Non-canonical Scalar Field Model Research Articles

Dynamical systems analysis of an interacting scalar field model in an anisotropic universe

In this paper, we investigate a non-canonical scalar field model in the background dynamics of anisotropic Locally Rotationally Symmetric (LRS) Bianchi type I universe where gravity is coupled minimally to scalar field which is taken as dark energy and pressureless dust as dark matter are the main matter content of the universe. We perform dynamical system analysis to characterize the cosmological evolution of the model with and without interaction in the dark sector separately. First, we convert the evolution equation into an autonomous system of ordinary differential equations by using a suitable choice of dimensionless variables, which are normalized over the Hubble scale. We choose scalar field coupling and potential in such a way that the autonomous system converted to a 2D system. Linear stability theory is employed to the extracted critical points to find the nature. From the analysis, we find some interesting cosmological scenarios, such as late-time scalar-field dominated solutions, which evolve in the quintessence era, cannot solve the coincidence problem. Accelerated scaling attractors are also obtained that correspond to the late phase evolution in agreement with present observational data, and these solutions also provide possible mechanisms to alleviate the coincidence problem. A complete cosmic evolution is obtained from early inflation to a late-time dark energy-dominated phase, connecting through a matter-dominated transient phase of the universe. Furthermore, we find that for different values of the interaction parameter α, the evolutionary trajectories of the Hubble parameter, and the distance modulus forecasted by the model are in quite well agreement with observational datasets.

Background Constraints on Dark Energy Models

Due to the gravitational attraction of all the matter in the universe, the expansion rate of the cosmos has changed over time, decreasing (decelerating) in past, and more recently speeding up (accelerating). The hypothesis that the Universe is expanding quickly and is spatially nearing its limit now has a lot of cosmological evidence to back it up (assuming the density is at least somewhat time-independent). The majority of cosmologists believe that “dark energy” is to blame for the accelerated cosmological expansion that has been witnessed. The cosmological constant, an additional constant to the Einstein field equation, can be used to explain why the universe is expanding faster than before. The ΛCDM model is the simplest and most common model in use. Besides this, there are also dark energy models like the Barotropic fluid model, canonical scalar field model, and non-canonical scalar field model. We analyse the background constraints on dark energy models using current cosmological data available. We also present the comparison between dark energy models using Bayesian statistics.

Study on early inflationary phase using a new form of non-canonical scalar field model

We study the inflationary phase of the early universe as modeled by a non-canonical scalar field. The homogeneous scalar field equation is derived from a Lagrangian density containing a new form of non-canonical kinetic term and a general potential function. The Lie symmetry is studied and a one parameter Lie point symmetry for the homogeneous scalar field equation is found. We use Lie symmetry generator to construct the exact analytical group invariant closed-form solution of the homogeneous scalar field equation without applying any slow-roll approximation from invariant curve condition. The solution thus obtained is seen to be consistent with the Friedmann equations subject to constraint conditions on the potential parameter $$\lambda $$ . In this scenario, we obtain the values for various inflationary parameters and make useful checks on the observational constraints on the parameters from Planck data by imposing a set of bounds on the parameter $$\lambda $$ of the potential. The results for scalar spectral index ( $$n_S$$ ) and tensor-to-scalar ratio (r) presented in the $$(n_S,\,r)$$ plane in the background of Planck2015 and Planck2018 data are in good agreement with cosmological observations. We find $$r\sim 10^{-3}$$ , the targeted value of r that will be detected by the future CMB observation such as LiteBIRD. Interestingly, most significant primordial non-Gaussianity is also achieved. For theoretical completeness of our non-canonical model, we obtain the allowed parameter space in which the ghosts and Laplacian instabilities are absent. We apply the formulas for slow-roll parameter to explain exit from the inflationary phase using the general potential. We also treat the non-canonical scalar field model equation by the dynamical system theory to provide useful checks on the stability of the critical points and show that the group invariant non-canonical inflationary solution is stable attractor in the phase space.

