We show that the Raychaudhuri equation remains form invariant for certain solutions of scalar fie... more We show that the Raychaudhuri equation remains form invariant for certain solutions of scalar fields φ whose Lagrangian is non-canonical and of the form L(X, φ) = -V (φ)F (X), with X = 1 2 gµν∇ µ φ∇ ν φ and V (φ) the potential. Solutions exist for both homogeneous and inhomogeneous fields that are like inflatons. Certain recent observations indicate that the cosmos is inhomogeneous and thus our results are in sync with latest observations. So the Raychaudhuri equation can accommodate primordial inhomogeneities as well as cosmologically relevant scenarios.
This article investigates on the radial and non-radial geodesic structures of the generalized Kes... more This article investigates on the radial and non-radial geodesic structures of the generalized Kessence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal equivalence to the conventional gravitational metric. This study employs a non-canonical action of the Dirac-Born-Infeld kind. In this work, we categorize the generalized K-essence Vaidya mass function into two distinct forms. Both the forms of the mass functions have been extensively utilized to analyze the radial and non-radial time-like or null geodesics in great details inside the comoving plane. Indications of the existence of wormhole can be noted during the extreme phases of spacetime, particularly in relation to black holes and white holes, which resemble the Einstein-Rosen bridge. In addition, we have also detected the distinctive indication of the quantum tunneling phenomenon around the central singularity.
The motto of this work is to generate a general formalism of f ( R, L(X))-gravity in the context ... more The motto of this work is to generate a general formalism of f ( R, L(X))-gravity in the context of dark energy under the framework of the K-essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, where R is the familiar Ricci scalar, L(X) is the DBI type non-canonical Lagrangian with X = 1 2 g µν ∇µφ∇ν φ and φ is the K-essence scalar field. The emergent gravity metric Ḡµν and the well known gravitational metric gµν are not conformally equivalent. We have constructed a modified field equation using the metric formalism in f ( R, L(X))-gravity incorporating the corresponding Friedmann equations in the framework of the background gravitational metric which is of Friedmann-Lemaître-Robertson-Walker (FLRW) type. The solution of modified Friedmann equations have been deduced for the specific choice of f ( R, L(X)), which is of Starobinskytype, using 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 φ2 = 8 9 = 0.888 < 1, which indicates that the present Universe is dark energy dominated. Graphical plots for the energy density (ρ), pressure (p) and equation of state parameter (ω) w.r.t. time (t) based on parametric values are interestingly consistent with the dark energy domination and hence accelerating features. We also put some light on the corresponding energy conditions and constraints of the f ( R, L(X)) theory with one basic example.
We establish a formal connection between the K-essence emergent gravity scenario and generalizati... more We establish a formal connection between the K-essence emergent gravity scenario and generalizations of Vaidya spacetime. Choosing the K-essence action to be of the Dirac-Born-Infeld variety, the physical spacetime to be a general static spherically symmetric black hole and restricting the K-essence scalar field to be a function solely of the advanced or the retarded time, we show that the emergent gravity metric resembles closely the generalized Vaidya metrics for null fluid collapse proposed by Husain. Imposing null energy conditions on the emergent energy-momentum tensor derived from the emergent Einstein equation, restrictions are obtained on the functions characterizing the emergent metric for consistent identification with generalized Vaidya spacetimes. We discuss the possibility of dynamical horizons in the K-essence emergent Vaidya spacetime. Admissible explicit black hole background metrics are discussed as examples.
The Hawking temperature for the Barriola-Vilenkin global monopole metric is shown to be TBV = (1-... more The Hawking temperature for the Barriola-Vilenkin global monopole metric is shown to be TBV = (1-α) 2 8πGM k B , where α is the global monopole charge,M the mass of the black hole, kB is the Boltzmann constant and speed of light c = 1. We then show that a similar metric can also be obtained for certain k-essence field configurations in an emergent gravity situation. Therefore, in the context of Belgiorno et al's recent demonstration of spontaneous emission of photons in a gravitational analogue experiment, any future observation of TBV need not necessarily imply the existence of global monopoles. An alternative implication might as well be a very indirect signature of dark energy in an emergent gravity scenario. This should lead to effects that may be detectable in refined and modified versions of Belgiorno et al's experiment.
