Variable $G$ and $\Lambda$ gravity theory and analytical Cosmological Solutions using Noether symmetry approach

Abstract

The present work deals with scalar field cosmology in the framework of a quantum gravity modified Einstein-Hilbert Lagrangian with variable $G$ and $\Lambda$. Using Renormalization group, variable $G$ behaves as a minimally coupled filed (not the scalar-tensor theory) and variable $\Lambda$ can be interpreted as a potential function. The point Lagrangian for this model in the background of homogeneous and isotropic flat FLRW space-time model experiences point-like Noether symmetry and equivalent potential function $\Lambda (G)$ is determined. Using a point transformation in the $3D$ augmented space is found that one of the variable become cyclic and as a consequence there is considerable simplification to the physical system. Lastly, the constants of motion can be written in compact form and it is possible to have analytic cosmological solutions in the present context.

arXiv comment10 pages, 6 figures

References in corpus (67)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Modified Gravity and Cosmology
• 4D Gravity on a Brane in 5D Minkowski Space
• The galileon as a local modification of gravity
• Dark torsion as the cosmic speed-up
• Nonperturbative Evolution Equation for Quantum Gravity
• Measuring the Baryon Acoustic Oscillation scale using the SDSS and 2dFGRS
• Constraints on Cosmological Models from Hubble Space Telescope Observations of High-z Supernovae
• Renormalization group improved black hole spacetimes
• Evolution of the Scale Factor with a Variable Cosmological Term
• Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation
• Cross-correlation Tomography: Measuring Dark Energy Evolution with Weak Lensing
• Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
• Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
• Cosmological constant and vacuum energy: old and new ideas
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Hessence: A New View of Quintom Dark Energy
• The Cosmology of Modified Gauss-Bonnet Gravity
• Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity
• On the renormalization group flow of f(R)-gravity
• Is Quantum Einstein Gravity Nonperturbatively Renormalizable?
• Cosmology with Self-Adjusting Vacuum Energy Density from a Renormalization Group Fixed Point
• Cosmological Solutions of $f(T)$ Gravity
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the large-scale two-point correlation function
• f(R) cosmology by Noether's symmetry
• Dynamical vacuum energy in the expanding Universe confronted with observations: a dedicated study
• Complete Cosmic History with a dynamical Lambda(H) term
• The Renormalization Group flow of unimodular f(R) gravity
• Using the Noether symmetry approach to probe the nature of dark energy
• Probing Gravitation, Dark Energy, and Acceleration
• On the evolution of universes in quadratic theories of gravity
• Quantum Gravity effects near the null black hole singularity
• A class of nonlocal truncations in Quantum Einstein Gravity and its renormalization group behavior
• Noether symmetry approach in phantom quintessence cosmology
• Noether symmetry in $f(R)$ cosmology
• Towards Nonperturbative Renormalizability of Quantum Einstein Gravity
• Lie and Noether symmetries of geodesic equations and collineations
• Dynamical analysis in scalar field cosmology
• Cosmological consequences of an adiabatic matter creation process
• Cosmological Perturbations in Renormalization Group Derived Cosmologies
• Reconstruction of the Scalar-Tensor Lagrangian from a LCDM Background and Noether Symmetry
• Two scalar field cosmology: Conservation laws and exact solutions
• Cosmological constant, renormalization group and Planck scale physics
• Two dimensional dynamical systems which admit Lie and Noether symmetries
• Observational Constraints on $f(T)$ gravity from varying fundamental constants
• Some Inflationary Einstein-Aether Cosmologies
• Cosmological equivalence between the Finsler-Randers space-time and the DGP gravity model
• LRS Bianchi type I universes exhibiting Noether symmetry in the scalar-tensor Brans-Dicke theory
• Noether Symmetry Approach in multiple scalar fields Scenario
• Arnowitt-Deser-Misner gravity with variable G and Lambda and fixed point cosmologies from the renormalization group
• Running vacuum in the Universe and the time variation of the fundamental constants of Nature
• Dynamical symmetries and observational constraints in scalar field cosmology
• Bouncing and emergent cosmologies from ADM RG flows
• A Class of Renormalization Group Invariant Scalar Field Cosmologies
• On exact solutions for quintessential (inflationary) cosmological models with exponential potentials
• Equation of state for Universe from similarity symmetries
• Cosmological dynamics in higher-dimensional Einstein-Gauss-Bonnet gravity
• Cosmological solutions with gravitational particle production and non-zero curvature
• Noether symmetry approach in pure gravity with variable G and Lambda
• Exact solutions, finite time singularities and non-singular universe models from a variety of $\Lambda (t)$ cosmologies
• On dark energy models of single scalar field
• Cosmological singularities and analytical solutions in varying vacuum cosmologies
• Gravitational Baryogenesis in Running Vacuum models
• A study of phantom scalar field cosmology using Lie and Noether symmetries
• Constants and Variations: From Alpha to Omega
• Non-minimally coupled scalar field in Kantowski--Sachs model and symmetry analysis