Early Inflationary Phase with Canonical and Noncanonical Scalar Fields: A Symmetry-Based Approach

We study the early inflationary phase of the universe driven by noncanonical scalar field models using an exponential potential. The noncanonical scalar field models are represented by Lagrangian densities containing square and square-root kinetic corrections to the canonical Lagrangian density. We investigate the Lie symmetry of the homogeneous scalar field equations obtained from noncanonical Lagrangian densities and find only a one-parameter Lie point symmetry for both canonical and noncanonical scalar field equations. We use the Lie symmetry generator to obtain an exact analytical group-invariant solution of the homogeneous scalar field equations from an invariant curve condition. The solutions obtained are consistent and satisfy the Friedmann equations subject to constraint conditions on the potential parameter $$\lambda$$ for the canonical case and on the parameter $$\mu$$ for the noncanonical case. In this scenario, we obtain the values of various inflationary parameters and make useful checks on the observational constraints on the parameters from Planck data by imposing a set of bounds on the parameters $$\lambda$$ and $$\mu$$ . The results for the scalar spectral index ( $$n_{S}$$ ) and the tensor-to-scalar ratio ( $$r$$ ) are presented in the $$(n_{S},r)$$ plane in the background of Planck-2015 and Planck-2018 data for noncanonical cases and are in good agreement with cosmological observations. For theoretical completeness of the noncanonical models, we verify that the noncanonical models under consideration are free from ghosts and Laplacian instabilities. We also treat the noncanonical scalar field model equations for two power-law (kinetic) corrections by the dynamical system theory. We provide useful checks on the stability of the critical points for both cases and show that the group-invariant analytical noncanonical inflation solutions are stable attractors in phase space.

Inflationary dynamics of non-canonical scalar field model well-known potentials

We present the inflation in the context of warm universe model by contemplating the Dirac-Born-Infeld non-canonical scalar field. We concentrate on warm DBI inflation considering the constant sound of speed. Inflationary theory has ability to provide strong solutions to cosmological puzzles of early universe. We contemplate the Anti-de Sitter warp factor for DBI inflation also, examine viability of the quadratic and quartic potential according to Planck 2018 observational data. We find the slow-roll parameters as well as different inflationary parameters in the presence of well-known potentials. We demonstrate graphical behavior of the $r-N$ , $n_{s}-N$ and $\alpha -N$ for both positive as well as negative potentials. The results of $n_{s}-N$ , $r-N$ and $\alpha -N$ are $0.9525^{+0.0125}_{-0.0125}$ , $-0.00015^{+0.00025}_{-0.00025}$ , $0.03375^{+0.03375}_{-0.03375}$ (for positive quadratic and quartic potential) and $0.98^{+0.03}_{-0.03}$ , $0.05^{+0.05}_{-0.05}$ , $0.0018125^{+0.0018125}_{-0.0018125}$ (for negative quadratic and quartic potential), respectively. Also, we conclude that results of the $r$ , $n_{s}$ and $\alpha $ are consistent with recent Planck data 2018.

Thermodynamics of scalar field models with kinetic corrections

In this work, we compare the thermodynamical viability of two types of noncanonical scalar field models with kinetic corrections: the square kinetic and square root kinetic corrections. In modern cosmology, the generalized second law of thermodynamics (GSLT) plays an important role in deciding thermodynamical compliance of a model as one cannot consider a model to be viable if it fails to respect GSLT. Hence, for comparing thermodynamical viability, we examine the validity of GSLT for these two models. For this purpose, by employing the Unified first law (UFL), we calculate the total entropy of these two models in apparent and event horizons. The validity of GSLT is then examined from the autonomous systems as the original expressions of total entropy are very complicated. Although, at the background level, both models give interesting cosmological dynamics, however, thermodynamically we found that the square kinetic correction is more realistic as compared to the square root kinetic correction. More precisely, the GSLT holds for the square kinetic correction throughout the evolutionary history except only during the radiation epoch where the scalar field may not represent a true description of the matter content. On the other hand, the square root kinetic model fails to satisfy the GSLT in major cosmological eras.

A non-canonical scalar field cosmological model: Stability and bifurcation analysis

In this work, cosmological implications of a non-canonical scalar field model have been studied in the background of homogeneous and isotropic flat FLRW spacetime by using dynamical system analysis. By suitable change of variables, the field equations are transformed to an autonomous system and the stability of the system of critical points are examined. For hyperbolic critical points, the analysis of the system is done by using Hartman–Grobman theorem, while the center manifold theory is used to study non-hyperbolic critical points. It is found that the parameters in the autonomous system play a crucial role for phase transition of the Universe. Finally, possible bifurcation scenarios are discussed to identify the point of phase transition.