We show that the Hawking temperature is modified in the presence of dark energy in an emergent gr... more 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 θ = 0. Also we show that the emergent black hole metrics are satisfying Einstein's equations for large r and θ = 0. Our analysis is done in the context of dark energy in an emergent gravity scenario having k-essence scalar fields φ with a Dirac-Born-Infeld type Lagrangian. In KN and KNAdS background, the scalar field φ(r, t) = φ 1 (r ) + φ 2 (t) satisfies the emergent gravity equations of motion at r → ∞ for θ = 0.
The motto of this work is to generate a general formalism of f (R, L(X))−gravity in the context o... more The motto of this work is to generate a general formalism of f (R, L(X))−gravity in the context of dark energy under the framework of the K-essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, whereR is the familiar Ricci scalar, L(X) is the DBI type non-canonical Lagrangian with X = 1 2 g µν ∇µφ∇ν φ and φ is the K-essence scalar field. The emergent gravity metricḠµν and the well known gravitational metric gµν are not conformally equivalent. We have constructed a modified field equation using the metric formalism in f (R, L(X))-gravity incorporating the corresponding Friedmann equations in the framework of the background gravitational metric which is of Friedmann-Lemaître-Robertson-Walker (FLRW) type. The solution of modified Friedmann equations have been deduced for the specific choice of f (R, L(X)), which is of Starobinskytype, using 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, asφ 2 = 8 9 = 0.888 < 1, which indicates that the present Universe is dark energy dominated. Graphical plots for the energy density (ρ), pressure (p) and equation of state parameter (ω) w.r.t. time (t) based on parametric values are interestingly consistent with the dark energy domination and hence accelerating features. We also put some light on the corresponding energy conditions and constraints of the f (R, L(X)) theory with one basic example.
In this work, we investigate for an analytical solution under modified gravity theory, specifical... more In this work, we investigate for an analytical solution under modified gravity theory, specifically the f (R, T) gravity for two different eras, i.e., matter and dark energy dominated accelerating universe from completely geometrical and mathematical point of view with the help of the Raychaudhuri equation. To construct f (R, T) gravity model, we consider the functional form of f (R, T) as the sum of two independent functions of the Ricci scalar R and the trace of the energy-momentum tensor T , respectively. Under the consideration of this type of power law expansion of the Universe we have studied the viability, stability and all the energy conditions. We note that the strong energy condition is not satisfied in our model, which is obvious for the present scenario of the Universe.
We investigate how the Raychaudhuri equation behaves in the k‐essence geometry. As far as we are ... more We investigate how the Raychaudhuri equation behaves in the k‐essence geometry. As far as we are concerned, both the early and current epochs of the universe are relevant to the k‐essence theory. Here, we have studied the k‐essence geometry using the Dirac‐Born‐Infeld (DBI) variety of non‐standard action. The corresponding k‐essence emergent spacetime is not conformally equivalent to the usual gravitational metric. We assume that the background gravitational metric is of the Friedmann‐Lemaitre‐Robertson‐Walker (FLRW) type in this case. We have found that both the conditional singular and non‐singular cosmological models of the universe through the modified Raychaudhuri equation are possible where we have used the spacetime as the flat k‐essence emergent FLRW‐type. We have also addressed the Focusing theorem and conditional caustic universe construction. These conditional effects are caused by the additional interactions that arise as a result of the coupling that exists between grav...
The objective of this work is to generate a general formalism of gravity in the context of dark e... more 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 t...
In this study, we investigate the collapsing scenario for the k-essence emergent Vaidya spacetime... more 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.
This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting ... more This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting f (R,T) gravity within the framework of a non-standard theory, called K-essence theory, whereR represents the Ricci scalar andT denotes the trace of the energy-momentum tensor associated with the K-essence geometry. The Dirac-Born-Infeld (DBI) non-standard Lagrangian has been employed to generate the emergent gravity metric (Ḡµν) associated with the K-essence. This metric is distinct from the usual gravitational metric (gµν). It has been shown that under a flat FLRW background gravitational metric, the modified field equations and the Friedmann equations of the f (R,T) gravity are distinct from the usual ones. In order to get the equation of state (EOS) parameter ω, we have solved the Friedmann equations by taking into account the function f (R,T) ≡ f (R) + λT , where λ represents a parameter within the model. We have found a relationship between ω and time for different kinds of f (R) by treating the kinetic energy of the K-essence scalar field (φ 2) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction onφ 2. By presenting graphical representations of the EOS parameter with time, we show that our model is consistent with the data of SN Ia+BAO+H(z) within a certain temporal interval.
