Anisotropic Spacetimes in f(G)-gravity: Bianchi I, Bianchi III and Kantowski-Sachs Cosmologies

IF 2.8 4区 物理与天体物理 Q2 ASTRONOMY & ASTROPHYSICS
R. S. Bogadi, A. Giacomini, M. Govender, C. Hansraj, G. Leon, A. Paliathanasis
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引用次数: 0

Abstract

We investigate the evolution of cosmological anisotropies within the framework of \(f\left( G\right) \)-gravity. Specifically, we consider a locally rotationally symmetric geometry in four-dimensional spacetime that describes the Bianchi I, Bianchi III, and the Kantowski-Sachs spacetimes. Within this context, we introduce a Lagrange multiplier which allows us to reformulate the geometric degrees of freedom in terms of a scalar field. The resulting theory is dynamically equivalent to an Einstein-Gauss-Bonnet scalar field model. We normalize the field equations by introducing dimensionless variables. The dynamics of our system is then explored by solving the resulting nonlinear differential equations numerically for various sets of initial conditions. Our analysis reveals the existence of two finite attractors: the Minkowski universe and an isotropic, spatially flat solution capable of describing accelerated expansion. Although de Sitter expansion may be recovered, it appears only as an unstable solution. In addition, the theory suffers from the existence of Big Rip singularities.

f(G)-重力中的各向异性时空:Bianchi I, Bianchi III和Kantowski-Sachs宇宙论
我们在\(f\left( G\right) \) -重力的框架内研究宇宙各向异性的演化。具体来说,我们考虑了四维时空中描述Bianchi I、Bianchi III和Kantowski-Sachs时空的局部旋转对称几何。在这种情况下,我们引入拉格朗日乘子,它允许我们用标量场重新表述几何自由度。由此产生的理论与爱因斯坦-高斯-博内标量场模型动态等效。我们通过引入无量纲变量使场方程归一化。然后,通过对各种初始条件的非线性微分方程进行数值求解,探索了系统的动力学。我们的分析揭示了两个有限吸引子的存在:闵可夫斯基宇宙和一个能够描述加速膨胀的各向同性、空间平坦解。虽然德西特膨胀可以恢复,但它似乎只是一个不稳定的解决方案。此外,该理论还受到大撕裂奇点存在的影响。
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来源期刊
General Relativity and Gravitation
General Relativity and Gravitation 物理-天文与天体物理
CiteScore
4.60
自引率
3.60%
发文量
136
审稿时长
3 months
期刊介绍: General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation. It welcomes in particular original articles on the following topics of current research: Analytical general relativity, including its interface with geometrical analysis Numerical relativity Theoretical and observational cosmology Relativistic astrophysics Gravitational waves: data analysis, astrophysical sources and detector science Extensions of general relativity Supergravity Gravitational aspects of string theory and its extensions Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations Quantum field theory in curved spacetime Non-commutative geometry and gravitation Experimental gravity, in particular tests of general relativity The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.
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