K-essence Scalar Field Research Articles

Collapsing scenarios of K-essence generalized Vaidya spacetime under [formula omitted] gravity

The paper investigates the collapse of the generalized emergent Vaidya spacetime in the setting of f(R̄,T̄) gravity, specifically in K-essence theory. In this study, the Dirac–Born–Infeld type non-standard Lagrangian is used to calculate the emergent metric Ḡμν, which is not conformally equivalent to the conventional gravitational metric. We use the function f(R̄,T̄) to reflect the additive nature of the emergent Ricci scalar (R̄) and the trace of the emergent energy–momentum tensor (T̄). Our study demonstrates that certain choices of f(R̄,T̄) may result in the existence of a naked singularity caused by gravitational collapse. The alternative f(R̄,T̄) values resulted in an accelerating universe dominated by dark energy. Moreover, the investigation showed the presence of both positive and negative masses, which might suggest the coexistence of dark matter and dark energy. In addition, when a certain amount of kinetic energy is present in the K-essence scalar field, mass is entirely converted into energy, indicating that spacetime is Minkowskian. The K-essence theory may also be employed as a dark energy framework and a basic gravitational theory, making it possible for researchers to investigate a wide ranges of cosmic phenomena.

Cosmological effects on f(R̄,T̄) gravity through a non-standard theory

This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting [Formula: see text] gravity within the framework of a nonstandard theory, called K-essence theory, where [Formula: see text] represents the Ricci scalar and [Formula: see text] denotes the trace of the energy–momentum tensor associated with the K-essence geometry. The Dirac–Born–Infeld (DBI) nonstandard Lagrangian has been employed to generate the emergent gravity metric [Formula: see text] associated with the K-essence. This metric is distinct from the usual gravitational metric [Formula: see text]. It has been shown that under a flat Friedmann–Lemaître–Robertson–Walker (FLRW) background gravitational metric, the modified field equations and the Friedmann equations of the [Formula: see text] gravity are distinct from the usual ones. In order to get the equation of state (EoS) parameter [Formula: see text], we have solved the Friedmann equations by taking into account the function [Formula: see text], where [Formula: see text] represents a parameter within the model. We have found a relationship between [Formula: see text] and time for different kinds of [Formula: see text] by treating the kinetic energy of the K-essence scalar field ([Formula: see text]) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction on [Formula: see text]. By presenting graphical representations of the EoS parameter with time, we show that our model is consistent with the data of SNIa[Formula: see text][Formula: see text][Formula: see text]BAO[Formula: see text][Formula: see text][Formula: see text][Formula: see text] within a certain temporal interval.

Constraints on the speed of sound in the k-essence model of dark energy

We consider a k-essence scalar field model for the late-time cosmic acceleration in which the sound speed, parametrized as cs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_s$$\\end{document} is constant. We compute the relevant background and perturbation quantities corresponding to the observables like cosmic microwave background, type Ia supernova, cosmic chronometers, baryon acoustic oscillations, and the fσ8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\sigma _8$$\\end{document}. We put constraints on the cs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_s^2$$\\end{document} parameter from these observations along with other parameters. We find lower values of cs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_s^2$$\\end{document} which are close to zero are tightly constrained. Particularly, we find mean value of log10(cs2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log _\ extrm{10} (c_s^2)$$\\end{document} to be -0.61\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-0.61$$\\end{document} and cs2≤10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_s^2 \\le 10^{-3}$$\\end{document} is more than 3σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} away from this mean value. This means these observations favor a homogeneous dark energy component compared to the clustering one.

Null geodesic structure for the Barriola–Vilenkin spacetime via k-essence

Based on the work of Chandrasekhar [The Mathematical Theory of Black Holes, Chap. 3, Sec. 20 (Oxford University Press, 1992)], we investigate the null geodesic structure of the emergent Barriola–Vilenkin (BV) spacetime in the context of k-essence theory. For k-essence, the emergent gravity metric is a one-to-one correspondence with the BV metric connected to the Schwarzschild background, where the global monopole charge is replaced by the dark energy density. This equivalence holds specifically for a certain class of k-essence scalar fields that have been constructed by Gangopadhyay and Manna [Eur. Phys. Lett. 100, 49001 (2012)]. We have traced out different trajectories for null geodesic in the presence of dark energy for the k-essence emergent BV spacetime. It is demonstrated that the outcomes deviate from the typical Schwarzschild spacetime owing to the fundamental configuration with a constant dark energy density.