In this work we reveal a strong and general formalism of f(R̅, L(X))-gravity under the framework ... more In this work we reveal a strong and general formalism of f(R̅, L(X))-gravity under the framework of the K-essence emergent geometry, where R̅ is the well known Ricci scalar of this geometry, L(X) is the Dirac-Born-Infeld (DBI) type non-canonical Lagrangian having the expression X=1 2g^μν∇_μϕ∇_νϕ where ϕ being the scalar field of the K-essence geometry. The emergent gravity metric G̅_μν is not conformally equivalent to the well known gravitational metric g_μν. We have set up a modified field equation by metric formalism in f(R̅, L(X))-gravity and also the corresponding Friedmann equations in the framework of the background gravitational metric considered as Friedmann-Lemaître-Robertson-Walker (FLRW) type. The modified Friedmann equations are solved for the Starobinsky type specific choice of f(R̅, L(X)) by using power law expansion method. It is shown that the model is consistent with the accelerating phase of the Universe when we restrict ourselves to the value of the dark energy de...
We develop a robust and general formalism on $f(\bar{R}, L(X))-$gravity in the context of the $\m... more We develop a robust and general formalism on $f(\bar{R}, L(X))-$gravity in the context of the $\mathbf{K}$-essence emergent geometry where $\bar{R}$ is the Ricci scalar of this geometry, $L(X)$, the Dirac-Born-Infeld (DBI) type non-canonical Lagrangian with $X = {1\over 2} g^{\mu\nu} \nabla_\mu \phi\nabla_\nu\phi$, $\phi$ being the $\mathbf{K}$-essence scalar field. The emergent gravity metric $\bar{G}_{\mu\nu}$ is not conformally equivalent to the gravitational metric $g_{\mu\nu}$. We construct the modified field equation by the metric formalism in $f(\bar{R}, L(X))$-gravity and also the Friedmann equations under the framework of the background gravitational metric considered as Friedman-Lemaitre-Robertson-Walker (FLRW) type. We highlight the corresponding energy conditions and constraints of the $f(\bar{R}, L(X))$ theory with some basic examples, which are also the interesting outcomes of the work.
In this paper, we study the gravitational collapse in the k-essence emergent gravity using a gene... more 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.
For a particular type of k-essence scalar field, the k-essence emergent gravity metric is exactly... more 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 S. 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.
The k-essence emergent Reissner-Nordstrom-de Sitter spacetime has exactly mapped on to the Robins... more The k-essence emergent Reissner-Nordstrom-de Sitter spacetime has exactly mapped on to the Robinson-Trautman (RT) type spacetime with cosmological constant Λ for certain configuration of k-essence scalar field. Theoretically, we evaluated that the thermodynamical quantities for the RT type emergent black hole is different from the usual one in the presence of kinetic energy of the k-essence scalar field i.e., the dark energy density. We restrict ourselves into the fact that the dark energy density (K) is to be unity, then the effective temperature and pressure both are negative for the RT type emergent black hole which implies that the system is thermodynamically unstable when the charge Q = 0 and the emergent spacetime is only dark energy dominated and it does not radiate when Q = 0. The thermodynamically unstable situation is physically plausible only when we consider spin degrees of freedom of a system. We have made this analysis in the context of dark energy in an emergent gravity scenario having k-essence scalar fields φ with a Dirac-Born-Infeld type lagrangian. The scalar field also satisfies the emergent equation of motion at r → ∞.
We obtain the analogues of the Friedman equations in an emergent gravity scenario in the presence... more We obtain the analogues of the Friedman equations in an emergent gravity scenario in the presence of dark energy. The background metric is taken to be Friedman-Lemaitre-Robertson-Walker (FLRW). We show that if $\dot\phi ^{2}$ is the dark energy density (in units of the critical density) then (a) for total energy density greater than the pressure (non-relativistic scenario, matter domination) the deceleration parameter $q(t)\approx\frac {1}{2} [1 + 27 \dot\phi ^{2}+...] > \frac{1}{2}$ (b) for total energy density equal to 3 times the pressure (relativistic case, radiation domination), the deceleration parameter $q(t)\approx 1 + 18\dot\phi ^{2} +... > 1$ and (c) for total energy density equal to the negative of the pressure (dark energy scenario), the deceleration parameter $q(t)< -1$. Our results indicate that many aspects of standard cosmology can be accommodated with the presence of dark energy right from the beginning of the universe where the time parameter $t\equiv \fra...
