Scalar-Tensor Gravity Cosmology: Noether symmetries and analytical solutions

Abstract

In this paper, we present a complete Noether Symmetry analysis in the framework of scalar-tensor cosmology. Specifically, we consider a non-minimally coupled scalar field action embedded in the FLRW spacetime and provide a full set of Noether symmetries for related minisuperspaces. The presence of symmetries implies that the dynamical system becomes integrable and then we can compute cosmological analytical solutions for specific functional forms of coupling and potential functions selected by the Noether Approach.

arXiv comment9 pages, accepted for publication by Phys. Rev. D

References in corpus (53)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Dynamics of dark energy
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Cosmological Imprint of an Energy Component with General Equation of State
• Extended Theories of Gravity
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• An alternative to quintessence
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• The 3D power spectrum of galaxies from the SDSS
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Curvature Quintessence
• Disappearing cosmological constant in f(R) gravity
• Improved Dark Energy Constraints from ~100 New CfA Supernova Type Ia Light Curves
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Scrutinizing Exotic Cosmological Models Using ESSENCE Supernova Data Combined with Other Cosmological Probes
• Evolution of the Scale Factor with a Variable Cosmological Term
• The Physics of Cosmic Acceleration
• Quintessence and Supergravity
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Power-Law Inflation from the Rolling Tachyon
• The Revival of the Unified Dark Energy-Dark Matter Model ?
• Stability of Cosmological Solution in f(R) Models of Gravity
• Hubble expansion & Structure Formation in Time Varying Vacuum Models
• Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
• Cosmology with massive neutrinos coupled to dark energy
• f(R) cosmology by Noether's symmetry
• Thermodynamics of Decaying Vacuum Cosmologies
• Power-law expansion in k-essence cosmology
• Noether symmetries and analytical solutions in f(T)-cosmology: A complete study
• Mapping the Cosmological Expansion
• Using the Noether symmetry approach to probe the nature of dark energy
• Noether Symmetry in $f(T)$ Theory
• Dark energy as a massive vector field
• Accelerating Cold Dark Matter Cosmology (${\Omega }_{\Lambda }\equiv 0$)
• Noether symmetry approach in phantom quintessence cosmology
• Noether symmetry in $f(R)$ cosmology
• Lie and Noether symmetries of geodesic equations and collineations
• Constraints and analytical solutions of $f(R)$ theories of gravity using Noether symmetries
• Constraining the cosmic equation of state from old galaxies at high redshift
• New Spherically Symmetric Solutions in f(R)-gravity by Noether Symmetries
• Reconstruction of the Scalar-Tensor Lagrangian from a LCDM Background and Noether Symmetry
• Two dimensional dynamical systems which admit Lie and Noether symmetries
• Scalar Tensor Teleparallel Dark Gravity via Noether Symmetry
• Conformally related metrics and Lagrangians and their physical interpretation in cosmology
• Noether Symmetry Approach in multiple scalar fields Scenario
• Can Old Galaxies at High Redshifts and Baryon Acoustic Oscillations Constrain H_0?
• Equation of state for Universe from similarity symmetries
• The distinctions between $\Lambda$CDM and $f(T)$ gravity according Noether symmetry
• Breaking the sigma_8-Omega_m degeneracy using the clustering of high-z X-ray AGN
• Analysis of the non-minimally coupled scalar field in the Palatini formalism by the Noether symmetry approach

Cited by in corpus (37)

• In the Realm of the Hubble tension $-$ a Review of Solutions
• Noether Symmetry Approach in Gauss-Bonnet Cosmology
• Dynamical analysis in scalar field cosmology
• Noether Symmetries in Gauss-Bonnet-teleparallel cosmology
• Two scalar field cosmology: Conservation laws and exact solutions
• Invariant solutions and Noether symmetries in Hybrid Gravity
• Noether Symmetries as a geometric criterion to select theories of gravity
• $f(R)$-gravity from Killing Tensors
• Classification of the Horndeski cosmologies via Noether Symmetries
• Dynamical symmetries and observational constraints in scalar field cosmology
• Classical and Quantum Solutions in Brans-Dicke Cosmology with a Perfect Fluid
• Noether Symmetry Approach for teleparallel-curvature cosmology
• Noether analysis of Scalar-Tensor Cosmology
• Dynamical symmetries in Brans-Dicke cosmology
• Noether Symmetry Approach in Energy-Momentum Squared Gravity
• Equivalence of non-minimally coupled cosmologies by Noether symmetries
• Classification of Teleparallel Horndeski Cosmology via Noether Symmetries
• Scalar-Tensor Teleparallel Gravity With Boundary Term by Noether Symmetries
• Anisotropic stellar models admitting conformal motion
• Cosmological models in Weyl geometrical scalar-tensor theory
• The Noether Bessel Hagen Symmetry Approach for Dynamical Systems
• Noether Symmetries and Some Exact Solutions in $f(R,T^2)$ Theory
• Exact cosmological solutions for MOG
• Exact Scalar-Tensor Cosmological Models
• Studying the Intervention of an Unusual Term in $f(T)$ Gravity via Noether Symmetry
• Exact Cosmological Solutions of $f(R)$ Theories via Hojman Symmetry
• Noether Symmetries in $f(T,T_G)$ Cosmology
• Noether symmetry in the Nash theory of gravity
• Noether symmetry in Horndeski Lagrangian
• Noether symmetry approach in the cosmological alpha-attractors
• Cosmological dynamics and bifurcation analysis of the general non-minimally coupled scalar field models
• Evaporation/Antievaporation and energy conditions in alternative gravity
• General analysis of Noether symmetries in Horndeski gravity
• Relativistic Ermakov-Milne-Pinney Systems and First Integrals
• Classical and quantum (2+1)-dimensional spatially homogeneous string cosmology
• Noether gauge symmetry of Dirac field in $2+1$ dimensional gravity
• Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field