Asymptotic safety in the f(R) approximation
By Juergen A. Dietz, T. Morris. 2012
145 citations recorded by the source corpus.
A bstractIn the asymptotic safety programme for quantum gravity, it is important to go beyond polynomial truncations. Three such approximations have been derived where the restriction is only to a general function f(R) of the curvature R > 0. We confront these with the requirement that a fixed point solution be smooth and exist for all R ≥ 0. Singularities induced by cutoff choices force the earlier versions to have no such solutions. However, we show that the most recent version has a number of lines of fixed points, each supporting a continuous spectrum of eigen-perturbations. We uncover and analyse the first five such lines. Sensible fixed point behaviour may be achieved if one consistently incorporates geometry/topology change. As an exploratory example, we analyse the equations analytically continued to R < 0, however we now find only partial solutions. We show how these results are always consistent with, and to some extent can be predicted from, a straightforward analysis of the constraints inherent in the equations.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/86d44074d83bdaa3f5c62eff3e40831b5f338794
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Citations in the corpus
- A polynomial f(R) inflation model (2013, background): “More relevant fundamental aspects on the gravity with higher derivatives are considered in [12–14] etc.”
- The nonperturbative functional renormalization group and its applications (2020, background): “Extensions to higher orders in Rn can be found in [1082, 1094, 1098, 1103–1106, 1162–1167], and inclusions of Ricci tensor invariants and Riemann tensor invariants in [1107, 1111, 1112, 1168].”