Ballester Theory Research Articles

Studies on Bianchi type-III cosmological model with parametrization of deceleration parameter in a SBST theory

In this paper, we delve into the cosmological assessments concerning the deceleration parameter [Formula: see text] in the context of the Bianchi type-III cosmological model within the framework of the Saez–Ballester theory of gravitation. By postulating a proportional relationship between the shear scalar ([Formula: see text]) and the expansion scalar ([Formula: see text]), we derive solutions for the corresponding field equations. Additionally, we conduct an examination and evaluation of the model’s physical and kinematic parameters, including the jerk parameter and snap parameter, while also discussing the energy condition of the model. Through the depiction of graphical representations, we illustrate the variations of the cosmological parameters for specific sets of constants.

Dynamics of Modified Rényi Holographic Dark Energy in Sáez–Ballester Theory of Gravitation

Dynamics of Modified Rényi Holographic Dark Energy in Sáez–Ballester Theory of Gravitation

Cosmology of Tsallis and Kaniadakis holographic dark energy in Saez–Ballester theory and consideration of viscous van der Waals fluid

In the framework of Saez–Ballester (SB) theory, the current study proposes a reconstruction scheme for Tsallis and Kaniadakis holographic dark energy, particular cases of a more generalised Nojiri–Odintsov holographic dark energy (Nojiri and Odintsov, 2006; The European Physical Journal C, 2017, 77, pp.1-8.), with Hubble horizon and future event horizons serving as the universe’s respective trapping horizons. The Hubble parameter was rebuilt by placing a constraint on the metric potential inside the conservation equation. As a result, the holographic dark energy of Tsallis and Kaniadakis are recreated, and the cosmology and thermodynamics are examined. Lastly, an interacting van der Waals (VDW) coupled fluid model was examined in the context of bulk viscosity, and the behaviour of the equation of state (EoS) parameter was examined.

Anisotropic dark matter distribution in Saez–Ballester theory of gravitation

Anisotropic dark matter distribution in Saez–Ballester theory of gravitation

Bianchi Type-V space time with Tsallis holographic dark energy

In this paper, using the framework of Saez–Ballester theory, Bianchi Type-V metric Tsallis holographic dark energy models with interacting and non-interacting elements have been constructed. To obtain solutions for the model, we used correlation between metric potentials and varying deceleration parameters. There is additional discussion of the models’ physical characteristics and behavior.

Particle creation and bulk viscosity in Bianchi-I universe in Saez–Ballester theory with different deceleration parameters

Particle creation and bulk viscosity in Bianchi-I universe in Saez–Ballester theory with different deceleration parameters

Causal viscous Universe in Sáez–Ballester theory

In this work, the authors examine the dynamics of viscous Universe in the Sáez–Ballester theory of gravity. The solutions of the Friedmann–Robertson–Walker field equations have been derived within the framework of full causal theories presented by Israel and Stewart using simple parametrization of scale factor a( t), i.e., power law relation a( t) = a0 tα and exponential law a( t) = b0eβ t. The power law cosmological model shows that the Universe transitioned from early cosmic deceleration to the present cosmic acceleration, and the exponential cosmological model shows the accelerated expansion of the Universe. It has been discovered that as time passes, energy density and viscosity decrease while temperature rises. Energy conditions are also investigated in which the strong energy condition is violated. The behaviour of the cosmological parameters such as the Hubble parameter, energy density, pressure, coefficient of viscosity, and state-finder parameter has been presented graphically.

Hyperbolic Scenario of Accelerating Universe in Modified Gravity

Throughout this study, locally rotationally symmetric (LRS) Bianchi type-V space-time is pondered with Tsallis holographic dark energy (THDE) with the Granda–Oliveros (GO) cut-off in the Sáez–Ballester (SB) theory of gravity. A parameterization of the deceleration parameter (q) has been suggested: q=α−βH2. The proposed deceleration parameterization demonstrates the Universe’s phase transition from early deceleration to current acceleration. Markov chain Monte Carlo (MCMC) was utilized to have the best-fit value for our model parameter and confirm that the model satisfies the recent observational data. Additional parameters such as deceleration parameter q with cosmographic parameters jerk, snap, and lerk have also been observed physically and graphically. The constructed model is differentiated from other dark energy models using statefinder pair analysis. Some important features of the model are discussed physically and geometrically.

