# Pairwise velocities in the "Running FLRW" cosmological model

## TL;DR

This paper analyzes pairwise velocity statistics in the novel R-FLRW cosmological model, which extends ΛCDM with a dynamic vacuum energy and gravitational coupling, comparing results with other dark energy models.

## Contribution

First study of velocities in R-FLRW cosmology, highlighting degeneracies with σ8 and potential for observational tests of dark energy models.

## Key findings

- Strong degeneracy between pairwise velocity and σ8 at z=0
- Degeneracy persists back to z=2
- Some coupled dark energy models show minimal degeneracy

## Abstract

We present an analysis of the pairwise velocity statistics from a suite of cosmological N-body simulations describing the "Running Friedmann-Lema\^itre-Robertson-Walker" (R-FLRW) cosmological model. This model is based on quantum field theory in a curved space-time and extends {\Lambda}CDM with a time-evolving vacuum energy density. To enforce local conservation of matter a time-evolving gravitational coupling is also included. Our results constitute the first study of velocities in the R-FLRW cosmology, and we also compare with other dark energy simulations suites, repeating the same analysis. We find a strong degeneracy between the pairwise velocity and {\sigma}_8 at z=0 for almost all scenarios considered, which remains even when we look back to epochs as early as z=2. We also investigate various Coupled Dark Energy models, some of which show minimal degeneracy, and reveal interesting deviations from {\Lambda}CDM which could be readily exploited by future cosmological observations to test and further constrain our understanding of dark energy.