Scalar Field Models Research Articles

On holographic Wilsonian renormalization group of massive scalar theory with its self-interactions in AdS

Holographic model of massive scalar field with its self-interaction $\lambda\phi^n$ in AdS space is able to give a logarithmic scale dependence to marginal multi trace deformation couplings on its dual conformal field theory, where $\lambda$ is the self-interaction coupling of the scalar field, $\phi$ and $n$ is an integral number. In arXiv:1501.06664, the authors realize this feature by looking at bulk scalar solutions near AdS boundary imposing a specific boundary condition between the coefficients of non-normalizable and normalizable modes of the scalar field excitations. We study the same holographic model to see scale dependence of marginal deformations on the dual conformal field theory by employing completely different method: {\it holographic Wilsonian renormalization group}. We solve Hamilton-Jacobi equation derived from the holographic model of massive scalar with $\lambda\phi^n$ interaction and obtain the solution of marginal multi trace deformations up to the leading order in $\lambda$. It turns out that the solution of marginal multi trace deformation also presents logarithmic behavior in energy scale near UV region.

Inflationary Dynamics of Tsallis Holographic Scalar Field Models in Chern-Simons Modified Gravity

The present study report reconstruction schemes for tachyon scalar field model of Dark Energy through Tsallis holographic dark fluid under the framework of Chern-Simons modified gravity. Emergent scale factor has been assumed. Reproducing the conservation equation for a coupled model with interaction term we have reconstructed the scalar field and the corresponding potential. The reconstructed energy density have been plotted for the case. Evolutionary behaviour of potential for the case have been pictorially presented.

Roles of modified Chaplygin–Jacobi and Chaplygin–Abel gases in FRW universe

In this paper, we have considered flat Friedmann–Robertson–Walker (FRW) model of the universe and reviewed the modified Chaplygin gas as the fluid source. Associated with the scalar field model, we have determined the Hubble parameter as a generating function in terms of the scalar field. Instead of hyperbolic function, we have taken Jacobi elliptic function and Abel function in the generating function and obtained modified Chaplygin–Jacobi gas (MCJG) and modified Chaplygin–Abel gas (MCAG) equation of states, respectively. Next, we have assumed that the universe is filled in dark matter, radiation, and dark energy. The sources of dark energy candidates are assumed as MCJG and MCAG. We have constrained the model parameters by recent observational data analysis. Using [Formula: see text] minimum test (maximum likelihood estimation), we have determined the best-fit values of the model parameters by OHD[Formula: see text]CMB[Formula: see text]BAO[Formula: see text]SNIa joint data analysis. To examine the viability of the MCJG and MCAG models, we have determined the values of the deviations of information criteria like △AIC, △BIC and △DIC. The evolutions of cosmological and cosmographical parameters (like equation of state, deceleration, jerk, snap, lerk, statefinder, Om diagnostic) have been studied for our best-fit values of model parameters. To check the classical stability of the models, we have examined the values of square speed of sound [Formula: see text] in the interval [Formula: see text] for expansion of the universe.

Time-averaging axion-like interacting scalar fields models

In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields phi _1 and phi _2 interacting through a term added to its potential. Introducing novel dynamical variables, and a dimensionless time variable, the resulting dynamical system is studied. The main difficulties arising in the standard dynamical systems approach, where expansion normalized dynamical variables are usually adopted, are due to the oscillations entering the nonlinear system through the Klein–Gordon (KG) equations. This motivates the analysis of the oscillations using methods from the theory of averaging nonlinear dynamical systems. We prove that time-dependent systems, and their corresponding time-averaged versions, have the same late-time dynamics. Then, we study the time-averaged system using standard techniques of dynamical systems. We present numerical simulations as evidence of such behavior.

Scattering of metastable lumps in a model with a false vacuum

In this work we consider the scalar field model with a false vacuum proposed by Avelar et al. (2008) [27]. The model depends on a parameter s>0. The model has unstable nontopological lump solutions with a bell shape for small s, acquiring a flat plateau around the maximum for large s. For s→∞ the ϕ4 model is recovered. We show that for s≳2 the lump is metastable with the only negative mode very close to zero. Metastable lumps can propagate and survive long enough to produce dynamical effects. Due to their simplicity, they can be an alternative to the procedure of stabilization which requires, for instance, a complex scalar field to construct nontopological solitons. We study lump-lump collisions in this model, describing the main characteristics of the scattering products at their dependence on s and the initial velocity modulus of each lump.

