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On de Sitter solutions in asymptotically safe $f(R)$ theories
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abstract
The availability of scaling solutions in renormalisation group improved versions of cosmology are investigated in the high-energy limit. We adopt $f(R)$-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 Pad\'e 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.
Forward citations
Cited by 3 Pith papers
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Spectral Functions of Lorentzian Quantum Gravity
Spectral functions for graviton and scalar graviton modes are derived in Lorentzian asymptotically safe quantum gravity via adapted FRG flow equations, yielding normalisable results consistent with infrared effective theory.
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Regulator and gauge dependence of the Abelian gauge coupling in asymptotically safe quantum gravity
The existence of an asymptotically safe UV completion for the Abelian gauge coupling is shown to survive simultaneous variations of the regulator and gauge parameters in certain minimal-sensitivity regions.
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Matter Spectral Functions from Quantum Gravity
Under asymptotically safe quantum gravity, photon and scalar propagators acquire Källén-Lehmann spectral functions that are non-normalizable and change sign in the ultraviolet.
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