Non-canonical Scalar Field Research Articles

Anisotropic k-essence

In this paper, we study the late time cosmology of a non-canonical scalar field ( k -essence) coupled to a vector field in a Bianchi-I background. Specifically, we study three cases: canonical scalar field (quintessence) with exponential potential as a warm up, the dilatonic ghost condensate, and the Dirac Born Infeld field with exponentials throat and potential. By using a dynamical system approach, we show that anisotropic dark energy fixed points can be attractors for a suitable set of parameters of each model. We also numerically integrate the associated autonomous systems for particular initial conditions chosen in the deep radiation epoch. We find that the three models can give an account of an equation of state of dark energy close to − 1 nowadays. However, a non-negligible spatial shear within the current observational bounds is possible only for the quintessence and the Dirac Born Infeld field. We also find that the equation of state of dark energy and the shear oscillate at late times, whenever the coupling of the k -essence field to the vector field is strong enough. The reason of these oscillations is explained in the appendix.

Inflation with non-canonical scalar fields revisited

We revisit inflation with non-canonical scalar fields by applying deformed-steepness exponential potentials. We show that the resulting scenario can lead to inflationary observables, and in particular to scalar spectral index and tensor-to-scalar ratio, in remarkable agreement with observations. Additionally, a significant advantage of the scenario is that the required parameter values, such as the non-canonicality exponent and scale, as well as the potential exponent and scale, do not need to acquire unnatural values and hence can accept a theoretical justification. Hence, we obtain a significant improvement with respect to alternative schemes, and we present distinct correlations between the model parameters that better fit the data, which can be tested in future probes. This combination of observational efficiency and theoretical justification makes the scenario at hand a good candidate for the description of inflation.

Unifying dark matter and dark energy with non-canonical scalars

Non-canonical scalar fields with the Lagrangian {{mathcal {L}}} = X^alpha - V(phi ), possess the attractive property that the speed of sound, c_s^{2} = (2,alpha - 1)^{-1}, can be exceedingly small for large values of alpha . This allows a non-canonical field to cluster and behave like warm/cold dark matter on small scales. We derive a general condition on the potential in order to facilitate the kinetic term X^alpha to play the role of dark matter, while the potential term V(phi ) playing the role of dark energy at late times. We demonstrate that simple potentials including V= V_0coth ^2{phi } and a Starobinsky-type potential can unify dark matter and dark energy. Cascading dark energy, in which the potential cascades to lower values in a series of discrete steps, can also work as a unified model.

CMB imprints of non-canonical anisotropic inflation

Effect of non-canonical scalar fields on the CMB imprints of the anisotropic inflation will be discussed in details in this paper. In particular, we are able to obtain the general formalism of the angular power spectra in the scalar perturbations, tensor perturbations, cross-correlations, and linear polarization in the context of the anisotropic inflation model involving non-canonical scalar fields. Furthermore, some significant numerical spectra will be plotted using the most recent data of Planck as well as the BICEP2 and Keck array. As a result, we find a very interesting point that the TT spectra induced by the tensor perturbations as well as by the linear polarization will increase when the speed of sound decreases.

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.

No-hair theorems for noncanonical self-gravitating static multiple scalar fields

We prove under certain assumptions no-hair theorems for non-canonical self-gravitating static multiple scalar fields in spherically symmetric spacetimes. It is shown that the only static, spherically symmetric and asymptotically flat black hole solutions consist of the Schwarzschild metric and a constant multi-scalar map. We also prove that there are no static, horizonless, asymptotically flat, spherically symmetric solutions with static scalar fields and a regular center. The last theorem shows that the static, asymptotically flat, spherically symmetric reflecting compact objects with Neumann boundary conditions can not support a non-trivial self-gravitating non-canonical (and canonical) multi-scalar map in their exterior spacetime regions. In order to prove the no-hair theorems we derive a new divergence identity.

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.