Degradation of domains with sequential field application

Recent experiments show striking unexpected features when alternating square magnetic field pulses are applied to ferromagnetic samples: domains show area reduction and domains walls change their roughness. We explain these phenomena with a simple scalar-field model, using a numerical protocol that mimics the experimental one. For a bubble and a stripe domain, we reproduce the experimental findings: the domains shrink by a combination of linear and exponential behavior. We also reproduce the roughness exponents found in the experiments. Our results suggest that the observed effects are due to a change in the disorder correlation length when the domain walls are subject to alternating fields during the first cycles, where the initial state of the interface plays a crucial role. Finally, our simulations explain the area loss by the interplay between disorder effects and effective fields induced by the local domain curvature.

Complete Cosmological Evolution Model of a Classical Scalar Field with a Higgs Potential. II. Numerical Simulation

A complete cosmological evolution model of the classical scalar field with a Higgs potential is studied and simulated on a computer without the assumption that the Hubble constant is nonnegative. It is shown that with most initial conditions, the cosmological model goes from the expansion stage to the compression stage. Thus, cosmological models based on the classical Higgs field are unstable to finite perturbations.

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.

Solutions of the Bullough–Dodd Model of Scalar Field through Jacobi-Type Equations

A technique based on multiple auxiliary equations is used to investigate the traveling wave solutions of the Bullough–Dodd (BD) model of the scalar field. We place the model in a flat and homogeneous space, considering a symmetry reduction to a 2D-nonlinear equation. It is solved through this refined version of the auxiliary equation technique, and multiparametric solutions are found. The key idea is that the general elliptic equation, considered here as an auxiliary equation, degenerates under some special conditions into subequations involving fewer parameters. Using these subequations, we successfully construct, in a unitary way, a series of solutions for the BD equation, part of them not yet reported. The technique of multiple auxiliary equations could be employed to handle several other types of nonlinear equations, from QFT and from various other scientific areas.

Cosmological dynamics and bifurcation analysis of the general non-minimal coupled scalar field models

Non-minimal coupled scalar field models are well-known for providing interesting cosmological features. These include a late-time dark energy behavior, a phantom dark energy evolution without singularity, an early-time inflationary Universe, scaling solutions, convergence to the standard Lambda CDM, etc. While the usual stability analysis helps us determine the evolution of a model geometrically, bifurcation theory allows us to precisely locate the parameters’ values describing the global dynamics without a fine-tuning of initial conditions. Using the center manifold theory and bifurcation analysis, we show that the general model undergoes a transcritical bifurcation, predicting us to tune our models to have certain desired dynamics. We obtained a class of models and a range of parameters capable of describing a cosmic evolution from an early radiation era towards a late time dark energy era over a wide range of initial conditions. There is also a possible scenario of crossing the phantom divide line. We also find a class of models where the late time attractor mechanism is indistinguishable from a structurally stable general relativity-based model; thus, we can elude the big rip singularity generically. Therefore, bifurcation theory allows us to select models that are viable with cosmological observations.

The impact of deformed space—space parameters into canonical scalar field model with exponential potential. The case of spatially flat Friedmann—Lemaître—Robertson—Walker (FLRW) universe

In this work, we propose a model of noncommutative cosmology through the deformation of minisuperspace. We focus on an exponentially potential with a homogeneous scalar field minimally coupled to gravity in the spatially flat universe. To process, we use a particular case of noncommutativity by making a deformation of space coordinates only. Then, we compare results in both the commutative model and the noncommutative one.