Parametrizations of dark energy models in the background of general non-canonical scalar field in D-dimensional fractal universe

We have explored non-canonical scalar field model in the background of non-flat D-dimensional fractal Universe on the condition that the matter and scalar field are separately conserved. The potential V, scalar field phi , function f, densities, Hubble parameter and deceleration parameter can be expressed in terms of the redshift z and these depend on the equation of state parameter w_{phi }. We have also investigated the cosmological analysis of four kinds of well known parametrization models. In graphically, we have analyzed the natures of potential, scalar field, function f, densities, the Hubble parameter and deceleration parameter. As a result, the best fitted values of the unknown parameters (w_{0},w_{1}) of the parametrization models due to the joint data analysis (SNIa+BAO+CMB+Hubble) have been found. Furthermore, the minimum values of chi ^{2} function have been obtained. Also we have plotted the graphs for different confidence levels 66%, 90% and 99% contours for (w_{0},~w_{1}) by fixing the other parameters.

Thermodynamics in loop quantum cosmology with non-canonical scalar field model

The cosmological scenario is built up within the framework of scalar field model possessing a noncanonical kinetic term in loop quantum gravity. The noncanonical scalar field is permitted to interact with dark matter field by assuming a specific form of coupling term. The equation of state parameter is set to be constant as well as variable (Chevallier–Polarski–Linder parametrization) and evaluated the behavior of universe through deceleration parameter and weak energy condition. These parameters favor the accelerated expansion of the universe for three values of equation of state parameter in both cases allowed by observational data. The squared speed of sound leads to the stability of the underlying models in both forms of equation of state parameter. Moreover, the validity of generalized second law of thermodynamics is analyzed by using first law of thermodynamics and assume the universe to be enclosed by apparent horizon. The Bekenstein, logarithmic and power-law entropy is being considered as entropy of horizon. The thermodynamic equilibrium condition is also discussed for all three cases of entropies. The generalized second law of thermodynamics and thermal equilibrium condition is satisfied for all the three types of entropies.

Low redshift observational constraints on tachyon models of dark energy

The background evolution of an accelerated, dark energy dominated universe is aptly described by non-canonical tachyon scalar field models. The accelerated expansion of the universe is determined by the choice of a suitable scalar field potential; in the case of a tachyon field, a `runaway' potential. In the absence of a fundamental theory, dark energy properties are studied in a phenomenological approach. This includes determining the model parameters using observations and to probe the allowed deviation from the cosmological constant model. In this paper, we present constraints on tachyon scalar field parameters from low redshift data for two different scalar field potentials. These scalar field potentials have been crucial in tachyon dark energy studies. The datasets considered in this paper include the supernova type Ia data, independent measurements of the Hubble parameter and the Baryon Acoustic Oscillation data. In this paper, we present constraints on tachyon field parameters using these observations and their combination. A combination of the datasets indicates that those model parameters are preferred which emulate the cosmological constant model. The initial value of the scalar field, in the unit of the Hubble constant, is bounded from below and does not require fine-tuning at larger values.

Cosmological dynamics of the general non-canonical scalar field models

We extend the investigation of cosmological dynamics of the general non-canonical scalar field models by dynamical system techniques for a broad class of potentials and coupling functions. In other words, we do not restrict the analysis to exponential or power-law potentials and coupling functions. This type of investigation helps in understanding the general properties of a class of cosmological models. In order to better understand the phase space of the models, we investigate the various special cases and discuss the stability and viability issues. Performing a detailed stability analysis, we show that it is possible to describe the cosmic history of the universe at the background level namely the early radiation dominated era, intermediate matter dominated era and the late time dark energy domination. Moreover, we find that we can identify a broad class of potentials and coupling functions for which it is possible to get an appealing unified description of dark matter and dark energy. The results obtained here, therefore, enlarge the previous analyses wherein only a specific potential and coupling functions describe the unification of dark sectors. Further, we also observe that a specific scenario can also possibly explain the phenomenon of slow-roll inflationary exit.