We show that the Raychaudhuri equation remains form invariant for certain solutions of scalar fie... more We show that the Raychaudhuri equation remains form invariant for certain solutions of scalar fields φ whose Lagrangian is non-canonical and of the form L(X, φ) = -V (φ)F (X), with X = 1 2 gµν∇ µ φ∇ ν φ and V (φ) the potential. Solutions exist for both homogeneous and inhomogeneous fields that are like inflatons. Certain recent observations indicate that the cosmos is inhomogeneous and thus our results are in sync with latest observations. So the Raychaudhuri equation can accommodate primordial inhomogeneities as well as cosmologically relevant scenarios.
This article investigates on the radial and non-radial geodesic structures of the generalized Kes... more This article investigates on the radial and non-radial geodesic structures of the generalized Kessence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal equivalence to the conventional gravitational metric. This study employs a non-canonical action of the Dirac-Born-Infeld kind. In this work, we categorize the generalized K-essence Vaidya mass function into two distinct forms. Both the forms of the mass functions have been extensively utilized to analyze the radial and non-radial time-like or null geodesics in great details inside the comoving plane. Indications of the existence of wormhole can be noted during the extreme phases of spacetime, particularly in relation to black holes and white holes, which resemble the Einstein-Rosen bridge. In addition, we have also detected the distinctive indication of the quantum tunneling phenomenon around the central singularity.
The motto of this work is to generate a general formalism of f ( R, L(X))-gravity in the context ... more The motto of this work is to generate a general formalism of f ( R, L(X))-gravity in the context of dark energy under the framework of the K-essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, where R is the familiar Ricci scalar, L(X) is the DBI type non-canonical Lagrangian with X = 1 2 g µν ∇µφ∇ν φ and φ is the K-essence scalar field. The emergent gravity metric Ḡµν and the well known gravitational metric gµν are not conformally equivalent. We have constructed a modified field equation using the metric formalism in f ( R, L(X))-gravity incorporating the corresponding Friedmann equations in the framework of the background gravitational metric which is of Friedmann-Lemaître-Robertson-Walker (FLRW) type. The solution of modified Friedmann equations have been deduced for the specific choice of f ( R, L(X)), which is of Starobinskytype, using 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 φ2 = 8 9 = 0.888 < 1, which indicates that the present Universe is dark energy dominated. Graphical plots for the energy density (ρ), pressure (p) and equation of state parameter (ω) w.r.t. time (t) based on parametric values are interestingly consistent with the dark energy domination and hence accelerating features. We also put some light on the corresponding energy conditions and constraints of the f ( R, L(X)) theory with one basic example.
We establish a formal connection between the K-essence emergent gravity scenario and generalizati... more We establish a formal connection between the K-essence emergent gravity scenario and generalizations of Vaidya spacetime. Choosing the K-essence action to be of the Dirac-Born-Infeld variety, the physical spacetime to be a general static spherically symmetric black hole and restricting the K-essence scalar field to be a function solely of the advanced or the retarded time, we show that the emergent gravity metric resembles closely the generalized Vaidya metrics for null fluid collapse proposed by Husain. Imposing null energy conditions on the emergent energy-momentum tensor derived from the emergent Einstein equation, restrictions are obtained on the functions characterizing the emergent metric for consistent identification with generalized Vaidya spacetimes. We discuss the possibility of dynamical horizons in the K-essence emergent Vaidya spacetime. Admissible explicit black hole background metrics are discussed as examples.
The Hawking temperature for the Barriola-Vilenkin global monopole metric is shown to be TBV = (1-... more The Hawking temperature for the Barriola-Vilenkin global monopole metric is shown to be TBV = (1-α) 2 8πGM k B , where α is the global monopole charge,M the mass of the black hole, kB is the Boltzmann constant and speed of light c = 1. We then show that a similar metric can also be obtained for certain k-essence field configurations in an emergent gravity situation. Therefore, in the context of Belgiorno et al's recent demonstration of spontaneous emission of photons in a gravitational analogue experiment, any future observation of TBV need not necessarily imply the existence of global monopoles. An alternative implication might as well be a very indirect signature of dark energy in an emergent gravity scenario. This should lead to effects that may be detectable in refined and modified versions of Belgiorno et al's experiment.
