New exact solutions of Bianchi I, Bianchi III and Kantowski-Sachs spacetimes in scalar-coupled gravity theories via Noether gauge symmetries

Abstract

The Noether symmetry approach is useful tool to restrict the arbitrariness in a gravity theory when the equations of motion are underdetermined due to the high number of functions to be determined in the ansatz. We consider two scalar-coupled theories of gravity, one motivated by induced gravity, the other more standard; in Bianchi I, Bianchi III and Kantowski-Sachs cosmological models. For these models, we present a full set of Noether gauge symmetries, which are more general than those obtained by the strict Noether symmetry approach in our recent work. Some exact solutions are derived using the first integrals corresponding to the obtained Noether gauge symmetries.

arXiv comment23 pages, 4 tables

References in corpus (17)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Extended Theories of Gravity
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• f(R) cosmology by Noether's symmetry
• Noether Symmetry Approach in f(R) Tachyon Model
• Noether symmetry approach in phantom quintessence cosmology
• Cosmological dynamics of Scalar--Tensor Gravity
• Selection Rules in Minisuperspace Quantum Cosmology
• Noether symmetry of F(T) cosmology with quintessence and phantom scalar fields
• Bianchi Type I Cosmology in Generalized Saez-Ballester Theory via Noether Gauge Symmetry
• Scalar Tensor Teleparallel Dark Gravity via Noether Symmetry
• Noether gauge symmetry for $f(R)$ gravity in Palatini formalism
• LRS Bianchi type I universes exhibiting Noether symmetry in the scalar-tensor Brans-Dicke theory
• Noether and some other dynamical symmetries in Kantowski-Sachs model
• Noether Gauge Symmetry of Modified Teleparallel Gravity Minimally Coupled with a Canonical Scalar Field
• Noether Symmetries of Some Homogeneous Universe Models in Curvature Corrected Scalar-Tensor Gravity
• Self-gravitating systems in Extended Gravity

Cited by in corpus (8)

• Cosmological Analysis of Scalar Field Models in f(R,T) Gravity
• Scalar-Tensor Teleparallel Gravity With Boundary Term by Noether Symmetries
• Noether Symmetries and Some Exact Solutions in $f(R,T^2)$ Theory
• Exact Kantowski-Sachs spacetimes in Einstein-Aether Scalar field theory
• Three-dimensional black holes via Noether symmetries
• Anisotropic solutions for $R^2$ gravity model with a scalar field
• Cylindrically symmetric and plane-symmetric solutions in $f(R)$ theory via Noether symmetries
• Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field