A Case for an Inhomogeneous Einstein-de Sitter Universe

We present a local-to-global cosmological framework in which cosmic acceleration emerges from structure formation in an inhomogeneous Einstein-de Sitter (iEdS) universe, without dark energy. The model exhibits a quasilinear coasting evolution toward an effective Milne state driven by growing inhomogeneities. We test the iEdS model with ${H_0=72.5\ \mathrm{km\ s^{-1}\ Mpc^{-1}}}$ and ${Ω_{\mathrm{m},0}=0.272}$ using CMB, BAO, and SN Ia data. The iEdS model fits the data comparably to $Λ$CDM and resolves the $H_0$ tension, while yielding a cosmic age ${t_0\simeq 13.67\ \mathrm{Gyr}}$ consistent with globular-cluster estimates.

💡 Research Summary

The authors propose a novel cosmological framework in which the observed accelerated expansion of the Universe arises from the growth of inhomogeneities in an Einstein‑de Sitter (EdS) background, without invoking any dark‑energy component. Their “local‑to‑global” approach rests on two principles: (i) the global scale factor a(t) obeys the Friedmann equations with a set of global parameters {θ}; (ii) the Universe can be regarded as an ensemble of finite‑volume regions, each evolving according to its own Friedmann equations with local scale factors a_i(t) and local parameters {θ_i}. The global scale factor is defined as the cubic‑volume average of the regional scale factors (Eq. 1). Crucially, they discard the third, often‑implicit assumption that all regions share identical parameters. This allows the regional curvature parameters Ω_k,i to differ, generating a non‑zero variance σ_H² in the Hubble rates across regions. Equation (3) shows that even if the average local deceleration ⟨q_i⟩ is non‑negative (no dark energy), a sufficiently large σ_H² can drive the global deceleration parameter q negative, i.e., global acceleration.

In the inhomogeneous EdS (iEdS) model, the early Universe is effectively flat (Ω_k≈0). As structures form, regions with positive curvature expand faster and dominate the volume average, causing the effective global curvature Ω_K to grow from zero toward unity while the matter density Ω_M declines. The model asymptotically approaches a Milne‑like universe (a ∝ t) where curvature dominates and the expansion coasts. By approximating the variance σ_H²/H² as a constant r², they obtain an effective Friedmann equation (Eq. 18) that contains a matter term ∝ a⁻³ and a curvature‑like term ∝ a⁻². The corresponding effective equation‑of‑state for the curvature fluid, w_K(a), is derived (Eq. 19) and yields w_K(z=0)≈−1.09, σ_H,0²/H₀²≈0.411, and a present‑day deceleration parameter q₀≈−0.69.

To test the model, the authors fit it to three high‑precision data sets: the Planck 2018 temperature power spectrum, the DESI DR2 BAO measurements, and the Pantheon+ Type Ia supernova compilation. For the CMB analysis they keep all standard ΛCDM parameters at their Planck best‑fit values, vary only H₀ (set to 72.5 km s⁻¹ Mpc⁻¹) and adjust r² to match the acoustic scale θ_MC. The resulting CMB spectrum is virtually indistinguishable from ΛCDM, with a slightly lower χ² and Anderson–Darling normality p‑values well above 0.05.

In the BAO analysis they employ dynamic nested sampling (dynesty) to fit the transverse and radial distance ratios D_M/r_d and D_H/r_d, allowing only H₀ to vary (uniform prior 63–83 km s⁻¹ Mpc⁻¹). The iEdS fit yields H₀≈72.5 km s⁻¹ Mpc⁻¹, while ΛCDM prefers H₀≈67 km s⁻¹ Mpc⁻¹. The Bayesian evidence slightly favors ΛCDM (log₁₀ B = −0.666), but both models pass normality tests. Importantly, the iEdS model eliminates the >4σ tension between CMB‑derived and BAO‑derived H₀ values that persists for ΛCDM.

For the supernova data they compute distance moduli using SALT2 parameters and the standard nuisance terms (α, β, γ, M_B). The iEdS model again yields H₀≈72.67±0.99 km s⁻¹ Mpc⁻¹, reducing the CMB‑SN tension from >4σ (in ΛCDM) to ≈2.5σ. χ² and Bayesian evidence are comparable between the two models.

Overall, the paper demonstrates that a universe with an initially flat EdS background, when allowed to develop realistic inhomogeneities, can generate an effective negative curvature that drives late‑time acceleration. This mechanism reproduces the key cosmological observables without a cosmological constant, resolves the H₀ tension, and predicts a cosmic age of ≈13.67 Gyr, consistent with globular‑cluster estimates. The authors acknowledge that a full relativistic treatment of σ_H² evolution and detailed N‑body simulations are needed to solidify the framework, but their phenomenological approach provides a compelling alternative to dark‑energy‑driven acceleration.