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![Fig. 3 Plots of R1[≡ f (t)] versus time for three values of k.](profile/Sudipto-Roy-5/publication/331981772/figure/fig1/AS:740653696835587@1553597010547/Plots-of-R1-f-t-versus-time-for-three-values-of-k_Q320.jpg)
![Fig. 6 Plots of R2 and R3 as functions of R1 [≡ f (t)].](profile/Sudipto-Roy-5/publication/331981772/figure/fig4/AS:740653696827405@1553597010627/Plots-of-R2-and-R3-as-functions-of-R1-f-t_Q320.jpg)
A cosmological model has been constructed in the framework of Brans-Dicke (BD) gravity,
based on an inter-conversion between matter and dark energy, for a spatially flat universe in the era of pressureless dust. To account for the non-conservation of the matter content, a function of time f(t) has been arbitrarily put into the expression for the de...
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Context 1
... approximate range of variation of the EoS param- eter (γ D ), for dark energy, is found to be −1.1 ≤ γ D ≤ −0.9, as obtained from some recent studies in this regard (Wood-Vasey et al. 2007;Davis et al. 2007). Three sets of values of the parameters discussed in the present study have been shown in Table 1. The values of these parameters (γ, ǫ, k) have been so chosen that the values of the depen- dent ones fall within their permissible limits. ...
Context 2
... values of these parameters (γ, ǫ, k) have been so chosen that the values of the depen- dent ones fall within their permissible limits. In Table 1, R 40 , R 50 and γ D0 denote the values of R 4 , R 5 and γ D at the present time (t = t 0 ) respectively. One may choose several such sets of values under the constraints of γ < 1, ǫ < 2.33, −5.44 < k < −2.73 and −2.15 < k < −0.99, as obtained earlier in this article. ...
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Citations
... It has a negative slope which becomes less negative with time. This behaviour is in agreement with the findings of many other investigations [12,13,[24][25][26][27][28][29][30][31]. ...
... Time evolution of gravitational constant ( ) is depicted by Figure 5. It is found to increase with time, which is consistent with the findings of other recent studies [23,24,[28][29][30][31]. Figure 6 depicts the time evolution of the equation of state (EoS) parameter . It is found to decrease steeply with time in the early universe (when it was positive) and it continues to decrease at a decreasing rate. ...
... Figure 7. It decreases with time at a gradually decreasing rate, which is consistent with the findings of one of our previous studies in Brans-Dicke framework [31]. Its present value is found to be 1.075 × 10 −10 −1 which is consistent with the values obtained from various observations [19]. ...
We formulate a cosmological model under the Kaluza-Klein framework, in flat space, to determine the nature of time dependence of some cosmological parameters. Field equations are solved with the help of suitable ansatzes for the equation of state (EoS) parameter and the cosmological constant. To determine the arbitrary constants associated with the model, the currently accepted values of some measurable parameters are used. To examine the effect of dark energy upon the cosmic evolution, we have plotted the scale factor and its time derivative (expansion rate) with respect to a function of the cosmological constant which represents dark energy. Time evolution of different cosmological quantities is shown graphically and these graphs are consistent with the results of some recent investigations. It is observed that, the gravitational constant increases with time. The cosmological constant is positive and it decreases with time at a gradually decreasing rate. The EoS parameter is positive in the early universe when it decreases steeply, becoming negative eventually with a much slower variation thereafter. Results of this study are in agreement with the findings based on recent observational data.
... Several models, based on the BDT, have been perfectly able to explain the properties of the expanding Universe with the help of various cosmological parameters [24][25][26][27]. Te models based on the generalized BDT have an extremely low value for the coupling parameter, unaccommodating the fndings during the implementation of the previous versions of the theory [20,[28][29][30]. A recent study in the BDT [31] has been made in the FRW models with a varying Λ-term and a dynamic deceleration parameter. ...
In this article, we analyze Bianchi type–II, VIII, and IX spatially homogeneous and anisotropic space-times in the background of the Brans–Dicke theory of gravity within the framework of viscous holographic dark energy. To solve the field equations, we have used the relation between the metric potentials as R = S n and the relation between the scalar field ϕ and the scale factor a as ϕ = a m . Also, we have discussed some of the dynamical parameters of the obtained models, such as the deceleration parameter q , the jerk parameter j , the EoS parameter ω v h d e , the density parameter Ω vhde , Om-diagnostic, squared speed of sound v s 2 , EoS plane ω v h d e − ω v h d e ′ , and statefinder plane r − s through graphical representation, which are significant in the discussion of cosmology. Furthermore, all the models obtained and graphically presented shown an expanding and accelerating Universe, which is in better agreement with the latest experimental data. The viscous holographic dark energy models are compatible with explaining the present cosmic accelerated expansion.
... The gravitational constant ( ) is found here to be increasing with time due to the negative values of . This nature of time variation of is in qualitative agreement with the findings of some recent studies based on models which are completely different from the present one [24][25][26]. Both and have been plotted here in logarithmic scales for a greater visual clarity of their values obtained from the graphs. ...
