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We investigate two classes of non-minimally coupled curvature-matter models in the FLRW universe with a perfect fluid and analyze their cosmological implications using Supernova Ia, Observed Hubble Data, and Baryon Acoustic Oscillation measurements. Non-minimal coupling is introduced via an additional term $\int d^4x \sqrt{-g} \mathcal{G}({\cal L}_{m}) f_2(R)$ in the Einstein-Hilbert action. To obtain observational constraints, we use an exponential-type fluid-pressure profile $p = p_0e^{ak}$ characterized by the dimensionless parameter $k$ and parameterize $f_2(R)$ as $R^n$ with another dimensionless parameter $n$. Two additional parameters, $\alpha$ and $\beta$ in the functional form of $\mathcal{G}({\cal L}_{m})$ determine the coupling strength. We identify significant regions in the $(n, k)$-parameter space for fixed coupling strength values where non-minimally coupled models align with observed late-time cosmic evolution. Additionally, we explore and discuss features of energy transfer between the curvature and matter sectors using observational data., Comment: 22 pages and 8 figures

We investigate an interacting quintessence dark energy - dark matter scenario and its impact on structure formation by analyzing the evolution of scalar perturbations. The interaction is introduced by incorporating a non-zero source term into the continuity equations of the two sectors (with opposite signs), modeled as $\bar{Q}_0 \equiv \alpha\bar{\rho}_{\rm m}(H + \kappa\dot{\phi})$. The coupling parameter $\alpha$ and the parameter $\lambda$ involved in quintessence potential $V(\phi) = V_0e^{-\lambda\kappa\phi}$, play crucial roles in governing the dynamics of evolution examined within the present framework. The cosmic evolution, within this context, is depicted as a first-order autonomous system of equations involving appropriately chosen dynamical variables. We analyzed the associated stability characteristics and growth rate of perturbations and obtained domains in the ($\alpha-\lambda$) parameter space for which fixed points can exhibit stable and non-phantom accelerating solutions. Depending on its magnitude, the coupling parameter $\alpha$ has the potential to change the characteristics of certain critical points, altering them from attractors to repellers. This model effectively captures the evolutionary features of the universe across its various phases at both the background and perturbation levels. The issue of cosmic coincidence can also be addressed within the framework of this model. We also observed that for a moderate strength of coupling, the growth rate of matter perturbation extends into the distant future., Comment: 23 pages, 2 tables and 6 figures

In this study, we analyze the dynamics of the interaction between dark matter and curvature-driven dark energy in viable $f(R)$ gravity models using the framework of dynamical system analysis. We incorporate this interaction by introducing a source term in their respective continuity equations, given by $Q = \frac{\kappa^2 \alpha}{3H}\tilde{\rho}_{\rm m}\rho_{\rm curv}$, and examine two $f(R)$ gravity models that comply with local gravity constraints and cosmological viability criteria. Our findings reveal subtle modifications to fixed points and their stability criteria when compared to the conventional dynamical analysis of $f(R)$ gravity models without matter-curvature interactions as proposed and examined in prior literature. We determine the parameter limits associated with the stability criteria of critical points of the dynamical system for both the models. Additionally, the introduction of interaction reveals variations in the dynamical aspects of cosmic evolution, contingent on the range of values for the relevant model parameters. These results are consistent with the observed features of cosmic evolution within specific limits of the $f(R)$ models parameters and the coupling parameter $\alpha$. We also examine the evolutionary dynamics of the universe in the interacting scenario through cosmological and cosmographic parameters. Our analysis demonstrates that the interacting scenario comprehensively accounts for all the observed phases of the universe's evolution and also results in a stable late-time cosmic acceleration. Additionally, we've studied how the coupling parameter affects evolutionary dynamics, particularly its impact on the matter-to-curvature energy density ratio. Our findings suggest that the chosen form of interaction can also address the cosmic coincidence problem., Comment: 25 pages, 5 tables and 4 figures. This version is accepted for publication in European Physical Journal C

