Constraining quantum gravity from observations is a challenge. We expand on the idea that the interplay of quantum gravity with matter could be key to meeting this challenge.Thus, we set out to confront different potential candidates for quantum gravity -unimodular asymptotic safety, Weyl-squared gravity and asymptotically safe gravity -with constraints arising from demanding an ultraviolet complete Standard Model. Specifically, we show that within approximations, demanding that quantum gravity solves the Landau-pole problems in Abelian gauge couplings and Yukawa couplings strongly constrains the viable gravitational parameter space. In the case of Weyl-squared gravity with a dimensionless gravitational coupling, we also investigate whether the gravitational contribution to beta functions in the matter sector calculated from functional Renormalization Group techniques is universal, by studying the dependence on the regulator, metric field parameterization and choice of gauge. I. INTRODUCTIONObservational constraints on quantum gravity are hard to come by. Based on a simple dimensional argument, one typically expects a power-law suppression of quantum-gravity effects 1 with (E/M Pl ) # , with E being the energy scale relevant for experiments, M Pl being the Planck mass and # > 0. Nevertheless, mathematical and internal consistency are not the only conditions that could * Electronic address: gpbrito@cbpf.br † Electronic address: eichhorn@sdu.dk ‡ Electronic address: adpjunior@id.uff.br 1 In the presence of a second "meso"-scale, as hinted at by some quantum-gravity approaches, e.g., [1], this situation can change.

We discover a weak-gravity bound in scalar-gravity systems in the asymptotic-safety paradigm. The weak-gravity bound arises in these systems under the approximations we make, when gravitational fluctuations exceed a critical strength. Beyond this critical strength, gravitational fluctuations can generate complex fixed-point values in higher-order scalar interactions. Asymptotic safety can thus only be realized at sufficiently weak gravitational interactions. We find that within truncations of the matter-gravity dynamics, the fixed point lies beyond the critical strength, unless spinning matter, i.e., fermions and vectors, is also included in the model.

We study the dependence on field parametrization of the functional renormalization group equation in the fðRÞ truncation for the effective average action. We perform a systematic analysis of the dependence of fixed points and critical exponents in polynomial truncations. We find that, beyond the Einstein-Hilbert truncation, results are qualitatively different depending on the choice of parametrization. In particular, we observe that there are two different classes of fixed points, one with three relevant directions and the other with two. The computations are performed in the background approximation. We compare our results with the available literature and analyze how different schemes in the regularizations can affect the fixed point structure.