We investigate the observational implications of a gravitational model wherein the gravitational constant $\textit{G}$ and the cosmological constant $$\Lambda $$ exhibit scale-dependent behavior at the perturbative level, while preserving the General Relativity (GR) field equations at the background. This model is motivated by the potential influence of large-scale (infrared) Renormalization Group (RG) corrections to gravity and is constructed upon an effective action incorporating a scale definition via Lagrange multipliers. We explore the effects of these modifications during the recombination epoch with particular focus on their impact on the structure of acoustic oscillations. Additionally, we perform a comprehensive parameter fitting analysis using data from the Cosmic Microwave background (CMB), type Ia Supernovae (SN Ia), Baryon Acoustic Oscilations (BAO) and Redshift Space Distortions (RSD). Our results indicate that the RG corrections here considered are consistent with the main predictions of the $$\Lambda $$ CDM model, and they slightly increase the uncertainties in the parameter estimations. Such small differences cannot be used to dismiss the current cosmological tensions. Although previous results indicated that this model is more flexible than $$\Lambda $$ CDM regarding RSD data, potentially alleviating tensions, this advantage becomes negligible with the current extended data set. The framework maintains its theoretical consistency and foundation; however, unless further generalized, it cannot effectively address current cosmological issues.

Brazil

Wiliam Hipólito-Ricaldi

Rodrigo Marttens

Felipe Melo-Santos

Davi Rodrigues

Scale-dependent and background-preserving gravity from an action: cosmological tests

The original version of this article used both the symbols

Nicolas Bertini

Erratum to: Cosmological framework for renormalization group extended gravity at the action level

General relativity (GR) extensions based on renormalization group (RG) flows may lead to scale-dependent couplings with nontrivial effects at large distance scales. Here we develop further the approach in which RG effects at large distance scales are fully encoded in an effective action and we apply it to cosmology. In order to evaluate the cosmological consequences, our main assumption is the use of a RG scale such that the (infrared) RG effects only appear at perturbative order (not at the background level). The emphasis here is on analytical results and qualitative understanding of the implied cosmology. We employ commonly used parametrizations for describing modified gravity in cosmology (as the slip parameter). From them, we describe the dynamics of the first order perturbations and estimate bounds on the single dimensionless parameter ($$\nu $$ <math><mi>ν</mi></math> ) introduced by this framework. Possible impacts on dark matter and dark energy are discussed. It is also shown here that the $$\nu $$ <math><mi>ν</mi></math>  parameter effects to $$f\sigma _8$$ <math><mrow><mi>f</mi><msub><mi>σ</mi><mn>8</mn></msub></mrow></math>  are stronger at low redshifts ($$z&lt;1.5$$ <math><mrow><mi>z</mi><mo>&lt;</mo><mn>1.5</mn></mrow></math> ), while different values for $$\nu $$ <math><mi>ν</mi></math>  do not appreciably change $$f\sigma _8$$ <math><mrow><mi>f</mi><msub><mi>σ</mi><mn>8</mn></msub></mrow></math>  at higher redshifts, thus opening a window to alleviate an issue that is currently faced by $$\Lambda $$ <math><mi>Λ</mi></math> CDM.