Infinite dimensional symmetry groups of the Friedmann equations

Abstract

We find the symmetry generators for the Friedman equations emanating from a perfect fluid source, in the presence of a cosmological constant term. The relevant dynamics is seen to be governed by two coupled, first order ordinary differential equations, the continuity and the quadratic constraint equation. Arbitrary functions appear in the components of the symmetry vector, indicating the infinity of the group. When the equation of state is considered as arbitrary but ab initio given, previously known results are recovered and/or generalized. When the pressure is considered among the dynamical variables, solutions for models with different equations of state are mapped to each other; thus enabling the presentation of solutions to models with complicated equations of state starting from simple known cases.

19 pages, no figures, Latex2e source file. Minor changes to match published version

References in corpus (5)

• Using the Noether symmetry approach to probe the nature of dark energy
• Two scalar field cosmology: Conservation laws and exact solutions
• Friedmann's Equations in All Dimensions and Chebyshev's Theorem
• Explicit Integration of Friedmann's Equation with Nonlinear Equations of State
• Cosmological analogies, Lagrangians, and symmetries for convective-radiative heat transfer

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• Cosmological analogies, Lagrangians, and symmetries for convective-radiative heat transfer
• Variational symmetries and superintegrability in multifield cosmology
• Quantum Mechanics from General Relativity and the Quantum Friedmann Equation
• Hidden Symmetries in Gravity : Black holes and other minisuperspaces