ULTRAVIOLET PROPERTIES OF f(R)-GRAVITY

Abstract

We discuss the existence and properties of a nontrivial fixed point in f (R)-gravity, where f is a polynomial of order up to six. Within this seven-parameter class of theories, the fixed point has three ultraviolet-attractive and four ultraviolet-repulsive directions; this brings further support to the hypothesis that gravity is nonperturbatively renormalizable.

Signature change of the metric in CDT quantum gravity?

“…The line has been extrapolated both to the top-left and to the bottom-right, where we conjecture that all four phases meet at a common point, becoming a quadruple point. 9 All these results will be presented in a separate article that will follow this work. …”

“…All results suggest that phase C persists in the infinite volume limit and the real phase transition is just very close to what we measure in the transfer matrix data for s = 60k (the biggest total volume in our measurements). 9 We use this data to update the CDT phase diagram with a new phase transition line -see figure 9. The line has been extrapolated both to the top-left and to the bottom-right, where we conjecture that all four phases meet at a common point, becoming a quadruple point.…”

“…Evidence for such a fixed point has come mainly from functional renormalization group methods [6][7][8][9][10][11] and lattice approaches to quantum gravity [12][13][14][15]. In a lattice formulation of quantum gravity a non-trivial fixed point would appear as a second-order critical point, the approach to which would define a continuum limit [16].…”

The Renormalization Group flow of unimodular f(R) gravity

“…Within quantum Einstein gravity, an analogous truncation has been considered in [29][30][31][32][33][34][35].…”

A functional renormalization group equation for foliated spacetimes

“…Starting from the seminal work [7] there is now a solid body of evidence supporting the existence and predictivity of this NGFP [8,9,10,11,12,13,14,15,16,17]. The more recent proposal advocated by Hořava [18] suggests that the UV completion of gravity is an action which is anisotropic in the space and time coordinates.…”