Quantum Fractionary Cosmology: K-Essence Theory

Using a particular form of the quantum K-essence scalar field, we show that in the quantum formalism, a fractional differential equation in the scalar field variable, for some epochs in the Friedmann–Lemaı^tre–Robertson–Walker (FLRW) model (radiation and inflation-like epochs, for example), appears naturally. In the classical analysis, the kinetic energy of scalar fields can falsify the standard matter in the sense that we obtain the time behavior for the scale factor in all scenarios of our Universe by using the Hamiltonian formalism, where the results are analogous to those obtained by an algebraic procedure in the Einstein field equations with standard matter. In the case of the quantum Wheeler–DeWitt (WDW) equation for the scalar field ϕ, a fractional differential equation of order β=2α2α−1 is obtained. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; that is to say, when ωX∈[0,1], the order belongs to the interval 1≤β≤2, and when ωX∈[−1,0), the order belongs to the interval 0<β≤1. The corresponding quantum solutions are also given.

Kaniadakis holographic dark energy with scalar field in Bianchi type-V universe

In this work, considering anisotropic and homogeneous Bianchi type-V universe we investigated Kaniadakis holographic dark energy (KHDE). It is demonstrated that the equation of state (EoS) parameter has a transition from the quintessence era to the phantom era for the chosen model. Additionally, in the late time of the universe, EoS parameter behaves like a cosmological constant ([Formula: see text]) with an IR (Infrared) cut-off apparent horizon in case of a particular form of deceleration parameter. We reconstructed correspondence between the KHDE and tachyon, quintessence and k-essence scalar fields. Also, our numerical solutions have been shown in graphs for EoS parameter and scalar fields.

-gravity in the context of dark energy with power law expansion and energy conditions* *G.M. and A.P. acknowledge the DSTB, Government of West Bengal, India for financial support through the Grants No.: 322(Sanc.)/ST/P/S&T/16G-3/2018 dated 06.03.2019. S.R. is thankful to the authority of IUCAA, Pune for providing Visiting Associateship under which a part of this work has been done

The objective of this work is to generate a general formalism of gravity in the context of dark energy under the framework of K-essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, where is the familiar Ricci scalar, is the DBI type non-canonical Lagrangian with , and ϕ is the K-essence scalar field. The emergent gravity metric () and the well known gravitational metric () are not conformally equivalent. We have constructed a modified field equation using the metric formalism in -gravity incorporating the corresponding Friedmann equations into the framework of the background gravitational metric, which is of Friedmann-Lemaître-Robertson-Walker (FLRW) type. The solution of the modified Friedmann equations have been deduced for the specific choice of , which is of Starobinsky-type, using the power law expansion method. The consistency of the model with the accelerating phase of the universe has been shown when we restrict ourselves to consider the value of the dark energy density as , which indicates that the present universe is dark-energy dominated. Graphical plots for the energy density (ρ), pressure (p), and equation of state parameter () with respect to (w.r.t.) time (t) based on parametric values are interestingly consistent with the dark energy domination theory, and hence the accelerating features. We also highlight the corresponding energy conditions and constraints of the theory with a basic example.

Collapsing scenario for the k-essence emergent generalized Vaidya spacetime in the context of massive gravity's rainbow

In this study, we investigate the collapsing scenario for the k-essence emergent Vaidya spacetime in the context of massive gravity's rainbow. For this study, we consider that the background metric is Vaidya spacetime in massive gravity's rainbow. We show that the k-essence emergent gravity metric closely resembles the new type of generalized Vaidya massive gravity metric with the rainbow deformations for null fluid collapse, where we consider the k-essence scalar field as a function solely of the advanced or the retarded time. The k-essence emergent Vaidya massive gravity rainbow mass function is also different. This new type k-essence emergent Vaidya massive gravity rainbow metric satisfies the required energy conditions. The existence of a locally naked central singularity and the strength and strongness of the singularities for the rainbow deformations of the k-essence emergent Vaidya massive gravity metric are the interesting outcomes of the present work.