We considered non-minimally coupled curvature-matter models of gravity in a FRW universe filled with perfect fluid and investigated its cosmological implications in the light of Pantheon compilation of 1048 Supernovae Ia data points along with 54 data points from Observed Hubble Data. The non-minimal curvature-matter coupling has been introduced by adding a term $\int \left[\lambda R^n \mathcal{L}_m\right] \sqrt{-g}d^4x$ to the usual action for Einstein gravity involving the Einstein Hilbert action and minimally coupled matter action. We investigate the observational constraints on the non-minimal models by choosing two different kinds of parametrization of fluid-pressure profiles using a dimensionless parameter $k$. The interplay of the three parameters $\lambda,n,k$ plays a pivotal role in testing the consistency of non-minimally coupled fluid-curvature scenarios with the observed data. We found there exist large domains in the ($\lambda,n,k$)-parameter space for which models with non-minimal curvature-matter mixing stand as viable cosmological models reproducing the observed features of late-time cosmic evolution. We also commented on the possibility of `gravitationally induced particle creation' in the context of SNe Ia data., Comment: 20 pages and 6 figures. This version is accepted for publication in Classical and Quantum Gravity (CQG)

It has been shown by \textit{Scherrer and Putter et.al} that, when dynamics of dark energy is driven by a homogeneous $k-$essence scalar field $\phi$, with a Lagrangian of the form $L = V_0F(X)$ with a constant potential $V_0$ and $X = \frac{1}{2}\nabla^\mu\phi \nabla_\mu\phi = \frac{1}{2}\dot{\phi}^2$, one obtains a scaling relation $X(dF/dX)^2 = Ca^{-6}$ , where $C$ is a constant and $a$ is the FRW scale factor of the universe. The separate energy conservation in the dark energy sector and the constancy of $k-$essence potential are instrumental in obtaining such a scaling. In this paper, we have shown that even when considering time-dependent interactions between dark energy and dark matter, the constancy of $k-$essence potential may lead to a modified form of scaling. We have obtained such a scaling relation for a particular class of parametrisation of the source term occurring in the continuity equation of dark energy and dark matter in the interacting scenario. We used inputs from the JLA analysis of luminosity distance and redshift data from Supernova Ia observations, to obtain the modified form of the scaling., Comment: 21 pages and 6 figures. This version has been accepted for publication in European Physical Journal Plus

In this paper, we analyse the JLA data on Supernova observations in the context of $k-$essence dark energy model with Lagrangian $L=VF(X)$, with a constant potential $V$ and the dynamical term $X = (1/2)\nabla_{\mu}\phi\nabla_{\nu}\phi = \dot{\phi}^2/2$ for a homogeneous scalar field $\phi(t)$, in a flat FRW spacetime background. Scaling relations are used to extract temporal behaviour of different cosmological quantities and the form of the function $F(X)$ from the data. We explore how the parameters of the model, viz. value of the constant potential $V$ and a constant $C$ appearing in the emergent scaling relation, control the dynamics of the model in the context of JLA data, by setting up and analysing an equivalent dynamical system described by a set of autonomous equations., Comment: 22 pages, 7 figures, 3 tables; Accepted for publication in European Physical Journal Plus

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 (SNe Ia) observations. We obtain constrains on different relevant parameters of this model from the observational data. We consider a homogeneous scalar field $\phi(t)$ driven by a $k-$essence Lagrangian of the from $L = V(\phi)F(X)$ with constant potential $V(\phi) = V$, 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 SNe Ia (JLA) data, we have obtained the time-dependence of the $k-$essence scalar field and also reconstructed form of the function $F(X)$ in the $k-$essence Lagrangian., Comment: 14 pages, 7 figures; Accepted for publication in Research in Astronomy and Astrophysics

