynamical aspects of scaling solutions for the dark energy component in the theoretical framework of teleparallel gravity are considered, where dark energy is represented by a scalar field nonminimally coupled with the torsion and with a boundary term, where the boundary coupling term represents the divergence of the torsion vector. The behavior and stability of the scaling solutions are studied for scalar fields endowed with inverse power law potentials and with exponential potentials. It is shown that for scalar fields endowed with inverse power-law potentials, the stability conditions are not affected by the coupling coefficients. For the scalar fields endowed with exponential potentials, two cases are studied: at first, we have considered an infinitesimal deviation from the scaling solution in the corresponding Klein–Gordon equation, and the impact of distinct coupling coefficients on the stability of the solution are analyzed. Secondly, the potential-free case is considered where the dominance of the coupling terms over the potential term is analyzed, discussing the validity of the corresponding particular solution.

Warm-tachyon Gauss–Bonnet inflation in the light of Planck 2015 data

We study a warm-tachyon inflationary model non-minimally coupled to a Gauss-Bonnet term. The general conditions required for reliability of the model are obtained by considerations of a combined hierarchy of Hubble and Gauss-Bonnet flow functions. The perturbed equations are comprehensively derived in the longitudinal gauge in the presence of slow-roll and quasi-stable conditions. General expressions for observable quantities of interest such as the tensor-to-scalar ratio, scalar spectral index and its running are found in the high dissipation regime. Finally, the model is solved using exponential and inverse power-law potentials, which satisfy the properties of a tachyon potential, with parameters of the model being constrained within the framework of the Planck 2015 data. We show that the Gauss-Bonnet coupling constant controls termination of inflation in such a way as to be in good agreement with the Planck 2015 data.

CONSTRAINTS ON NON-FLAT COSMOLOGIES WITH MASSIVE NEUTRINOS AFTER PLANCK 2015

ABSTRACT We investigate two dark energy cosmological models (i.e., the ΛCDM and ϕCDM models) with massive neutrinos assuming two different neutrino mass hierarchies in both the spatially flat and non-flat scenarios, where in the ϕCDM model the scalar field possesses an inverse power-law potential, V(ϕ) ∝ ϕ −α (α &gt; 0). Cosmic microwave background data from Planck 2015, baryon acoustic oscillation data from 6dFGS, SDSS-MGS, BOSS-LOWZ and BOSS CMASS-DR11, the joint light-curve analysis compilation of SNe Ia apparent magnitude observations, and the Hubble Space Telescope H 0 prior, are jointly employed to constrain the model parameters. We first determine constraints assuming three species of degenerate massive neutrinos. In the spatially flat (non-flat) ΛCDM model, the sum of neutrino masses is bounded as Σm ν &lt; 0.165(0.299) eV at 95% confidence level (CL). Correspondingly, in the flat (non-flat) ϕCDM model, we find Σm ν &lt; 0.164(0.301) eV at 95% CL. The inclusion of spatial curvature as a free parameter results in a significant broadening of confidence regions for Σm ν and other parameters. In the scenario where the total neutrino mass is dominated by the heaviest neutrino mass eigenstate, we obtain similar conclusions to those obtained in the degenerate neutrino mass scenario. In addition, the results show that the bounds on Σm ν based on two different neutrino mass hierarchies have insignificant differences in the spatially flat case for both the ΛCDM and ϕCDM models; however, the corresponding differences are larger in the non-flat case.