Abstract
The availability of scaling solutions in renormalisation group improved versions of cosmology are investigated in the high-energy limit. We adopt -type models of quantum gravity which display an interacting ultraviolet fixed point at shortest distances. Expanding the gravitational fixed point action to very high order in the curvature scalar, we detect a convergence-limiting singularity in the complex field plane. Resummation techniques including Padé approximants as well as infinite order approximations of the effective action are used to maximise the domain of validity. We find that the theory displays near de Sitter solutions as well as an anti-de Sitter solution in the UV whereas real de Sitter solutions, for small curvature, appear to be absent. The significance of our results for inflation, and implications for more general models of quantum gravity are discussed.
Highlights
The asymptotic safety conjecture for gravity [1] stipulates that a quantum theory of gravity may very well exist as a conventional local quantum field theory provided it develops an interacting UV fixed point at highest energies
We find that de Sitter solutions occur within the radius of convergence, as determined from E(R), but only low orders in the approximation, without persisting to higher orders
We have studied the availability of inflationary solutions for cosmology from asymptotically safe models of quantum gravity in the high-energy regime
Summary
The asymptotic safety conjecture for gravity [1] stipulates that a quantum theory of gravity may very well exist as a conventional local quantum field theory provided it develops an interacting UV fixed point at highest energies. We are interested in de Sitter solutions for cosmology, and whether these may arise through fluctuations of the metric field To answer this question, the quantum effective action in the fixed point regime needs to be available. We will employ resummation techniques for the effective action including Pade resummation and numerical integration beyond polynomial orders This allows us to investigate the existence (or not) of cosmological scaling solutions in the fixed point regime both for small and moderate Ricci curvature even beyond polynomial approximations. After recalling the key features of inflationary scenarios and gravitational renormalisation group equations, we analyse the fixed point solutions, the radius of convergence of high order polynomial approximations, convergence-limiting singularities in the complex field plane, and compare findings with resummations and numerical integration
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