We show that the Hawking temperature is modified in the presence of dark energy in an emergent gr... more 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 θ = 0. Also we show that the emergent black hole metrics are satisfying Einstein's equations for large r and θ = 0. Our analysis is done in the context of dark energy in an emergent gravity scenario having k-essence scalar fields φ with a Dirac-Born-Infeld type Lagrangian. In KN and KNAdS background, the scalar field φ(r, t) = φ 1 (r ) + φ 2 (t) satisfies the emergent gravity equations of motion at r → ∞ for θ = 0.
The motto of this work is to generate a general formalism of f (R, L(X))−gravity in the context o... more The motto of this work is to generate a general formalism of f (R, L(X))−gravity in the context of dark energy under the framework of the K-essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, whereR is the familiar Ricci scalar, L(X) is the DBI type non-canonical Lagrangian with X = 1 2 g µν ∇µφ∇ν φ and φ is the K-essence scalar field. The emergent gravity metricḠµν and the well known gravitational metric gµν are not conformally equivalent. We have constructed a modified field equation using the metric formalism in f (R, L(X))-gravity incorporating the corresponding Friedmann equations in the framework of the background gravitational metric which is of Friedmann-Lemaître-Robertson-Walker (FLRW) type. The solution of modified Friedmann equations have been deduced for the specific choice of f (R, L(X)), which is of Starobinskytype, using 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, asφ 2 = 8 9 = 0.888 < 1, which indicates that the present Universe is dark energy dominated. Graphical plots for the energy density (ρ), pressure (p) and equation of state parameter (ω) w.r.t. time (t) based on parametric values are interestingly consistent with the dark energy domination and hence accelerating features. We also put some light on the corresponding energy conditions and constraints of the f (R, L(X)) theory with one basic example.
In this work, we investigate for an analytical solution under modified gravity theory, specifical... more In this work, we investigate for an analytical solution under modified gravity theory, specifically the f (R, T) gravity for two different eras, i.e., matter and dark energy dominated accelerating universe from completely geometrical and mathematical point of view with the help of the Raychaudhuri equation. To construct f (R, T) gravity model, we consider the functional form of f (R, T) as the sum of two independent functions of the Ricci scalar R and the trace of the energy-momentum tensor T , respectively. Under the consideration of this type of power law expansion of the Universe we have studied the viability, stability and all the energy conditions. We note that the strong energy condition is not satisfied in our model, which is obvious for the present scenario of the Universe.
We investigate how the Raychaudhuri equation behaves in the k‐essence geometry. As far as we are ... more We investigate how the Raychaudhuri equation behaves in the k‐essence geometry. As far as we are concerned, both the early and current epochs of the universe are relevant to the k‐essence theory. Here, we have studied the k‐essence geometry using the Dirac‐Born‐Infeld (DBI) variety of non‐standard action. The corresponding k‐essence emergent spacetime is not conformally equivalent to the usual gravitational metric. We assume that the background gravitational metric is of the Friedmann‐Lemaitre‐Robertson‐Walker (FLRW) type in this case. We have found that both the conditional singular and non‐singular cosmological models of the universe through the modified Raychaudhuri equation are possible where we have used the spacetime as the flat k‐essence emergent FLRW‐type. We have also addressed the Focusing theorem and conditional caustic universe construction. These conditional effects are caused by the additional interactions that arise as a result of the coupling that exists between grav...
The objective of this work is to generate a general formalism of gravity in the context of dark e... more 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 t...
In this study, we investigate the collapsing scenario for the k-essence emergent Vaidya spacetime... more 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.
This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting ... more This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting f (R,T) gravity within the framework of a non-standard theory, called K-essence theory, whereR represents the Ricci scalar andT denotes the trace of the energy-momentum tensor associated with the K-essence geometry. The Dirac-Born-Infeld (DBI) non-standard Lagrangian has been employed to generate the emergent gravity metric (Ḡµν) associated with the K-essence. This metric is distinct from the usual gravitational metric (gµν). It has been shown that under a flat FLRW background gravitational metric, the modified field equations and the Friedmann equations of the f (R,T) gravity are distinct from the usual ones. In order to get the equation of state (EOS) parameter ω, we have solved the Friedmann equations by taking into account the function f (R,T) ≡ f (R) + λT , where λ represents a parameter within the model. We have found a relationship between ω and time for different kinds of f (R) by treating the kinetic energy of the K-essence scalar field (φ 2) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction onφ 2. By presenting graphical representations of the EOS parameter with time, we show that our model is consistent with the data of SN Ia+BAO+H(z) within a certain temporal interval.
