Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Generalized Noether Theorem for Gauss-Bonnet Cosmology (1906.05989v2)

Published 14 Jun 2019 in gr-qc

Abstract: Generalized Noether's theory is a useful method for researching the modified gravity theories about the conserved quantities and symmetries. A generally Gauss-Bonnet gravity $f(R,\mathcal{G})$ theory was proposed as an alternative gravity model. Through the generalized Noether symmetry, polynomial and product forms of the $f(R,\mathcal{G})$ theory with corresponding conserved quantities and symmetries are researched. Then suitable general forms of the polynomial form $f(R,\mathcal{G}) !=! k_1 Rn + (6){\frac{n}{2}}(-1){n+1} k_1 \mathcal{G}{\frac{n}{2}}$ and the product form $f(R,\mathcal{G}) !=! k ( R / \sqrt{\mathcal{G}} )n \mathcal{G}$ are found out, to contain the solution of accelerated expansion cosmology. Both forms of $f(R,\mathcal{G})$ concerned in this paper only possess time translational symmetry. And energy condition of these solutions are also checked. To some extent, the consistency of conservation of symmetry and energy condition is demonstrated. For the specific form of different $n$, it needs further detailed study. Noting that, the corresponding conserved quantities are both zero, and the only conservation relation is conservation of energy.

Summary

We haven't generated a summary for this paper yet.