Classification of Cosmic Scale Factor via Noether Gauge Symmetries

Abstract

In this paper, a complete classification of Friedmann-Robertson-Walker (FRW) spacetime by using approximate Noether approach is presented. Considered spacetime is discussed for three different types of universe i.e. flat, open and closed. Different forms of cosmic scale factor $a$ with respect to the nature of the universe, which posses the nontrivial Noether gauge symmetries (NGS) are reported. The perturbed Lagrangian corresponding to FRW metric in the Noether equation is used to get Noether operators. For different types of universe minimal and maximal set of Noether operators are reported. A list of Noether operators are also computed which is not only independent from the choice of the cosmic scale factor but also the choice type of universe. Further, corresponding energy type first integral of motions are also calculated.

arXiv comment16 Pages

References in corpus (38)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Dynamics of dark energy
• The Cosmological Constant and Dark Energy
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• Cosmological parameters from SDSS and WMAP
• The Supernova Legacy Survey: Measurement of Omega_M, Omega_Lambda and w from the First Year Data Set
• Curvature Quintessence
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Constraints on dark energy from Chandra observations of the largest relaxed galaxy clusters
• The Third Data Release of the Sloan Digital Sky Survey
• f(R) Gravity and scalar-tensor theory
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday
• Modified gravity with arbitrary coupling between matter and geometry
• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• Modified non-local-F(R) gravity as the key for the inflation and dark energy
• Wormholes in a viable f(T) gravity
• Violation of First Law of Thermodynamics in f(R,T) Gravity
• Exact Solutions of Bianchi Types $I$ and $V$ Spacetimes in $f(R)$ Theory of Gravity
• On the non-minimal gravitational coupling to matter
• Noether Symmetry Approach in f(R) Tachyon Model
• Generalized Second Law of Thermodynamics in $f(T)$ Gravity with Entropy Corrections
• Constraints and analytical solutions of $f(R)$ theories of gravity using Noether symmetries
• New Spherically Symmetric Solutions in f(R)-gravity by Noether Symmetries
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• Bianchi Type I Cosmology in Generalized Saez-Ballester Theory via Noether Gauge Symmetry
• Noether Gauge Symmetry Approach in f(R) Gravity
• Resolution of dark matter problem in f(T) gravity
• Conserved Quantities in $f(R)$ Gravity via Noether Symmetry
• Energy conditions in generalized teleparallel gravity models
• Noether gauge symmetry for $f(R)$ gravity in Palatini formalism
• Latest supernovae constraints on f(R) cosmologies
• Cosmological solutions in multidimensional model with multiple exponential potential
• Re-Scaling of Energy in the Stringy Charged Black Hole Solutions using Approximate Symmetries
• Energy of Bardeen Model Using Approximate Symmetry Method
• Energy Content of Colliding Plane Waves using Approximate Noether Symmetries

Cited by in corpus (6)

• Generalized second law of thermodynamics in f(R,T) theory of gravity
• Exact Cosmological Solutions of $f(R)$ Theories via Hojman Symmetry
• Classification of the Lie and Noether point symmetries for the Wave and the Klein-Gordon equations in pp-wave spacetimes
• Hojman Symmetry in $f(T)$ Theory
• Closed-form solutions of the Wheeler-DeWitt equation in a scalar-vector field cosmological model by Lie symmetries
• Comment on "Classification of Cosmic Scale Factor via Noether Gauge Symmetries" [Int. J. Theor. Phys. 54, 2343 (2015)]