Late-time Cosmology of scalar field assisted f(𝒢) gravity

In this work, we present the late-time behaviour of the universe in the context of Einstein–Gauss–Bonnet gravitational theory. The theory involves a scalar field, which represents low-effective quantum corrections, assisted by a function [Formula: see text] solely depending from the Gauss–Bonnet topological invariant [Formula: see text]. It is considered that the dark energy serves as the impact of all geometric terms, which are included in the gravitational action and the density of dark energy acts as a time-dependent cosmological constant evolving with an infinitesimal rate and driving the universe into an accelerating expansion. We examine two cosmological models of interest. The first involves a canonical scalar field in the presence of a scalar potential while the second, involves a scalar field which belongs to a generalized class of theories [Formula: see text] namely the k-essence scalar field in the absence of scalar potential. As it is proved, the aforementioned models are in consistency with the latest Planck data and in relatively good agreement with the [Formula: see text]CDM standard cosmological model. The absence of dark energy oscillations at the early stages of matter-dominated era, which appear in alternative scenarios of cosmological dynamics in the context of modified [Formula: see text] gravitational theories, indicates an advantage of the theory for the interpretation of late-time phenomenology.

Bit rate bound on superluminal communication

We study semi-classical communication in positivity-violating k-essence scalar field theories, with superluminal modes propagating on a rolling background. The self-interactions due to the non-linear nature of these theories pose a constraint on the rate of superluminal information transfer. We derive a novel bit rate bound on superluminal communication within a conceptual model, to which a general class of k-essence theories naturally reduces. Our result implies the possibility that, even if these positivity-violating k-essence theories may not possess a maximal information propagation speed, there is nevertheless an upper bound on the rate of information transfer.

An accelerated universe with negative equation of state parameter in inhomogeneous cosmology with k-essence scalar field

We obtain a scaling relation for spherically symmetric k-essence scalar fields $\phi(r,t)$ for an inhomogeneous cosmology with the Lemaitre-Tolman- Bondi (LTB) metric. We show that this scaling relation reduces to the known relation for a homogeneous cosmology when the LTB metric reduces to the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric under certain identifications of the metric functions. A k-essence lagrangian is set up and the Euler-Lagrangian equations solved assuming $\phi(r,t)=\phi_{1}(r) + \phi_{2}(t)$. The solutions enable the LBT metric functions to be related to the fields. The LTB inhomogeneous universe exhibits late time accelerated expansion i.e.cosmic acceleration driven by negative pressure.

Time-dependent diffusive interactions between dark matter and dark energy in the context of k-essence cosmology

We investigated the scenario of time-dependent diffusive interaction between dark matter and dark energy and showed that such a model can be accommodated within the observations of luminosity distance-redshift data in Supernova Ia (SN Ia) observations. We obtain constraints on different relevant parameters of this model from the observational data. We consider a homogeneous scalar field ϕ(t) driven by a k-essence Lagrangian of the form L = V(ϕ)F(X) with constant potential V(ϕ) = V, to describe the dynamics of dark energy in this model. Using the temporal behaviour of the FRW scale factor, the equation of state and total energy density of the dark fluid, extracted from the analysis of SN Ia (JLA) data, we have obtained the time-dependence of the k-essence scalar field and also reconstructed the form of the function F(X) in the k-essence Lagrangian.

