Observational constraints on viscous free-$γ$ fluid in $f(Q)$ gravity

TL;DR

The paper investigates late-time cosmic acceleration in a flat FLRW universe within exponential $f(Q)$ gravity, augmented by a bulk viscous fluid with a free equation-of-state parameter $\gamma$. The authors derive the background evolution, implement numerical solutions for the Hubble parameter, and constrain the model using cosmic chronometers, DESI DR2 BAO, GRBs, and Union3 supernova data via MCMC, employing statefinder and Om$(z)$ diagnostics to contrast with $\Lambda$CDM. They find that both viscous GR and viscous $f(Q)$ scenarios can reproduce accelerated expansion, with $H_0$ around $65$–$68$ km s$^{-1}$ Mpc$^{-1}$; the $f(Q)$ modification reduces the required viscosity and yields expansion histories that remain close to $\Lambda$CDM. Geometrical diagnostics show trajectories near the $\Lambda$CDM fixed point at late times and modest redshift dependence in Om$(z)$, while Union3 strengthens the constraints and mildly prefers the dynamical models over $\Lambda$CDM in some dataset combinations.

Abstract

We study the late-time cosmological dynamics of a spatially flat FLRW universe in the framework of $f(Q)$ gravity, where $Q$ denotes the nonmetricity scalar. The matter sector is modeled as a bulk viscous fluid with a free equation-of-state parameter $γ$, allowing for a generalized description of cosmic matter beyond the standard dust approximation. We derive the background evolution equations and analyze the resulting expansion history. The model parameters are constrained using a combination of observational datasets, including cosmic chronometers (CC), baryon acoustic oscillations from DESI DR2, and Type~Ia supernovae (GRBs and Union3). Using the best-fit parameters, we further employ the statefinder and $\mathrm{Om}(z)$ diagnostics to distinguish the viscous $f(Q)$ scenario from the standard $Λ$CDM model. In addition, we examine the evolution of the deceleration parameter, which exhibits a transition from an early decelerated phase to the current accelerated expansion, and analyze the effective equation of state behavior. Our results show that bulk viscosity within $f(Q)$ gravity provides a viable and observationally consistent description of late-time cosmic acceleration.

Figures (11)

• Figure 1: The $1\sigma$ and $2\sigma$ likelihood contours for the bulk viscous model, for $\gamma=1$ and free $\gamma$.
• Figure 2: The $1\sigma$ and $2\sigma$ likelihood contours for the viscous exponential $f(Q)$ model, for $\gamma=1$ and free $\gamma$.
• Figure 3: Best-fit reconstructed expansion histories for the considered models. The panels show the predictions for $H(z)/(1 + z)$ within each individual model, with best-fit parameters determined from different dataset combinations.
• Figure 4: Reconstructed distance modulus $\mu(z)$ for the viscous (upper panel) and exponential $f(Q)$ (lower panel) cosmological models. Solid curves denote the posterior mean predictions from different data combinations, with GRBs and Union3 data shown for reference.
• Figure 5: Deceleration parameter for the viscous fluid model with $\gamma=1$ and free $\gamma$, reconstructed from observational data. The $1\sigma$ and $2\sigma$ regions are obtained using posterior samples from the MCMC chains.