The Inflationary Mechanism in Asymptotically Safe Gravity

Abstract

According to the asymptotic safety conjecture, gravity is a renormalizable quantum field theory whose continuum limit is defined by an interacting fixed point of the renormalization group flow. In these proceedings we review some implications of the existence of this nontrivial fixed point in cosmological contexts. Specifically, we discuss a toy model exemplifying how the departure from the fixed-point regime can explain the approximate scale-invariance of the power spectrum of temperature fluctuations in the cosmic microwave background. I. INTRODUCTIONPrimordial quantum fluctuations occurring in the pre-inflationary epoch have left indelible imprints which we measure today in the form of tiny temperature anisotropies, δT /T ∼ 10 −5 , in the Cosmic Microwave Background (CMB) radiation. The inflationary mechanism furnishes a simple explanation for the presence of these anisotropies [1] and it has become a paradigm in the description of the primordial evolution of the universe within the standard cosmological model.The spectrum of the CMB reproduces an almost perfect black-body radiation at an average temperature T ∼ 2.7K. The distribution of temperature fluctuations in the CMB is described by the power spectra of scalar and tensorial perturbations. These spectra are essentially characterized by two parameters: the spectral index n s , giving information on the scale dependence of the power spectrum of scalar fluctuations, and the tensor-to-scalar ratio r, measuring the suppression of tensorial perturbations against the scalar ones. The values of the spectral index n s and tensorto-scalar ratio r can be obtained from the observational data. In particular, the most recent observations to date [2] constrain the spectral index to be n s = 0.9649 ± 0.0042 at 68% CF, and limit the tensor-to-scalar ratio to values r < 0.064. Note that, although the scalar power spectrum is almost scale invariant, perfect scale invariance, corresponding to n s = 1, seems to be excluded.The extraordinary predictive power of the inflationary scenario, combined with the current limits on the determination of r, makes it difficult to distinguish between different models of cosmic inflation [3]. The simplest inflationary model capable of explaining the current observational data is * a.platania@thphys.uni-heidelberg.de arXiv:1908.03897v1 [gr-qc]

Curvature bound from gravitational catalysis

“…In a specific cosmological model, the temperature would be connected with a relevant cosmological scale, say, a time parameter or an expansion scale. Within asymptotically-safe cosmologies, such scales are assumed to be linked to some suitable power of k by RG-improvement arguments [84][85][86][87][88][89][90][91][92]. In fact, several scale-setting procedures have been discussed in the literature [85,[92][93][94].…”

From Renormalization Group Flows to Cosmology

“…This condition should also hold in the more general case of f k (R) theories, if the running of the gravitational couplings is approximated with the corresponding fixed-point scaling [88,91].…”

“…In this subsection we review the results in Bonanno et al [61] and Platania [91]. As the initial conditions for inflation are placed at trans-Planckian scales and since the effective action at inflationary scales depends on how the RG-trajectory realized by Nature emerges from the NGFP, the Planck data on CMB anisotropies can in principle put constraints on the universality properties of the gravitational RG flow.…”

Critical Reflections on Asymptotically Safe Gravity

“…Proceeding in a similar way in a gravitational context, it has been a common strategy to retain the dependence of some of the couplings, G k and k say, on the RG scale k and identify the latter with a geometrical quantity or momentum. Based on such RG improvement ideas there is a substantial body of work investigating black-hole physics [341][342][343][344][345][346][347][348][349][350][351][352][353][354][355], gravitational collapse [356][357][358][359][360][361][362], and cosmological scenarios [320,360,[363][364][365][366][367][368][369][370][371][372][373][374][375][376] inspired by Asymptotic Safety. One might expect that this procedure could be justified in some cases where the external scale in question acts as an IR cutoff for fluctuations.…”