Asymptotically safe gravity as a scalar-tensor theory and its
  cosmological implications
  We study asymptotically safe gravity with Einstein-Hilbert truncation taking
into account the renormalization group running of both gravitational and
cosmological constants. We show the classical behavior of the theory is
equivalent to a specific class of Jordan-Brans-Dicke theories with vanishing
Brans-Dicke parameter, and potential determined by the renormalization group
equation. The theory may be reformulated as an $f(R)$ theory. In the simplest
cosmological scenario, we find large--field inflationary solutions near the
Planck scale where the effective field theory description breaks down. Finally,
we discuss the implications of a running gravitational constant to background
dynamics via cosmological perturbation theory. We show that compatibility with
General Relativity requires contributions from the running gravitational
constant to the stress energy tensor to be taken into account in the
perturbation analysis.
