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Register a new userNovel aspects of C-theories in Cosmology
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The field equations in FRW background for the so called C-theories are presented and investigated. In these theories the usual Ricci scalar is substituted with $f(mathcal{R})$ where $mathcal{R}$ is a Ricci scalar related to a conformally scaled metric $hat{g}_{mu u} = mathcal{C}(mathcal{R})g_{mu u}$, where the conformal factor itself depends on $mathcal{R}$. It is shown that homogeneous perturbations of this Ricci scalar around general relativity FRW background of a large class of these theories are either inconsistent or unstable.
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Shift-symmetric Horndeski theories admit an interesting class of Schwarzschild black hole solutions exhibiting time-dependent scalar hair. By making use of Lema^{i}tre coordinates, we analyze perturbations around these types of black holes, and demonstrate that scalar perturbations around black hole backgrounds inevitably have gradient instabilities. Taken together with previously established results, this newly-discovered instability rules out black holes with time-dependent scalar hair in Horndeski theories.
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