Structure formation in clustering DBI dark energy model with constant sound speed

ABSTRACT Within the framework of DBI non-canonical scalar field model of dark energy, we study the growth of dark matter perturbations in both the linear and non-linear regimes. In our DBI model, we consider the anti-de Sitter warp factor $f(\phi)=f_0\, \phi ^{-4}$ with constant f0 > 0 and assume the DBI dark energy to be clustered and its sound speed cs to be constant. In the linear regime, we use the pseudo-Newtonian formalism to obtain the growth factor of dark matter perturbations and conclude that for smaller cs (or $\tilde{f_0} \equiv f_0 H_0^2/M_P^2$), the growth factor of dark matter is smaller for clustering DBI model compared to the homogeneous one. In the non-linear regime based on the spherical collapse model, we obtain the linear overdensity δc($z$c), the virial overdensity Δvir($z$c), overdensity at the turn around ζ($z$c), and the rate of expansion of collapsed region hta($z$). We point out that for the smaller cs (or $\tilde{f_0}$), the values of δc($z$c), Δvir($z$c), ζ($z$c), and hta($z$) in non-clustering DBI models deviate more than the ΛCDM compared to the clustering DBI models. Finally, with the help of spherical collapse parameters we calculate the relative number density of halo objects above a given mass and conclude that the differences between clustering and homogeneous DBI models are more pronounced for the higher mass haloes at high redshift.

Cosmological implications of non-canonical scalar field model in fractal universe

Abstract The cosmological parameters as well as generalized second law of thermodynamics are investigated in the framework of fractal universe taking flat FRW universe filled with scalar field dark energy possessing a non-canonical kinetic term. The non-canonical scalar field model is allowed to interact with dark matter by assuming a specified form of coupling term. With the assumption that the universe is enveloped by apparent horizon, we investigate the validity of generalized second law of thermodynamics by using first law of thermodynamics as well as Bekenstein, logarithmic and power-law horizon entropies. For the illustration of results in more clear way, we set the equation of state parameter as constant as well as variable (Chevallier–Polarski–Linder parametrization). In the above mentioned scenario, the results of cosmological quantities such as squared speed of sound, weak energy condition and deceleration parameter are interpreted for both cases of equation of state parameter and found their compatibility with recent observations. It is also found that the generalized second law of thermodynamics holds for all cases of horizon entropies as well as equation of state parameters under specific constant parameters. The thermodynamic equilibrium is also observed for all cases of entropies.

Dynamical system of scalar field from 2-dimension to 3-D and its cosmological implications

We give the three-dimensional dynamical autonomous systems for most of the popular scalar field dark energy models including (phantom) quintessence, (phantom) tachyon, k-essence and general non-canonical scalar field models, change the dynamical variables from variables $(x, y, \lambda)$ to observable related variables $(w_{\phi}, \Omega_{\phi}, \lambda)$, and show the intimate relationships between those scalar fields that the three-dimensional system of k-essence can reduce to (phantom) tachyon, general non-canonical scalar field can reduce to (phantom) quintessence and k-essence can also reduce to (phantom) quintessence for some special cases. For the applications of the three-dimensional dynamical systems, we investigate several special cases and give the exactly dynamical solutions in detail. In the end of this paper, we argue that, it is more convenient and also has more physical meaning to express the differential equations of dynamical systems in $(w_{\phi}, \Omega_{\phi}, \lambda)$ instead of variables $(x, y, \lambda)$ and to investigate the dynamical system in 3-Dimension instead of 2-Dimension. We also raise a question about the possibility of the chaotic behavior in the spatially flat single scalar field FRW cosmological models in the presence of ordinary matter.

Study of parametrized dark energy models with a general non-canonical scalar field

In this paper, we have considered various dark energy models in the framework of a non-canonical scalar field with a Lagrangian density of the form ${\cal L}(\phi, X)=f(\phi)X{\left(\frac{X}{M^{4}_{Pl}}\right)}^{\alpha -1} - V(\phi)$, which provides the standard canonical scalar field model for $\alpha=1$ and $f(\phi)=1$. In this particular non-canonical scalar field model, we have carried out the analysis for $\alpha=2$. We have then obtained cosmological solutions for constant as well as variable equation of state parameter ($\omega_{\phi}(z)$) for dark energy. We have also performed the data analysis for three different functional forms of $\omega_{\phi}(z)$ by using the combination of SN Ia, BAO and CMB datasets. We have found that for all the choices of $\omega_{\phi}(z)$, the SN Ia $+$ CMB/BAO dataset favors the past decelerated and recent accelerated expansion phase of the universe. Furthermore, using the combined dataset, we have observed that the reconstructed results of $\omega_{\phi}(z)$ and $q(z)$ are almost choice independent and the resulting cosmological scenarios are in good agreement with the $\Lambda$CDM model (within the $1\sigma$ confidence contour). We have also derived the form of the potentials for each model and the resulting potentials are found to be a quartic potential for constant $\omega_{\phi}$ and a polynomial in $\phi$ for variable $\omega_{\phi}$.

