Asymptotic solutions in asymptotic safety Article Swipe
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·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1103/physrevd.95.106010
· OA: W2610288757
We explain how to find the asymptotic form of fixed point solutions in\nfunctional truncations, in particular $f(R)$ approximations. We find that\nquantum fluctuations do not decouple at large $R$, typically leading to\nelaborate asymptotic solutions containing several free parameters. By a\ncounting argument, these can be used to map out the dimension of the fixed\npoint solution spaces. They are also necessary to validate the numerical\nsolution, and provide the physical part in the limit that the cutoff is\nremoved: the fixed point equation of state. As an example we apply the\ntechniques to a recent $f(R)$ approximation by Demmel et al, finding asymptotic\nmatches to their numerical solution. Depending on the value of the endomorphism\nparameter, we find many other asymptotic solutions and fixed point solution\nspaces of differing dimensions, yielding several alternative scenarios for the\nequation of state. Asymptotic studies of other $f(R)$ approximations are needed\nto clarify the picture.\n