The growth of DM and DE perturbations in DBI non-canonical scalar field scenario

We study the effect of varying sound speed on clustering dark energy in the Dirac–Born–Infeld (DBI) scenario. The DBI action is included in the class of k-essence models, and it has an important role in describing the effective degrees of freedom of D-branes in the string theory. In the DBI setup, we take the anti-de Sitter (AdS) warp factor f(ϕ)=f0ϕ−4, and investigate the self-interacting quartic potential V(ϕ)=λϕ4∕4. We calculate the full expression of the effective sound speed for our model, and show that it can evolve with time during the cosmological evolution. Besides, the adiabatic sound speed evolves with time here, and this influences the background dynamics to some extent. We show that the effective sound speed is very close to the adiabatic sound speed. We examine the effect of the variable sound speed on growth of the perturbations in both the linear and non-linear regimes. In the linear regime, we apply the Pseudo-Newtonian formalism, and show that dark energy suppresses the growth of perturbations at low redshifts. From study of the Integrated Sachs–Wolfe (ISW) effect in our setup, we see that the model manifests some deviation from the concordance ΛCDM model. In the non-linear regime, we follow the approach of spherical collapse model, and calculate the linear overdensity δc(zc), the virial overdensity Δvir(zc), overdensity at the turn around ζ(zc) and the rate of expansion of collapsed region hta(z). Our results imply that the provided values of δc(zc), Δvir(zc), ζ(zc) and hta(z) in our clustering DBI dark energy model approach the fiducial value in the EdS universe at high enough redshifts. We further compute relative number density of halo objects above a given mass in our setting, and show that the number of structures with respect to the ΛCDM model is reduced more in the high mass tail at high redshifts.

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.

Perturbations in tachyon dark energy and their effect on matter clustering

A non-canonical scalar tachyon field is a viable candidate for dark energy and has been found to be in good agreement with observational data. Background data alone cannot completely rule out degeneracy between this model and others. To further constrain the parameters, apart from the distance measurements, we study perturbations in tachyon scalar field and how they affect matter clustering. We consider two tachyon potentials for this study, an inverse square potential and an exponential potential. We study the evolution of the gravitational potential, matter density contrast and dark energy density contrast, and compare them with the evolution in the ΛCDM model. Although perturbations in dark energy at sub-Hubble scales are negligible in comparison with matter perturbations, they cannot be ignored at Hubble and super-Hubble scales (λp > 1000 Mpc). We also study the evolution of growth function and growth rate of matter, and find that the growth rate is significantly suppressed in dark energy dominated era with respect to the growth rate for Λ CDM model. A comparison of these models with Redshift Space Distortion growth rate data is presented by way of calculating fσ8(z). There is a tension of 2.9σ (2.26σ) between growth rate data and Planck-2015 (Planck-2018) Cosmic Microwave Background Radiation data for Λ CDM model. We present constraints on free parameters of these models and show that perturbations in tachyon scalar field reduce this tension between different data sets.

Generalized scalar\u2013tensor theory of gravity reconstruction from physical potentials of a scalar field

We describe how to reconstruct generalized scalar–tensor gravity (GSTG) theory, which admits exact solutions for a physical type of potentials. Our consideration deals with cosmological inflationary models based on GSTG with non-minimal coupling of a (non-canonical) scalar field to the Ricci scalar. The basis of proposed approach to the analysis of these models is an a priori specified relation between the Hubble parameter H and a function of a non-minimal coupling F=1+delta F, Hpropto sqrt{F}. Deviations from Einstein gravity delta F induce corresponding deviations of the potential delta V from a constant value and modify the dynamics from a pure de Sitter exponential expansion. We analyze the models with exponential power-law evolution of the scale factor and we find the equations of influence of non-minimal coupling, choosing it in the special form, on the potential and kinetic energies. Such a consideration allows us to substitute the physical potential into the obtained equations and then to calculate the non-minimal coupling function and kinetic term that define the GSTG parameters. With this method, we reconstruct GSTG for the polynomial, exponential, Higgs, Higgs–Starobinsky and Coleman–Weinberg potentials. Special attention we pay to parameters of cosmological perturbations and prove the correspondence of the obtained solutions to observational data from Planck.