Kantowski–Sachs Barrow holographic dark energy model in Saez–Ballester theory of gravitation

In this paper, we have studied a spatially homogeneous and anisotropic Kantowski–Sachs universe in the presence of Barrow Holographic Dark Energy in the background of Saez–Ballester scalar–tensor theory of gravitation. To find the exact solution of the SB field equations, we have assumed that the shear scalar is directly proportional to expansion scalar. This assumption leads to relation between metric potentials of the models. We have discussed non-interacting and interacting cosmological models. Moreover, we have discussed several cosmological parameters such as energy densities of DM and DE (ρm &ρb), deceleration (q), equation of state (ωb) and skewness (α) parameters, squared sound speed (vs2), ωb−ωb′ plane statefinders and Om-diagnostics parameters through graphical representation for both the interacting models. Also, we have observed that the current values of deceleration and EoS parameters of our constructed models are coincide with the recent observational data.

On the equivalence between Sáez–Ballester theory and Einstein-scalar field system

Here, we discuss a topic that comes up more often than expected: A same theory or theoretical model arises in two different presentations which are assumed to be actually different theories so that these are independently developed. Sometimes this leads to an unwanted doubling of the results. In this paper, we illustrate this issue with the example of two apparently different gravitational theories: (i) the (minimally coupled) Einstein-massless-scalar (EMS) system and (ii) the Sáez–Ballester theory (SBT). We demonstrate that the latter is not a scalar–tensor theory of gravity, as widely acknowledged. Moreover, SBT is identified with the EMS theory. As illustrations of this identification we show that several known solutions of SBT are also solutions of the EMS system and vice versa. Cosmological arguments are also considered. In particular, a dynamical systems-based demonstration of the dynamical equivalence between these theories is given. The study of the asymptotic dynamics of the Sáez–Ballester-based cosmological model shows that there are no equilibrium points which could be associated with accelerated expansion, unless one includes a cosmological constant term or a self-interacting scalar field. This is a well-known result for cosmological models which are based on the Einstein-self-interacting-scalar theory, also known as quintessence.

The study of accelerating DE models in Saez–Ballester theory of gravitation

The study of accelerating DE models in Saez–Ballester theory of gravitation

Geodesic deviation in Sáez–Ballester theory

We study the geodesic deviation (GD) equation in a generalized version of the Sáez–Ballester (SB) theory in arbitrary dimensions. We first establish a general formalism and then restrict to particular cases, where (i) the matter-energy distribution is that of a perfect fluid, and (ii) the spacetime geometry is described by a vanishing Weyl tensor. Furthermore, we consider the spatially flat FLRW universe as the background geometry. Based on this setup, we compute the GD equation as well as the convergence condition associated with fundamental observers and past directed null vector fields. Moreover, we extend that framework and extract the corresponding geodesic deviation in the modified Sáez–Ballester theory (MSBT), where the energy–momentum tensor and potential emerge strictly from the geometry of the extra dimensions. In order to examine our herein GD equations, we consider two novel cosmological models within the SB framework. Moreover, we discuss a few quintessential models and a suitable phantom dark energy scenario within the mentioned SB and MSBT frameworks. Noticing that our herein cosmological models can suitably include the present time of our Universe, we solve the GD equations analytically and/or numerically. By employing the correct energy conditions plus recent observational data, we consistently depict the behavior of the deviation vector η ( z ) and the observer area distance r 0 ( z ) for our models. Concerning the Hubble constant problem, we specifically focus on the observational data reported by the Planck collaboration and the SH0ES collaboration to depict η ( z ) and r 0 ( z ) for our herein phantom model. Subsequently, we contrast our results with those associated with the Λ CDM model. We argue that the MSBT can be considered as a fitting candidate for a proper description of the late evolution of the universe.

Noncompactified Kaluza–Klein Gravity

We present a brief description of noncompactified higher-dimensional theories from the perspective of general relativity. More concretely, the Space–Time–Matter theory, or Induced Matter theory, and the reduction procedure used to construct the modified Brans–Dicke theory and the modified Sáez–Ballester theory are briefly explained. Finally, we apply the latter to the Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological models in arbitrary dimensions and analyze the corresponding solutions.

Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation

This paper presents a noncommutative (NC) version of an extended Sáez–Ballester (SB) theory. Concretely, considering the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric, we propose an appropriate dynamical deformation between the conjugate momenta and, applying the Hamiltonian formalism, obtain deformed equations of motion. In our model, the NC parameter appears linearly in the deformed Poisson bracket and the equations of the NC SB cosmology. When it goes to zero, we get the corresponding commutative counterparts. Even by restricting our attention to a particular case, where there is neither an ordinary matter nor a scalar potential, we show that the effects of the noncommutativity provide interesting results: applying numerical endeavors for very small values of the NC parameter, we show that (i) at the early times of the universe, there is an inflationary phase with a graceful exit, for which the relevant nominal condition is satisfied; (ii) for the late times, there is a zero acceleration epoch. By establishing an appropriate dynamical framework, we show that the results (i) and (ii) can be obtained for many sets of the initial conditions and the parameters of the model. Finally, we indicate that, at the level of the field equations, one may find a close resemblance between our NC model and the Starobinsky inflationary model.