In this work we reveal a strong and general formalism of f(R̅, L(X))-gravity under the framework ... more In this work we reveal a strong and general formalism of f(R̅, L(X))-gravity under the framework of the K-essence emergent geometry, where R̅ is the well known Ricci scalar of this geometry, L(X) is the Dirac-Born-Infeld (DBI) type non-canonical Lagrangian having the expression X=1 2g^μν∇_μϕ∇_νϕ where ϕ being the scalar field of the K-essence geometry. The emergent gravity metric G̅_μν is not conformally equivalent to the well known gravitational metric g_μν. We have set up a modified field equation by metric formalism in f(R̅, L(X))-gravity and also the corresponding Friedmann equations in the framework of the background gravitational metric considered as Friedmann-Lemaître-Robertson-Walker (FLRW) type. The modified Friedmann equations are solved for the Starobinsky type specific choice of f(R̅, L(X)) by using power law expansion method. It is shown that the model is consistent with the accelerating phase of the Universe when we restrict ourselves to the value of the dark energy de...
We develop a robust and general formalism on $f(\bar{R}, L(X))-$gravity in the context of the $\m... more We develop a robust and general formalism on $f(\bar{R}, L(X))-$gravity in the context of the $\mathbf{K}$-essence emergent geometry where $\bar{R}$ is the Ricci scalar of this geometry, $L(X)$, the Dirac-Born-Infeld (DBI) type non-canonical Lagrangian with $X = {1\over 2} g^{\mu\nu} \nabla_\mu \phi\nabla_\nu\phi$, $\phi$ being the $\mathbf{K}$-essence scalar field. The emergent gravity metric $\bar{G}_{\mu\nu}$ is not conformally equivalent to the gravitational metric $g_{\mu\nu}$. We construct the modified field equation by the metric formalism in $f(\bar{R}, L(X))$-gravity and also the Friedmann equations under the framework of the background gravitational metric considered as Friedman-Lemaitre-Robertson-Walker (FLRW) type. We highlight the corresponding energy conditions and constraints of the $f(\bar{R}, L(X))$ theory with some basic examples, which are also the interesting outcomes of the work.
In this paper, we study the gravitational collapse in the k-essence emergent gravity using a gene... more 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.
For a particular type of k-essence scalar field, the k-essence emergent gravity metric is exactly... more 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 S. 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.
The k-essence emergent Reissner-Nordstrom-de Sitter spacetime has exactly mapped on to the Robins... more The k-essence emergent Reissner-Nordstrom-de Sitter spacetime has exactly mapped on to the Robinson-Trautman (RT) type spacetime with cosmological constant Λ for certain configuration of k-essence scalar field. Theoretically, we evaluated that the thermodynamical quantities for the RT type emergent black hole is different from the usual one in the presence of kinetic energy of the k-essence scalar field i.e., the dark energy density. We restrict ourselves into the fact that the dark energy density (K) is to be unity, then the effective temperature and pressure both are negative for the RT type emergent black hole which implies that the system is thermodynamically unstable when the charge Q = 0 and the emergent spacetime is only dark energy dominated and it does not radiate when Q = 0. The thermodynamically unstable situation is physically plausible only when we consider spin degrees of freedom of a system. We have made this analysis in the context of dark energy in an emergent gravity scenario having k-essence scalar fields φ with a Dirac-Born-Infeld type lagrangian. The scalar field also satisfies the emergent equation of motion at r → ∞.
We obtain the analogues of the Friedman equations in an emergent gravity scenario in the presence... more We obtain the analogues of the Friedman equations in an emergent gravity scenario in the presence of dark energy. The background metric is taken to be Friedman-Lemaitre-Robertson-Walker (FLRW). We show that if $\dot\phi ^{2}$ is the dark energy density (in units of the critical density) then (a) for total energy density greater than the pressure (non-relativistic scenario, matter domination) the deceleration parameter $q(t)\approx\frac {1}{2} [1 + 27 \dot\phi ^{2}+...] > \frac{1}{2}$ (b) for total energy density equal to 3 times the pressure (relativistic case, radiation domination), the deceleration parameter $q(t)\approx 1 + 18\dot\phi ^{2} +... > 1$ and (c) for total energy density equal to the negative of the pressure (dark energy scenario), the deceleration parameter $q(t)< -1$. Our results indicate that many aspects of standard cosmology can be accommodated with the presence of dark energy right from the beginning of the universe where the time parameter $t\equiv \fra...
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Papers by Goutam Manna