Tsallis HDE with an IR cutoff as Ricci horizon in a flat FLRW universe

The THDE (Tsallis HDE) model using an IR cut off as Ricci horizon has been investigated in the context of a flat Friedmann-Lemaı^tre-Robertson-Walker Universe by describing an accelerated expansion stage which Universe is experiencing. Evolution of Universe from decelerated (earlier) to the accelerated (current) phase exhibits by deceleration parameter (DP) attained in the model of THDE. The good behavior of cosmos is represented by Tsallis parameter δ and the EoS parameter’s values as phantom era (ωT<−1) and the quintessence era (ωT≥−1). Stability of the THDE model has been suggested by squared sound speed vs2. Additionally, for the THDE model the relation between phantom, quintessence and k-essence scalar fields has been analysed which helps to annotate the accelerated phase of the expanded Universe.

Gravitational collapse for the K-essence emergent Vaidya spacetime

In this paper, we study the gravitational collapse in the k-essence emergent gravity using a generalized Vaidya-type metric as a background. We also analyze the cosmic censorship hypothesis for this system. We show that the emergent gravity metric resembles closely to the new type of the generalized Vaidya metrics for null fluid collapse with the k-essence emergent mass function, where we consider the k-essence scalar field being a function solely of the advanced or the retarded time. This new type of k-essence emergent Vaidya metric has satisfied the required energy conditions. The existence of the locally naked central singularity, the strength and the strongness of the singularities for the k-essence emergent Vaidya metric are the interesting outcomes of the present work.

Time-like geodesic structure for the emergent Barriola–Vilenkin type spacetime

For a particular type of k-essence scalar field, the k-essence emergent gravity metric is exactly mapped on to the Barriola–Vilenkin (BV) type metric for Schwarzschild background established by Gangopadhyay and Manna. Based on the Chandrasekhar, we report the exciting features of the time-like geodesic structure in the presence of dark energy in an emergent gravity scenario for this Barriola–Vilenkin type metric. We trace the different kinds of trajectories for time-like geodesic in the presence of dark energy for the k-essence emergent Barriola–Vilenkin spacetime, which is same as the Schwarzchild spacetime in view of the basic orientation, but the allowed ranges of the aphelion and perihelion distances are much more different. The bound and unbound orbits are plotted for a fixed value of the dark energy density.

F(R) GRAVITY WITH K-ESSENCE SCALING RELATION AND COSMIC ACCELERATION

A modified gravity theory with f(R) = R2 coupled to a dark energy lagrangian L= − V(φ)f (X) , X = ∇µφ∇µφ, gives plausible cosmological scenarios when the modified Friedman equations are solved subject to the scaling relation &lt;mml:math&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;X&lt;/mml:mi&gt;&lt;mml:msup&gt;&lt;mml:mrow&gt;&lt;mml:mfenced&gt;&lt;mml:mrow&gt;&lt;mml:mfrac&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;d&lt;/mml:mi&gt;&lt;mml:mi&gt;F&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow/&gt;&lt;/mml:mfrac&gt;&lt;/mml:mrow&gt;&lt;/mml:mfenced&gt;&lt;/mml:mrow&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;/mml:msup&gt;&lt;mml:mo&gt;=&lt;/mml:mo&gt;&lt;mml:mi&gt;C&lt;/mml:mi&gt;&lt;mml:mi&gt;a&lt;/mml:mi&gt;&lt;mml:msup&gt;&lt;mml:mrow&gt;&lt;mml:mfenced&gt;&lt;mml:mi&gt;t&lt;/mml:mi&gt;&lt;/mml:mfenced&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mo&gt;−&lt;/mml:mo&gt;&lt;mml:mn&gt;6&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msup&gt;&lt;/mml:mrow&gt;&lt;/mml:math&gt;. This relation is already known to be valid, for constant potential V(φ), when Lis coupled to Einstein gravity. φ is the k-essence scalar field and a(t) is the scale factor. The various scenarios are: (1) Radiation dominated Ricci flat universe with deceleration parameter Q = 1. The solution for φ is an inflaton field for small times. (2) Q is always negative and we have accelerated expansion of the universe right from the beginning of time and φ is an inflaton for small times. (3)The deceleration parameter Q = −5, i.e., we have an accelerated expansion of the universe. φ is an inflaton for small times. (4)A generalisation to f(R) = Rn shows that whenever n &gt;1.780 or n &lt; −0.280 , Q will be negative and we will have accelerated expansion of the universe. At small times φ is again an inflaton.The results remind us of other physical phenomena where existence of scaling relations signal some sort of universality for theories with different microscopic lagrangians. Here this is seen in the case of Einstein gravity and modified gravity theories.