Cosmological models of generalized ghost pilgrim dark energy (GGPDE) in the gravitation theory of Saez–Ballester

In this paper, we study the mechanism of the cosmic model in the presence of generalized ghost pilgrim dark energy (GGPDE) and matter in locally rotationally symmetric (LRS) Bianchi type-I space-time by the utilization of new holographic DE in Saez–Ballester theory. Here, we discuss all the data for three scenarios, the first is supernovae type-Ia union data, the second is SN Ia data in combination with baryon acoustic oscillation and cosmic microwave background observations and the third is a combination with observational Hubble data and joint light-curve analysis observations. From this, we get a model of our universe, where transit state exists from deceleration to acceleration phase. Here, we have observed that the results yielded by cosmological parameters like [Formula: see text] (energy density), equation of state [Formula: see text], squared speed of sound [Formula: see text] and [Formula: see text]–[Formula: see text] are compatible with the recent observations. The [Formula: see text]–[Formula: see text] trajectories lie in both thawing and freezing regions and the correspondence of the quintessence field with GGPDE is also discussed. Some physical aspects of the GGPDE models are mainly highlighted.

Kantowski–Sachs viscous Ricci dark energy model in Saez–Ballester theory of gravitation

Kantowski–Sachs viscous Ricci dark energy model in Saez–Ballester theory of gravitation

Late time cosmic acceleration in modified Sáez–Ballester theory

We establish an extended version of the modified S\'{a}ez-Ballester (SB) scalar-tensor theory in arbitrary dimensions whose energy momentum tensor as well as potential are pure geometrical quantities. This scenario emerges by means of two scalar fields (one is present in the SB theory and the other is associated with the extra dimension) which widens the scope of the induced-matter theory. Moreover, it bears a close resemblance to the standard S\'{a}ez-Ballester scalar-tensor theory, as well as other alternative theories to general relativity, whose construction includes either a minimally or a non-minimally coupled scalar field. However, contrary to those theories, in our framework the energy momentum tensor and the scalar potential are not added by hand, but instead are dictated from the geometry. Concerning cosmological applications, our herein contribution brings a new perspective. We firstly show that the dark energy sector can be naturally retrieved within a strictly geometric perspective, and we subsequently analyze it. Moreover, our framework may provide a hint to understand the physics of lower gravity theories.

Hypersurface-homogeneous modified holographic Ricci dark energy cosmological model by hybrid expansion law in Saez–Ballester theory of gravitation

The main motive of this investigation is to study the behavior of cosmological model in the presence of matter and a modified holographic Ricci dark energy for homogeneous hypersurface in the scalar tensor theory of gravitation, proposed by Saez–Ballester (Phys. Lett. A, 113, 467 (1986)). The hybrid expansion law (Akarsu et al., JCAP, 01, 022 (2014)) has been used to get a determinate solution. The physical condition that is shear scalar proportional to the expansion scalar is used to obtain the solution of the field equations. The various physical and geometrical aspects of the model are also discussed.

Anisotropic new holographic dark energy model in Saez–Ballester theory of gravitation

This work is devoted to the investigation of new holographic dark energy (infrared cutoff is the Hubble radius) in locally rotationally symmetric Bianchi type- $I$ universe within the framework of Saez–Ballester (Phys. Lett. A 113:467, 1986) scalar–tensor theory of gravitation. We construct interacting and non-interacting dark energy models by solving the field equations using a relationship between the metric potentials. This leads to a variable deceleration parameter model which exhibits a transition of the universe from deceleration to acceleration. We evaluate various cosmological parameters of our models. We have observed that the energy density parameters, equation of state and important cosmological planes ( $\omega _{\mathit{de}} - \omega _{\mathit{de}}'$ and $r - s$ ) yield the results compatible with the modern observational data. We have, also, discussed the stability analysis of our models.

Kantowski–Sachs modified holographic Ricci dark energy model in Saez–Ballester theory of gravitation

We have considered Kantowski–Sachs space–time in the presence of matter and anisotropic modified holographic Ricci dark energy components in the scalar–tensor theory of gravitation formulated by Saez and Ballester (Phys. Lett. A, 113, 467, 1986) and derived the field equations of the theory. We have used (i) hybrid expansion law proposed by Akarsu et al. (JCAP, 022, 2014), (ii) a relation between metric potentials, and (iii) modified holographic Ricci dark energy density given by Chen and Jing (Phys. Lett. B, 679, 144, 2009) to obtain an exact solution of the field equations that describes a Kantowski–Sachs holographic modified Ricci dark energy universe in this theory. Physical and kinematical parameters are also computed and their physical behavior is discussed.