The present article demonstrates a very simple mathematical way to determine the time-dependence of the dynamical gravitational constant () in the framework of the Brans-Dicke theory of gravity. Brans-Dicke field equations, for a matter-dominated, pressure-less and spatially flat universe with homogeneous and isotropic space-time, have been used for this formulation. The gravitational constant () is the reciprocal of the Brans-Dicke scalar field (). Using a simple ansatz, which represents the Brans-Dicke scalar field () as a function of time, the possible values of a constant parameter (constituting the ansatz) have been calculated with the help of the field equations, using the values of some cosmological parameters at the present time. The values of that parameter (belonging to the ansatz) lead to the conclusion that the scalar field () decreases and consequently the gravitational constant () increases with time. The value of the relative time-rate of change of the gravitational constant (i.e., ) has also been estimated and this quantity has been found to be independent of time. Time-dependence of and has been depicted graphically for all values of the parameter belonging to the ansatz. The novel features of this study are that the gravitational field equations did not have to be solved, unlike other studies, to arrive at the results and the mathematical scheme for calculations is extremely easy in comparison to other recent studies in this regard.
... The gravitational constant ( ) is found here to be increasing with time due to the negative values of . This nature of time variation of is in qualitative agreement with the findings of some recent studies based on models which are completely different from the present one [24][25][26]. Both and have been plotted here in logarithmic scales for a greater visual clarity of their values obtained from the graphs. ...
The present article demonstrates a very simple mathematical way to determine the time-dependence of the dynamical gravitational constant (G) in the framework of the Brans-Dicke theory of gravity. Brans-Dicke field equations, for a matter-dominated, pressure-less and spatially flat universe with homogeneous and isotropic space-time, have been used for this formulation. The gravitational constant (G) is the reciprocal of the Brans-Dicke scalar field (𝜙). Using a simple ansatz, which represents the Brans-Dicke scalar field (𝜙) as a function of time, the possible values of a constant parameter (constituting the ansatz) have been calculated with the help of the field equations, using the values of some cosmological parameters at the present time. The values of that parameter (belonging to the ansatz) lead to the conclusion that the scalar field (𝜙) decreases and consequently the gravitational constant (G) increases with time. The value of the relative time-rate of change of the gravitational constant (i.e., 1/𝜙) has also been estimated and this quantity has been found to be independent of time. Time-dependence of and has been depicted graphically for all values of the parameter belonging to the ansatz. The novel features of this study are that the gravitational field equations did not have to be solved, unlike other studies, to arrive at the results and the mathematical scheme for calculations is extremely easy in comparison to other recent studies in this regard.
... Solving equation (35) by integration and using a scale such that ( 0 ) = 1 we get, ...
... here and are constants. This expression for the Hubble parameter (H) has been derived from an empirical scale factor of the form = 0 ( / 0 ) ( − 0 ) used in one of our previous studies on cosmology [35]. Using equation (37), one obtains the following expression for the deceleration parameter (q). ...
In the present study we have determined the nature of time dependence of various cosmological parameters with the help of four mathematical models. Our theoretical derivations are based on gravitational field equations (involving a dynamical cosmological constant) obtained for a homogeneous and isotropic space-time with zero curvature. In the models proposed here, we have assumed four ansatzes in the form of expressions involving the cosmological constant, Hubble parameter and time. Substituting these ansatzes into the field equations and solving them, we have derived expressions for the scale factor, Hubble parameter, deceleration parameter, energy density, gravitational constant, equation of state (EoS) parameter, cosmological constant and the relative rate of change of the gravitational constant. Using these expressions, the characteristics of time evolution of these cosmological parameters can be completely determined. Signature flip of the deceleration parameter, which is evident from astrophysical observations, has been obtained from all models of the present study. The gravitational constant has been found to be decreasing with time. The cosmological constant increases from negative to positive values while the EoS parameter decreases from positive to negative values with time. The rate of change for each of them decreases with time. It has been found that an accelerated expansion of the universe, preceded by a phase of deceleration, can also be caused by a time-independent cosmological constant with a negative value.
... For the accelerated expansion of the universe, the coupling parameter ( ) needs to have a very low negative value, as obtained from models based on the generalized BD theory, contrary to what was found during the applications of the initial version of the theory [12,[20][21][22]. In the framework of BD theory, the findings from the FRW models with a dynamic Λ-term and a variable deceleration parameter have been analyzed in detail in a recent study in this field [23]. ...
... The scale factor, used in Model-1, was obtained as the solution of the BD field equations, based on an assumption of the conservation of matter (dark + baryonic). For the formulation of the present model, the dark energy content of the universe has been assumed to increase with time at the cost of the matter content (dark + baryonic), as obtained from some interpretations of the astrophysical observations [21,27,28]. ...
... Expressions for the Hubble parameter ( ) and the deceleration parameter ( ), based on equation (37) According to some cosmological studies, the change of phase of the cosmic expansion from deceleration to acceleration took place due to the dark energy content of the universe, which has been shown to be increasing with time [21,27,28]. Based on this observation, we propose the following ansatz for describing the time dependence of the dark energy content of the universe. ...