Rescaled Einstein-Hilbert gravity from f(R) gravity: Inflation, dark energy, and the swampland criteria

We consider a class of exponential models of $f(R)$ gravity, in the presence of a canonical scalar field, for which at early times the effective Lagrangian of the theory becomes that of a rescaled canonical scalar field with the Einstein-Hilbert term becoming $\sim \alpha R$, with $\alpha$ a dimensionless constant. This rescaled Einstein-Hilbert scalar field theory at early times alters the inflationary phenomenology of well-known scalar field models of inflation, but more importantly, in the context of this rescaled theory, the Swampland criteria are easily satisfied, assuming that the scalar field is slowly rolling. We consider two models of inflation to exemplify our study, a fibre inflation model and a model that belongs to the general class of supergravity $\alpha$-attractor models. The inflationary phenomenology of the models is demonstrated to be viable, and for the same set of values of the free parameters of each model which ensure their inflationary viability, all the known Swampland criteria are satisfied too, and we need to note that we assumed that the first Swampland criterion is marginally satisfied by the scalar field, so $\phi\sim M_p$ during the inflationary era. Finally, we examine the late-time phenomenology of the fibre inflation potential in the presence of the full $f(R)$ gravity, and we demonstrate that the resulting model produces a viable dark energy era, which resembles the $\Lambda$-Cold-Dark-Mater model. Thus in the modified gravity model we present, the Universe is described by a rescaled Einstein-Hilbert gravity at early times, hence in some sense the modified gravity effect is minimal primordially, and the scalar field controls mainly the dynamics with a rescaled Ricci scalar gravity. However $f(R)$ gravity dominates at late-times, where it controls the dynamics, synergistically with the scalar field.

Dynamics of tachyon dark energy on large scales and its imprint on the observed galaxy power spectrum

In the present work, we study the large scale matter power spectrum as well as the observed galaxy power spectrum for a noncanonical tachyon field dark energy model considering the full general relativistic perturbation equations. We form a set of coupled autonomous equations, including both the background and linearly perturbed quantities, and obtain their solutions numerically with proper set of initial conditions. We consider different scalar field potentials for our study. Deviations from the concordance $\mathrm{\ensuremath{\Lambda}}$ cold dark matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$) model are studied for different relevant quantities. Our study shows that the noncanonical tachyon dark energy model produces enhanced gravitational potentials and comoving density contrast, as well as linear growth factor for matter perturbations compared to $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. It is also observed that, for tachyon dark energy models, there is suppression of power on large scales compared to both the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model as well as previously studied canonical scalar field models.

The scalar field models of Tsallis holographic dark energy with Granda–Oliveros cutoff in modified gravity

This research explores the Tsallis holographic quintessence, k-essence, and tachyon models of dark energy in the modified f(R, T) gravity framework with Granda–Oliveros cutoff. We have analyzed the energy density through [Formula: see text]. We study the correspondence between the quintessence, k-essence, and tachyon energy density with the Tsallis holographic dark energy density in a flat FRW Universe. The reconstruction is performed for different values of Tsallis parameter δ in the region of ωΛ > –1 for the EoS parameter. This correspondence allows reconstruction of the potentials and the dynamics for the scalar field models, if we set some constraints for the model parameters, which describe the accelerated expansion of the Universe.

Dynamical diffeomorphisms

We construct a general effective dynamics for diffeomorphisms of spacetime, in a fixed external metric. Though related to familiar models of scalar fields as coordinates, our models have subtly different properties, both at kinematical and dynamical level. The energy–momentum (EM) tensor consists of two independently conserved parts. The background solution is the identity diffeomorphism and the EM tensor of this solution gives rise to an effective cosmological constant.

Reconstruction of Tachyon, Dirac-Born-Infeld-essence and Phantom model for Tsallis holographic dark energy in [formula omitted] gravity

In this work, we study the Tsallis holographic dark energy with Hubble horizon as IR cut-off with the energy density given by ρΛ=3β2Mp2H−2δ+4 in f(R,T) theory. Considering a flat FRW Universe, we obtain the equation of state parameter guided by f(R,T) gravity. We investigate the correspondence between the tachyon, Dirac-Born-Infeld-essence, and the phantom scalar field models with the Tsallis holographic dark energy in the context of f(R,T) gravity. By equating the equation of state parameter in f(R,T) theory and ρΛ with scalar field models, we reconstruct potentials and dynamics for these models for different Tsallis parameter δ. By analysis, we can show that for Tsallis holographic tachyon, Dirac-Born-Infeld-essence, and the phantom models, if the related model parameters fulfill some constraints, the accelerated expansion can be obtained in the framework of f(R,T) gravity.

