We review our contribution to infrared Renormalization Group (RG) effects to General Relativity in the context of galaxies. Considering the effective action approach to Quantum Field Theory in curved background, we argued that the proper RG energy scale, in the weak field limit, should be related to the Newtonian potential. In the galaxy context, even without dark matter, this led to a remarkably small gravitational coupling G variation (about or less than 10 −12 of its value per light-year), while also capable of generating galaxy rotation curves about as good as the best phenomenological dark matter profiles (considering both the rotation curve shape and the expected mass-to-light ratios). Here we also comment on related developments, open issues and perspectives.

This version does not match the published version at Nature Astronomy. The published version can be freely found at https://rdcu.be/ZXNT.The Radial Acceleration Relation 1 confirms that a nontrivial acceleration scale can be found in the average internal dynamics of galaxies. The existence of such a scale is not obvious as far as the standard cosmological model is concerned, and it has been interpreted as a possible sign of modified gravity 2, 3 . The implications could be profound: it could in principle explain galactic dynamics without large amounts of yet-undetected dark matter 4, 5 and address issues that the standard cosmological model faces at galactic scales 6-10 . Here, we consider 193 disk galaxies from the SPARC 11 and THINGS 12, 13 databases and, using Bayesian inference, we show that the probability of existence of a fundamental acceleration that is common to all the galaxies is essentially zero: the p-value is smaller than 10 −20 or, equivalently, the null hypothesis is rejected at more than 10σ. We conclude that the acceleration scale unveiled by the Radial Acceleration Relation is of emergent nature, possibly caused by a complex interplay between baryons and dark matter. In particular, the MOND theory 14-17 , or any other theory that behaves like it at galactic scales, is ruled out as a fundamental theory for galaxies at more than 10σ.Dark matter is currently one of the main mysteries of the universe. There are many strong indirect evidences that support its existence, from galactic rotation curves and galaxy cluster dynamics to cosmological structure formation and cosmic microwave background anisotropies, but there is yet no sign of a direct detection 4,5 . Moreover, at the scales of galaxies, there is tension between the theoretically expected dark matter distribution in the universe (from the standard cosmological model, ΛCDM) and its indirectly observed distribution 6-10 . Therefore, phenomena associated to dark matter have a chance of serving as a window towards new physics.

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There are evidences that the cosmic microwave background (CMB) large-angle anomalies imply a departure from statistical isotropy and hence from the standard cosmological model. We propose a CDM model extension whose dark energy component preserves its nondynamical character but wields anisotropic vacuum pressure. Exact solutions for the cosmological scale factors are presented, upper bounds for the deformation parameter are evaluated and its value is estimated considering the elliptical universe proposal to solve the quadrupole anomaly. This model can be constructed from a Bianchi I cosmology with a cosmological constant from two different ways: (i) a straightforward anisotropic modification of the vacuum pressure consistently with energy-momentum conservation; (ii) a Poisson structure deformation between canonical momenta such that the dynamics remain invariant under scale factors rescalings.

Abstract. We show that Renormalization Group extensions of the Einstein-Hilbert action for large scale physics are not, in general, a particular case of standard Scalar-Tensor (ST) gravity. We present a new class of ST actions, in which the potential is not necessarily fixed at the action level, and show that this extended ST theory formally contains the Renormalization Group case. We also propose here a Renormalization Group scale setting identification that is explicitly covariant and valid for arbitrary relativistic fluids.

We show that a class of bi-gravity theories contain solutions describing dark matter. A particular member of this class is also shown to be equivalent to the Eddington-Born-Infeld gravity, recently proposed as a candidate for dark matter. Bigravity theories also have cosmological de Sitter backgrounds and we find solutions interpolating between matter and acceleration eras. PACS numbers:Observations show that most of the energy density in the universe is in the form of dark matter and dark energy [1,2,3,4,5]. It is therefore of importance to have a simple and natural candidate for these components.Motivated by Yang-Mills theory, multi-graviton actions are attractive extensions of general relativity. Consider several metrics g a µν , a = 1..n. The physical properties and geometric interpretation of such a theory present great challenges. It is known that the full (diff) n symmetry cannot be preserved by consistent interactions [6]. The most general action preserving the full symmetry group is a sum of decoupled Einstein-Hilbert terms for each metric.However, interesting theories can be built by breaking the (diff) n symmetry down to the diagonal subgroup. For n = 2, a particular "bi-gravity" theory with metrics {g µν ,q µν } and actionhas been extensively studied [7,8,9,10,11,12,13,14,15]. Here Λ and λ are cosmological constants for each sector of the theory. q µν and g µν are the inverses of q µν and g µν respectively. K is the Ricci scalar for the metric q µν . κ is a dimensionless coupling. A class of bi-measure theories have been considered in [16] and references therein. The interaction term above was first proposed in Ref.[7] (see note [36]). A key feature of this interaction term is that it gives rise to Fierz-Pauli mass terms[17] for the spin-2 fields. The above is not the most general mixing term that satisfies this condition. In particular, the density √ −q could be replaced by (−q) u (−g) 1/2−u for any real u. However, for this theory to give rise to a dark matter dominated era, we find that, under the assumptions described below, u = 1/2 is required.In this short note we point out the following properties of (1). First we prove that for κ = 0 the action (1) is equivalent to the Eddington-Born-Infeld (EBI) theory proposed in [18] as a theory for dark matter and dark energy. When one generalizes to the case κ = 0, it is a natural question to ask whether or not the dark matter/dark energy interpretation still holds. The answer is in the affirmative. The metric q µν can behave both as matter or as dark energy, and there exist solutions interpolating between them. We present two types of de Sitter vacua and study their stability under a certain set of perturbations. One is the well known solution in which the metrics are proportional. In the other case, which has received less attention, the de Sitter line elements of the two metrics are not proportional. These type of backgrounds were pointed out in different contexts (e.g., in [19] for the flat case, and in [20] in static coordinates). We also display wh...

The N-body dark matter (DM) simulations point that DM density profiles, e.g. the NFW halo, should be cuspy in its center, but observations disfavour this kind of DM profile. Here we consider wether the observed rotation curves close to the galactic centre can favour modified gravity models in comparison to the NFW halo, and how to quantify such difference. Two explicit modified gravity models are considered, MOND and a more recent approach called RGGR (in reference to Renormalization Group effects in General Relativity). It is also the purpose of this work to significantly extend the sample on which RGGR has been tested in comparison to other approaches.By analysing 62 galaxies from five samples, we find that: i) there is a radius, given by half the disk scale length, below which RGGR and MOND can match the data about as well or better than NFW, albeit the formers have fewer free parameters; ii) considering the complete rotation curve data, RGGR could achieve fits with better agreement than MOND, and almost as good as a NFW halo with two free parameters (NFW and RGGR have respectively two and one more free parameters than MOND).

We review the difficulties of the generalized Chaplygin gas model to fit observational data, due to the tension between background and perturbative tests. We argue that such issues may be circumvented by means of a self-interacting scalar field representation of the model. However, this proposal seems to be successful only if the self-interacting scalar field has a non-canonical form. The latter can be implemented in Rastall's theory of gravity, which is based on a modification of the usual matter conservation law. We show that, besides its application to the generalized Chaplygin gas model, other cosmological models based on Rastall's theory have many interesting and unexpected new features.PACS numbers: 04.50. Kd, 95.35.+d, 95.36.+x, 98.80.-k * Based on a talk presented by Júlio C. Fabris during the IWARA 2011 conference.