Stability analysis for cosmological models in f(R) gravity using dynamical system analysis

Shah, Parth; Samanta, Gauranga C.

doi:10.1140/epjc/s10052-019-6934-x

Cited by 55 publications

(32 citation statements)

References 88 publications

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“…To construct the dynamical autonomous system for our f (T, B) cosmological model, we follow the approach outlined in Refs. [61][62][63]. As a first step we introduce a set of conveniently specified variables which allow us to rewrite the evolution equations as an autonomous phase system.…”

Section: F (T B) Dynamical System Structurementioning

confidence: 99%

Stability analysis for cosmological models in f(T, B) gravity

2020

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In this paper we study cosmological solutions of the f(T, B) gravity using dynamical system analyses. For this purpose, we consider cosmological viable functions of f(T, B) that are capable of reproducing the dynamics of the Universe. We present three specific models of f(T, B) gravity which have a general form of their respective solutions by writing the equations of motion as an autonomous system. Finally, we study its hyperbolic critical points and general trajectories in the phase space of the resulting dynamical variables which turn out to be compatible with the current late-time observations.

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Section: F (T B) Dynamical System Structurementioning

confidence: 99%

Stability analysis for cosmological models in f(T, B) gravity

2020

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“…In the framework of f (R) gravity, the dynamical behavior of matter and curvature fields has been studied in several works. See, for example, [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic compact stars in f(R) gravity

Nashed

Capozziello

2021

Eur. Phys. J. C

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We derive a new interior solution for stellar compact objects in $$f\mathcal {(R)}$$ f ( R ) gravity assuming a differential relation to constrain the Ricci curvature scalar. To this aim, we consider specific forms for the radial component of the metric and the first derivative of $$f\mathcal {(R)}$$ f ( R ) . After, the time component of the metric potential and the form of $$f({\mathcal {R}})$$ f ( R ) function are derived. From these results, it is possible to obtain the radial and tangential components of pressure and the density. The resulting interior solution represents a physically motivated anisotropic neutron star model. It is possible to match it with a boundary exterior solution. From this matching, the components of metric potentials can be rewritten in terms of a compactness parameter C which has to be $$C=2GM/Rc^2<<0.5$$ C = 2 G M / R c 2 < < 0.5 for physical consistency. Other physical conditions for real stellar objects are taken into account according to the solution. We show that the model accurately bypasses conditions like the finiteness of radial and tangential pressures, and energy density at the center of the star, the positivity of these components through the stellar structure, and the negativity of the gradients. These conditions are satisfied if the energy-conditions hold. Moreover, we study the stability of the model by showing that Tolman–Oppenheimer–Volkoff equation is at hydrostatic equilibrium. The solution is matched with observational data of millisecond pulsars with a withe dwarf companion and pulsars presenting thermonuclear bursts.

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“…Numerous applications of f(R) can be found in the context of theoretical cosmology [31,[42][43][44][45][46][47][48] and in astrophysics. Spherically symmetric vacuum black hole solutions in f(R) have been derived in [1,[49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic compact stars in higher-order curvature theory

2021

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In this paper we shall consider spherically symmetric spacetime solutions describing the interior of stellar compact objects, in the context of higher-order curvature theory of the $${{\mathrm {f(R)}}}$$ f ( R ) type. We shall derive the non-vacuum field equations of the higher-order curvature theory, without assuming any specific form of the $${{\mathrm {f(R)}}}$$ f ( R ) theory, specifying the analysis for a spherically symmetric spacetime with two unknown functions. We obtain a system of highly non-linear differential equations, which consists of four differential equations with six unknown functions. To solve such a system, we assume a specific form of metric potentials, using the Krori–Barua ansatz. We successfully solve the system of differential equations, and we derive all the components of the energy–momentum tensor. Moreover, we derive the non-trivial general form of $${{\mathrm {f(R)}}}$$ f ( R ) that may generate such solutions and calculate the dynamic Ricci scalar of the anisotropic star. Accordingly, we calculate the asymptotic form of the function $${\mathrm {f(R)}}$$ f ( R ) , which is a polynomial function. We match the derived interior solution with the exterior one, which was derived in [1], with the latter also resulting to a non-trivial form of the Ricci scalar. Notably but rather expected, the exterior solution differs from the Schwarzschild one in the context of general relativity. The matching procedure will eventually relate two constants with the mass and radius of the compact stellar object. We list the necessary conditions that any compact anisotropic star must satisfy and explain in detail that our model bypasses all of these conditions for a special compact star $$\textit{Her X--1}$$ Her X - - 1 , which has an estimated mass and radius $$(mass = 0.85 \pm 0.15M_{\circledcirc }\ and\ radius = 8.1 \pm 0.41~\text {km}$$ ( m a s s = 0.85 ± 0.15 M ⊚ a n d r a d i u s = 8.1 ± 0.41 km ). Moreover, we study the stability of this model by using the Tolman–Oppenheimer–Volkoff equation and adiabatic index, and we show that the considered model is different and more stable compared to the corresponding models in the context of general relativity.

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Stability analysis for cosmological models in f(R) gravity using dynamical system analysis

Cited by 55 publications

References 88 publications

Stability analysis for cosmological models in f(T, B) gravity

Stability analysis for cosmological models in f(T, B) gravity

Anisotropic compact stars in f(R) gravity

Anisotropic compact stars in higher-order curvature theory

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