Gauss–Bonnet Inflation after Planck2018

Abstract We study the primordial perturbations and reheating process in the models where the Gauss–Bonnet (GB) term is nonminimally coupled to the canonical and noncanonical (DBI and tachyon) scalar fields. We consider several potentials and GB coupling terms as power-law, dilaton-like, cosh-type, E-model, and T-model. To seek the observational viability of these models, we study the scalar perturbations numerically and compare the results with the Planck2018 TT, TE, EE+lowE+lensing+BK14+BAO joint data at 68% CL and 95% CL. We also study the tensor perturbations in confrontation with the Planck2018 TT, TE, EE+lowE+lensing+BK14+BAO+ LIGO, and Virgo2016 joint data at 68% CL and 95% CL. In this regard, we obtain some constraints on the GB coupling parameter β. Another important process in the early universe is the reheating phase after inflation, which is necessary to reheat the universe for subsequent evolution. In this regard, we study the reheating process in these models and find some expressions for the e-folds number and temperature during that era. Considering that from Planck TT, TE, EE+lowEB+lensing data and BICEP2/Keck Array 2014, based on the ΛCDM model, we have n s = 0.9658 ± 0.0038 and r < 0.072, we obtain some constraints on the e-folds number and temperature. From the values of the e-folds number and the effective equation of state and also the observationally viable value of the scalar spectral index, we explore the capability of the models in explaining the reheating phase.

Chaplygin gas inspired non-canonical scalar field warm inflation

We consider a warm inflation universe model in the presence of generalized Chaplygin gas and modified Chaplygin gas by taking Dirac-Born-Infeld non-canonical scalar field. For developing various inflationary parameters, we assume quadratic potential and quartic potential and Anti-de-Sitter warp factor for the Dirac-Born-Infeld inflation. We develop the number of e-folds, scalar as well as tensor power spectrum, scalar spectral index and tensor-scalar ratio in the terms of ϕ under slow-roll approximation by assuming the constant sound speed. We establish the graphical behavior of r−N,ns−N and α−N for both Chaplygin gas models. The results of r−N,ns−N and α−N are 0.972−0.02+0.02,−0.0005−0.001+0.001,0.0004−0.0004+0.0004 (for generalized Chaplygin gas with quadratic potential) and 0.97−0.05+0.05,0.0045−0.0055+0.0055,0.0045−0.0045+0.0045 (generalized Chaplygin gas with quartic potential), respectively. Also, the results of inflationary parameters are 0.97−0.02+0.02,0.0015−0.0025+0.0025,0.125−0.125+0.125 (for modified Chaplygin gas with quadratic potential) and 0.94−0.05+0.05,0.01−0.015+0.015,0.0185−0.0185+0.0185 (modified Chaplygin gas with quartic potential), respectively. It is found that these results are well matched with 68% and 95% CL constraints of the Planck 2018 TT,TE,EE+lowP+lensing data.

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.

Intermediate inflation with non-canonical scalar field in the low anisotropy Universe

The behavior of a non-canonical scalar field within an anisotropic Bianchi type I, spatially homogeneous Universe in the framework of the intermediate inflation will be studied. It will be examined on the condition that both the anisotropy and non-canonical sources come together if there is any improvement in compatibility with the observational data originated from Planck 2015. Based on this investigation, it can be observed that automatically a steep potential which can manage inflation in a better way will be obtained. Additionally, as a common procedure for an inflationary study, we shall try to calculate the related inflationary observables such as the amplitude of the scalar perturbations, scalar and tensor spectral indices, tensor-to-scalar ratio, the running spectral index and the number of e-folds. As an exciting part of our results, we will find that our model has a good consistency compared to data resulting from CMB and different Planck results. To justify our claims, the well-known canonical inflationary scenario in an anisotropic Bianchi type I Universe will also be evaluated.

Constant-roll approach to noncanonical inflation

The scenario of constant-roll inflation is studied where the inflaton is a scalar field with modified kinetic term, known as non-canonical scalar field. This modification leads to some changes in the slow-roll parameters, and also by taking the second slow-roll parameter as a constant, the differential equation for the Hubble parameter is altered as well. Assuming $\eta=\beta$ and reconsidering the perturbation equations makes it clear that there should be some modified terms in the scalar spectral index and amplitude of scalar perturbations. After finding the exact solution, the main perturbation parameters are obtained at the horizon crossing time. Then by plotting the $r-n_s$ diagram it is shown that for some specific values of $\beta$ one could find a good agreement with observational data. In addition, considering the attractor behavior of the model leads to this result that this feature could be appropriately satisfied.

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.

Commutative–non-commutative dualities

We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way. This construction exploits a generalization of the exact renormalization group equation (ERG). We apply this to the simple case of the Landau problem and then generalize it to the free and interacting non-canonical scalar field theory. This constructive approach offers the advantage of tracking the implementation of the Lorentz symmetry in the non-commutative dual theory. In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly non-trivial and non-local manner.

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.