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Exact Cosmological Solutions of $f(R)$ Theories via Hojman Symmetry | | Hao Wei
; Hong-Yu Li
; Xiao-Bo Zou
; | | Date: |
2 Nov 2015 | | Abstract: | Nowadays, $f(R)$ theory has been one of the leading modified gravity theories
to explain the current accelerated expansion of the universe, without invoking
dark energy. It is of interest to find the exact cosmological solutions of
$f(R)$ theories. In fact, symmetry has been proved as a powerful tool to find
exact solutions in physics. As is well known, Noether symmetry has been
extensively used in cosmology and gravity theories. Recently, the so-called
Hojman symmetry was also considered in the literature. Hojman symmetry directly
deals with the equations of motion, rather than Lagrangian or Hamiltonian,
unlike Noether symmetry. In this work, we consider Hojman symmetry in $f(R)$
theories in both the metric and Palatini formalisms, and find the corresponding
exact cosmological solutions of $f(R)$ theories via Hojman symmetry. We show
that the results are different from the ones obtained by using Noether symmetry
in $f(R)$ theories. The present work confirms that Hojman symmetry can bring
new features to cosmology and gravity theories. | | Source: | arXiv, 1511.0376 | | Services: | Forum | Review | PDF | Favorites | |
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