Noether symmetric minisuperspace model of $f(R)$ cosmology

Abstract

We study the metric $f(R)$ cosmology using Noether symmetry approach by utilizing the behavior of the corresponding Lagrangian under infinitesimal generators of the desired symmetry. The existence of Noether symmetry of the cosmological $f(R)$ minisuperspace helps us to find out the form of $f(R)$ function for which such symmetry exist. It is shown that the resulting form for $f(R)$ yields a power law expansion for the cosmic scale factor. We also show that in the corresponding Noether symmetric quantum model, the solutions to the Wheeler-DeWitt equation can be expressed as a superposition of states of the form $e^{iS}$. It is shown that in terms of such wavefunctions the classical trajectories can be recovered.

5 pages, Talk given at "The Grassmannian Conference in Fundamental Cosmology (Grasscosmofun'09)", Szczecin, Poland, 14-19th September 2009

References in corpus (3)

• f(R) cosmology by Noether's symmetry
• Noether symmetry in $f(R)$ cosmology
• Noether symmetric $f(R)$ quantum cosmology and its classical correlations

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