The Hawking temperature in the context of dark energy for Kerr\u2013Newman and Kerr\u2013Newman\u2013AdS backgrounds

We show that the Hawking temperature is modified in the presence of dark energy in an emergent gravity scenario for Kerr–Newman(KN) and Kerr–Newman–AdS(KNAdS) background metrics. The emergent gravity metric is not conformally equivalent to the gravitational metric. We calculate the Hawking temperatures for these emergent gravity metrics along theta =0. Also we show that the emergent black hole metrics are satisfying Einstein’s equations for large r and theta =0. Our analysis is done in the context of dark energy in an emergent gravity scenario having k-essence scalar fields phi with a Dirac–Born–Infeld type Lagrangian. In KN and KNAdS background, the scalar field phi (r,t)=phi _{1}(r)+phi _{2}(t) satisfies the emergent gravity equations of motion at rrightarrow infty for theta =0.

Diffusive dark matter and dark energy scenario and k -essence in the context of Supernova Ia observations

We consider a unified model of interacting dark matter and dark energy to account for coincidence of present day dark energy and dark matter densities. We assume dark energy to be represented by a homogeneous scalar field $\phi$ whose dynamics is driven by a (non-canonical) $k$-essence Lagrangian with constant potential and the particles of dark matter fluid undergoing velocity diffusion in background medium of the $k-$essence scalar field $\phi$. This results in a transfer of energy from the fluid of dark matter to that of dark energy. This effect shows up as a source term in the continuity equation for dark matter and dark energy fluids. The source term involves a diffusion coefficient which is a measure of average energy transferred per unit time due to diffusion. We use time evolutions of the scale factor of background FRW spacetime, energy density and pressure of the dark fluid obtained from analysis of Supernova Ia data to obtain bounds on the diffusion parameter. For a constant potential in the $k$-essence Lagrangian, the temporal behaviour of a homogeneous $k$-essence field $\phi$ is obtained for different values of the diffusion parameter. The obtained temporal behaviour may be expressed as $\phi(t/t_0) = \phi_0 + \varepsilon_1 (t/t_0 - 1) + \varepsilon_2 (t/t_0 -1)^2$, where $t_0$ is the time corresponding to present epoch. The coefficients $\varepsilon_1$ and $\varepsilon_2$ have been found and obtained as linear functions of diffusion parameter.

Mimetic gravity as DHOST theories

We show that theories of mimetic gravity can be viewed as degenerate higher-order scalar-tensor (DHOST) theories that admit an extra local (gauge) symmetry in addition to the usual diffeomorphism invariance. We reformulate and classify mimetic theories in this perspective. Using the effective theory of dark energy, recently extended to include DHOST theories, we then investigate the linear perturbations about a homogeneous and isotropic background for all mimetic theories. We also include matter, in the form of a k-essence scalar field, and we derive the quadratic action for linear perturbations in this case.

New holographic dark energy in bianchi- III universe with k-essence

The proposed dark energy, holographic, with new infrared cut-off (IR) of Granda and Oliveros (2009) has been investigated in Bianchi-III anisotropic model with the matter. The solutions of Einstein’s field equations are found by assuming the time-dependent deceleration parameter. The deceleration parameter obtained in our model demonstrates the universe transition from early decelerating to the current accelerating stage. It has seen that our new holographic dark energy (NHDE) model corresponds to an accelerating universe with k-essence (ω<−1/3). The statefinder diagnostic has also been performed in our model. In addition, correspondence between k-essence scalar field and our new holographic dark energy model has been reformulated. The k-essence dynamics of the potential and scalar field are reformulated, which depicts the accelerated expansion of the universe.