Renormalization group scale-setting from the action - a road to modified gravity theories

Details Renormalization group scale-setting from the action - a road to modified gravity theories Renormalization group scale-setting from the action - a road to modified gravity theories

2012-04-06

arxiv.org/abs/1204.1483v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages

Scientific paper

The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the renormalization group is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG corrected gravitational theories yields the effective $f(R)$ modified gravity theories with negative powers of the Ricci scalar $R$. The scale-setting at the level of the action at the non-gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in Ricci tensor. Recently obtained analytical solutions for the quadratic action in $R$ are summarized as an illustration of the dynamics at the non-gaussian fixed point.

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