In the framework of the generalized Brans-Dicke theory of gravity, time dependence of various cosmological parameters has been determined in the present study for a spatially flat, homogeneous and isotropic universe filled with pressure-less matter. Mathematical formulations have been carried out with the help of two models, based upon two different expressions for the scale factor. In the first model, the entire matter content (dark matter + baryonic matter) of the universe has been assumed to be conserved. A smooth transition from a state of decelerated expansion to a state of accelerated expansion of the universe has been obtained from an exact solution of the field equations, without incorporating any parameter in the theoretical formulation that represents the dark energy. Time dependence of the scalar field has been determined from this solution with the help of astrophysical characteristics of the expanding universe. The nature of dependence of the Brans-Dicke parameter upon time and also upon the scalar field has been found. The Brans-Dicke parameter has been found to have a small negative value and it becomes more negative as the scalar field decreases with time. It has been found in the present study that the gravitational constant, which is reciprocal of the scalar field parameter, increases with time. In the second of the two models discussed here, an ansatz has been assumed regarding the mode of change of the dark energy content of the universe with time. Using this model, the time dependence of the densities of matter and dark energy and also the density parameters corresponding to these two constituents of the universe has been determined.
... It can be even considered that the matter itself is a "condensed" form of energy and that energy is stored in the atoms and molecules of which matter is composed [7][8][9]. ...
Starting from the equation of Einstein (E = m·c 2), the chapter proposes a simple and fundamental presentation of the fission and fusion principles, together with some of their applications: nuclear reactors and nuclear propulsion vessels and submarines. Fission and fusion are chosen between the multiple forms of energy, as being the most important forms of nuclear energy, directly related with the equation of Einstein. Some characteristics of solar energy, produced from the fusion process inside the Sun, are deducted from the same equation of Einstein: thermal power of solar radiation; specific power of solar radiation; surface temperature of the Sun; solar constant on different planets, etc. The yearly variation of the solar radiation on each planet of the solar system is also presented.
... Here, initially decreases and subsequently increases with time. There are cosmological models where has been shown to be increasing with time [28,29]. There are models where this parameter is found to be a decreasing function of time [19,26]. ...
A theoretical model, regarding the time dependence of several cosmological parameters, has been constructed in the present study, in the framework of Kaluza-Klein theory, using its field equations for a spatially flat metric. Time dependent empirical expressions of the cosmological constant and the equation of state (EoS) parameter have been substituted into the field equations to determine the time dependence of various cosmological parameters. Time variations of these parameters have been shown graphically. The cosmological features obtained from this model are found to be in agreement with the observed characteristics of the accelerating universe. Interestingly, the signature flipping of the deceleration parameter, from positive to negative, is predicted by this model, indicating a transformation of the universe from a state of decelerated expansion to accelerated expansion, as obtained from astrophysical observations. Time dependence of the gravitational constant (G), energy density (ρ), cosmological constant (Λ) and the EoS parameter (ω) have been determined and depicted graphically in the present study.
... Using equation (25) we get the following expression for ̇⁄ . increasing with time [28,29]. There are models where this parameter is found to be a decreasing function of time [19,26]. ...
A theoretical model, regarding the time dependence of several cosmological parameters, has been constructed in the present study, in the framework of Kaluza-Klein theory, using its field equations for a spatially flat metric. Time dependent empirical expressions of the cosmological constant and the equation of state (EoS) parameter have been substituted into the field equations to determine the time dependence of various cosmological parameters. Time variations of these parameters have been shown graphically. The cosmological features obtained from this model are found to be in agreement with the observed characteristics of the accelerating universe. Interestingly, the signature flipping of the deceleration parameter, from positive to negative, is predicted by this model, indicating a transformation of the universe from a state of decelerated expansion to accelerated expansion, as obtained from astrophysical observations. Time dependence of the gravitational constant (G), energy density (?), cosmological constant (?) and the EoS parameter (?) have been determined and depicted graphically in the present study.
... The ansatz of , given by equation (14), has been taken from some earlier studies in this regard [15,19,20]. The logic behind choosing the above ansatz for is the fact that this is considered to be a function of the scalar field ( ) in the generalized version of ...
... From various studies, it is known that the dark energy content of the universe increase with time, at the cost of matter, due to some interaction between them that causes inter-conversion [20,21,29]. ...
In the framework of Brans-Dicke (BD) theory of gravitation, the time dependence of some cosmological parameters have been determined in the present study, for an universe having a FRW space-time with zero spatial curvature. The time variations of the energy density, BD parameter, equation of state (EoS) parameter have been determined, from the field equations of the BD theory, in the initial part of this model. For this purpose, we have used ansatzes relating the scalar field with the scale factor and also linking the BD parameter with the scalar field. For these calculations, an empirical expression for the scale factor has been used. This scale factor has been so chosen that it leads to a signature flip of the deceleration parameter from positive to negative in the course of its evolution with time, indicating a change of phase from decelerated expansion to accelerated expansion. Time dependence of the density parameters for matter and dark energy has been studied here. Using their expressions we have determined the time dependence of the densities of matter and dark energy. The time variations of all these parameters have been shown graphically. Apart from them, we have also shown the
variations of the deceleration parameter and the BD parameter as functions of the scalar field graphically.
