Asymptotic Safety, Emergence and Minimal Length

There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that 1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and 2) there is a sense in which asymptotic safety implies a minimal length. In so doing we also discuss possible signatures of asymptotic safety in scattering experiments.Comment: LaTEX, 20 pages, 2 figures; v.2: minor changes, reflecting published versio

Inflationary solutions in asymptotically safe f(R) theories

We discuss the existence of inflationary solutions in a class of renormalization group improved polynomial f(R) theories, which have been studied recently in the context of the asymptotic safety scenario for quantum gravity. These theories seem to possess a nontrivial ultraviolet fixed point, where the dimensionful couplings scale according to their canonical dimensionality. Assuming that the cutoff is proportional to the Hubble parameter, we obtain modified Friedmann equations which admit both power-law and exponential solutions. We establish that for sufficiently high-order polynomial the solutions are reliable in the sense that considering still higher-order polynomials is very unlikely to change the solution