Constraining rapidly oscillating scalar dark matter using dynamic decoupling

We propose and experimentally demonstrate a method for detection of a light scalar dark matter (DM) field through probing temporal oscillations of fundamental constants in an atomic optical transition. Utilizing the quantum information notion of dynamic decoupling (DD) in a tabletop setting, we are able to obtain model-independent bounds on variations of $\ensuremath{\alpha}$ and ${m}_{e}$ at frequencies up to the MHz scale. We interpret our results to constrain the parameter space of light scalar DM field models. We consider the generic case, where the couplings of the DM field to the photon and the electron are independent, as well as the case of a relaxion DM model, including the scenario of a DM boson star centered around Earth. Given the particular nature of DD, allowing one to directly observe the oscillatory behavior of coherent DM and considering future experimental improvements, we conclude that our proposed method could be complimentary to, and possibly competitive with, gravitational probes of light scalar DM.

Primordial black holes and secondary gravitational waves from ultraslow roll and punctuated inflation

[Abridged] The primordial scalar power spectrum is well constrained on large scales, primarily by the observations of the anisotropies in the cosmic microwave background (CMB). Over the last few years, it has been recognized that a sharp rise in power on small scales will lead to enhanced formation of primordial black holes (PBHs) and also generate secondary gravitational waves (GWs) of higher and, possibly, detectable amplitudes. It is well understood that scalar power spectra with COBE normalized amplitude on the CMB scales and enhanced amplitudes on smaller scales can be generated due to deviations from slow roll in single, canonical scalar field models of inflation. In fact, an epoch of so-called ultra slow roll inflation can lead to the desired amplification. We find that scenarios that lead to ultra slow roll can be broadly classified into two types, one wherein there is a brief departure from inflation (a scenario referred to as punctuated inflation) and another wherein such a departure does not arise. We consider a set of single field inflationary models involving the canonical scalar field that lead to ultra slow roll and punctuated inflation and examine the formation of PBHs as well as the generation of secondary GWs in these models. Apart from considering specific models, we reconstruct potentials from certain functional choices of the first slow roll parameter leading to ultra slow roll and punctuated inflation and investigate their observational signatures. In addition to the secondary tensor power spectrum, we calculate the secondary tensor bispectrum in the equilateral limit in these scenarios. Moreover, we calculate the inflationary scalar bispectrum that arises in all the cases and discuss the imprints of the scalar non-Gaussianities on the extent of PBHs formed and the amplitude of the secondary GWs.

A Sufficient Condition for Asymptotic Stability of Kinks in General (1+1)-Scalar Field Models

We study stability properties of kinks for the (1+1)-dimensional nonlinear scalar field theory models $$\begin{aligned} \partial _t^2\phi -\partial _x^2\phi + W'(\phi ) = 0, \quad (t,x)\in \mathbb {R}\times \mathbb {R}. \end{aligned}$$ The orbital stability of kinks under general assumptions on the potential W is a consequence of energy arguments. Our main result is the derivation of a simple and explicit sufficient condition on the potential W for the asymptotic stability of a given kink. This condition applies to any static or moving kink, in particular no symmetry assumption is required. Last, motivated by the Physics literature, we present applications of the criterion to the $$P(\phi )_2$$ theories and the double sine-Gordon theory.

Perturbations in a scalar field model with virtues of ΛCDM

In the era of precision cosmology, the cosmological constant Λ gives quite an accurate description of the evolution of the Universe, but it is still plagued with the fine-tuning problem and the cosmic coincidence problem. In this work, we investigate the perturbations in a scalar field model that drives the recent acceleration in a similar fashion that the cosmological constant does and has the dark energy (DE) density comparable to the dark matter (DM) energy density at the recent epoch starting from arbitrary initial conditions. The perturbations show that this model, though it keeps the virtues of a ΛCDM model, has a distinctive qualitative feature, particularly it reduces the amplitude of the matter power spectrum on a scale of 8 h-1 Mpc, σ8 at the present epoch.