Asymptotic solutions in asymptotic safety

Understand

We explain how to find the asymptotic form of fixed point solutions in functional truncations, in particular $f(R)$ approximations.

• We find that quantum fluctuations do not decouple at large $R$, typically leading to elaborate asymptotic solutions containing several free parameters.
• By a counting argument, these can be used to map out the dimension of the fixed point solution spaces.
• They are also necessary to validate the numerical solution, and provide the physical part in the limit that the cutoff is removed: the fixed point equation of state.