We investigated implications of recently released `Joint Light-curve Analysis' (JLA) supernova Ia (SNe Ia) data for dark energy models with time varying equation of state of dark energy, usually expressed as $w(z)$ in terms of variation with corresponding redshift $z$. From a comprehensive analysis of the JLA data, we obtain the observational constraints on the different functional forms of $w(z)$, corresponding to different varying dark energy models often considered in literature, \textit{viz.} CPL, JBP, BA and Logarithmic models. The constraints are expressed in terms of parameters ($w_a, w_b$) appearing in the chosen functional form for $w(z)$, corresponding to each of the above mentioned models. Realising dark energy with varying equation of state in terms of a homogeneous scalar field $\phi$, with its dynamics driven by a $k-$essence Lagrangian $L=VF(X)$ with a constant potential $V$ and a dynamical term $F(X)$ with $X=(1/2)\nabla^\mu\phi\nabla_\mu\phi$ we reconstructed form of the function $F(X)$. This reconstruction has been performed for different varying dark energy models at best-fit values of parameters ($w_a, w_b$) obtained from analysis of JLA data. In the context of $k-$essence model, we also investigate the variation of adiabatic sound speed squared, $c_s^2(z)$, and obtained the domains in ($w_a, w_b$) parameter space corresponding to the physical bound $ c_s^2>0$ implying stability of density perturbations., Comment: 21 pages, 4 figures, accepted for publication in European Physical Journal Plus

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., Comment: 14 pages, 4 figures

In this paper we exploit dynamics of a $k-$essence scalar field to realise interactions between dark components of universe resulting in a evolution consistent with observed features of late time phase of cosmic evolution. Stress energy tensor corresponding to a $k-$essence Lagrangian $L=V( \phi)F(X)$ (where $X=\frac{1}{2}g^{\mu\nu}\nabla_\mu\phi \nabla_\nu\phi$) is shown to be equivalent to an ideal fluid with two components having same equation of state. Stress energy tensor of one of the components may be generated from a constant potential $k-$essence Lagrangian of form $L_1=V_0F(X)$ ($V_0$ constant) and that of other from another Lagrangian of form $L_2=V_1(\phi)F(X)$ with $V=V_0 + V_1(\phi)$. We have shown that, the unified dynamics of dark matter and dark energy described by a single scalar field $\phi$ driven by a $k-$essence Lagrangian $L= V(\phi)F(X)$ may be viewed in terms of diffusive interactions between the two hypothetical fluid components `1' and `2' with stress energy tensors equivalent to that of Lagrangians $L_1$ and $L_2$ respectively. The energy transfer between the fluid components is determined by functions $V(\phi)$, $F(X)$ and their derivatives. Such a realisation is shown to be consistent with the Supernova Ia data with certain constraints on the temporal behaviour of $k-$essence potential $V(\phi)$. We have described a methodology to obtain such constraints., Comment: 13 pages, 4 figures

A phenomenological model is described for Cosmic Microwave Background Radiation (CMBR) evolution with dark energy an essential ingredient in the form of a $k-$essence scalar field. The following features of this evolution can be successfully obtained from this model: (a) the {\it observed} variation of the rate of change of scale factor $a(t)$, i.e. $\dot a$, with time and (b) the {\it observed} value of the epoch when the universe went from a decelerating phase to an accelerated phase. These two features have been matched with graphical transcriptions of SNe Ia data. The model also indicates that the evolution is sensitive to the presence of inhomogeneity and this sensitivity increases as one goes further into the past. Further, the value of the inhomogeneity parameter determines the epoch of switch over to an accelerated phase. A positive value of inhomogeneity parameter leads to switch over at earlier epochs, while a negative value leads to switch over at later epochs. If the value of the inhomogeneity parameter is a bit negative then the crossover point from deceleration to acceleration gives better agreement with the observed value., Comment: 19 pages, Latex2e

A $k$-essence scalar field model having (non canonical) Lagrangian of the form $L=-V(\phi)F(X)$ where $X=1/2g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi$ with constant $V(\phi)$ is shown to be consistent with luminosity distance-redshift data observed for type Ia Supernova. For constant $V(\phi)$, $F(X)$ satisfies a scaling relation which is used to set up a differential equation involving the Hubble parameter $H$, the scale factor $a$ and the $k$-essence field $\phi$. $H$ and $a$ are extracted from SNe Ia data and using the differential equation the time dependence of the field $\phi$ is found to be: $\phi(t) \sim \lambda_0 + \lambda_1 t + \lambda_2 t^2$. The constants $\lambda_i$ have been determined. The time dependence is similar to that of the quintessence scalar field (having canonical kinetic energy) responsible for homogeneous inflation. Furthermore, the scaling relation and the obtained time dependence of the field $\phi$ is used to determine the $X$-dependence of the function $F(X)$., Comment: 8 pages, 5 figures, Latex