Stability of a Noncanonical Scalar Field Model during Cosmological Date

Using the noncanonical model of scalar field, the cosmological consequences of a pervasive, self-interacting, homogeneous, and rolling scalar field are studied. In this model, the scalar field potential is “nonlinear” and decreases in magnitude with increasing the value of the scalar field. A special solution of the nonlinear field equations ofϕthat has time dependency as fixed point is obtained. The fixed point relies on the noncanonical term of action andγ-parameter; this parameter appeared in energy density of scalar field redshift. By means of such fixed point the different eigenvalues of the equation of motion will be obtained. In different epochs in the evolution of the Universe for different values ofqandn, the potentials as a function of scalar field are attained. The behavior of baryonic perturbations in linear perturbation scenario as a considerable amount of energy density of scalar field at low redshifts prevents the growth of perturbations in the ordinary matter fluid. The energy density in the scalar field is not appreciably perturbed by nonrelativistic gravitational fields, in either the radiation or matter dominant or scalar field dominated epoch.

Generalized second law of thermodynamics for non-canonical scalar field model with corrected-entropy

In this work, we have considered a non-canonical scalar field dark energy model in the framework of flat FRW background. It has also been assumed that the dark matter sector interacts with the non-canonical dark energy sector through some interaction term. Using the solutions for this interacting non-canonical scalar field dark energy model, we have investigated the validity of generalized second law (GSL) of thermodynamics in various scenarios using first law and area law of thermodynamics. For this purpose, we have assumed two types of horizons viz apparent horizon and event horizon for the universe and using first law of thermodynamics, we have examined the validity of GSL on both apparent and event horizons. Next, we have considered two types of entropy-corrections on apparent and event horizons. Using the modified area law, we have examined the validity of GSL of thermodynamics on apparent and event horizons under some restrictions of model parameters.

Intermediate inflation with modified kinetic term

Intermediate inflation is considered in a non-canonical scalar field model, in which the kinetic term of scalar field is taken as a power-law function. The free parameters of the model are constrained by using the most recent observational data related to scalar spectra index, tensor-to-scalar ratio, and scalar perturbation amplitude. The results are used to depict the potential behavior of the model and estimate the initial and final time of inflation.

Study of non-canonical scalar field model using various parametrizations of dark energy equation of state

In this present work, we try to build up a cosmological model using a non-canonical scalar field within the framework of a spatially flat FRW space–time. In this context, we have considered four different parametrizations of the equation of state parameter of the non-canonical scalar field. Under this scenario, analytical solutions for various cosmological parameters have been found out. It has been found that the deceleration parameter shows a smooth transition from a positive value to some negative value which indicates that the universe was undergoing an early deceleration followed by late time acceleration which is essential for the structure formation of the universe. With these four parametrizations, the future evolution of the models are also discussed. It has been found that one of the models (Generalized Chaplygin gas model, GCG) mimics the concordance $$\Lambda $$ CDM in the near future, whereas two other models (CPL and JBP) diverge due to future singularity. Finally, we have studied these theoretical models with the latest datasets from SN Ia $$+$$ H(z) $$+$$ BAO/CMB.

Light of Planck-2015 on Noncanonical Inflation

Slow-roll inflationary scenario is considered in noncanonical scalar field model supposing a power-law function for kinetic term and using two formalisms. In the first approach, the potential is picked out as a power-law function, that is, the most common approach in studying inflation. Hamilton-Jacobi approach is selected as the second formalism, so that the Hubble parameter is introduced as a function of scalar field instead of the potential. Employing the last observational data, the free parameters of the model are constrained, and the predicted form of the potential and attractor behavior of the model are studied in detail.