Noether symmetry analysis of anisotropic universe in modified gravity

2017/04/21 by M. Farasat Shamir, Fiza Kanwal
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #De Sitter universe #Geometry #Homogeneous space #Lagrangian #Mathematical physics #Mathematics #Noether's theorem #Physics #Quantum mechanics #Universe #gr-qc

paper · pdf · doi:10.1140/epjc/s10052-017-4869-7

published as Eur. Phys. J. C 77(2017)286 · 17 Pages

arxiv created 2017/04/21 · openalex publication_date 2017/05/01 · arxiv updated 2017/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper we study the anisotropic universe using Noether symmetries in modified gravity. In particular, we choose a locally rotationally symmetric Bianchi type-I universe for the analysis in f(R,\mathcal G) gravity, where R is the Ricci scalar and \mathcal G is the Gauss–Bonnet invariant. Firstly, a model f(R,\mathcal G)=f₀R^l+f₁\mathcal Gⁿ is proposed and the corresponding Noether symmetries are investigated. We have also recovered the Noether symmetries for f(R) and f(\mathcal G) theories of gravity. Secondly, some important cosmological solutions are reconstructed. Exponential and power-law solutions are reported for a well-known f(R,\mathcal G) model, i.e., f(R,\mathcal G)=f₀Rⁿ\mathcal G^1-n . Especially, Kasner’s solution is recovered and it is anticipated that the familiar de Sitter spacetime giving Λ CDM cosmology may be reconstructed for some suitable value of n.

Citations

• Noether gauge symmetry approach in f(R) gravity
• Noether symmetry approach in f(R)–tachyon model
• The Large Scale Structure of Space-Time
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Dark energy in modified Gauss-Bonnet gravity: Late-time acceleration and the hierarchy problem
• First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Preliminary Maps and Basic Results
• Study of Bianchi I anisotropic model in f(R,T) gravity
• Modified Gauss-Bonnet theory as gravitational alternative for dark energy
• Dynamics of dark energy
• Gauss-Bonnet dark energy
• Three‐YearWilkinson Microwave Anisotropy Probe(WMAP) Observations: Implications for Cosmology
• Locally rotationally symmetric Bianchi type I cosmology in f(R, T) gravity
• Relativistic Cosmology. I
• INTRODUCTION TO MODIFIED GRAVITY AND GRAVITATIONAL ALTERNATIVE FOR DARK ENERGY