Cosmological evolution driven by polytropic fluids in an inhomogeneous spacetime

TL;DR

This study embeds a generalized Chaplygin gas within an inhomogeneous, anisotropic spacetime to model late-time cosmic acceleration. It derives analytic expressions for the Hubble parameter, including a clean FLRW limit for the homogeneous sector, and shows that inhomogeneities decouple from cosmological dynamics. Through SN Ia and BAO data with Bayesian analysis, it constrains the parameters to α ≈ $0.15$, $Ω_m ≈ 0.35$, and $H_0 ≈ 68.8$ km s$^{-1}$ Mpc$^{-1}$, finding that ΛCDM is slightly statistically preferred but the α-extended model remains viable. The work demonstrates that a single polytropic fluid in an inhomogeneous background can reproduce observed acceleration and offers a competitive alternative to a cosmological constant, with distinctive parameter degeneracies that merit further observational tests.

Abstract

Addressing the late-time accelerated expansion of the universe, known as the "dark energy problem", remains a central challenge in cosmology. While the cosmological constant is the standard explanation, alternative models such as quintessence, phantom fluids, and Chaplygin gas have been proposed. This work investigates the generalized Chaplygin gas (GCG) model, which is characterized by a polytropic equation of state. We explore this model within the framework of an anisotropic fluid, by means of a metric that reduces to the standard form of the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime at cosmological scales. To assess the model's viability, we derive analytical expressions for the scale factor, the Hubble parameter, and the deceleration parameter. Finally, the model is tested against observational data to constrain its parameters and evaluate its consistency.

Figures (11)

• Figure 1: Comparison of $H(z)$ with $\Lambda$CDM considering observational Hubble data. Ratio $A/B=4/3$ for upper panel and $A/B=2$ for lower panel.
• Figure 2: Comparison of $q(z)$ with $\Lambda$CDM. With ratio $A/B=4/3$ for the upper panel and $A/B=2$ for the lower one.
• Figure 3: $H(z)$ and $q(z)$ compared to the $\Lambda$CDM for different values of parameters $\alpha$ and $A$.
• Figure 4: Predicted distance modulus as function of red-shift from our model overlapped to the observed modulus for Union 2.2 supernovae. The values of the parameters for this model corresponds to $\Omega_m=0.3$, $H_0 =70\,\mathrm{km/s/Mpc}$ and $0\leq\alpha\leq1$.
• Figure 5: Traverse comoving distance predicted in a sample of models with various values of $\alpha$ along with BAO distance measurements inferred from the 12th release of SDSS reported in BOSS:2016wmc