A Case for an Inhomogeneous Einstein-de Sitter Universe

TL;DR

The paper investigates whether cosmic acceleration can be explained without dark energy by introducing an inhomogeneous Einstein–de Sitter (iEdS) universe, where local structure formation induces an effective curvature that drives global acceleration. It develops a local-to-global framework in which the global expansion is a volume-average of locally Friedmann regions, allowing acceleration even when local deceleration parameters are nonnegative, and it expresses this with an emergent component having a time-dependent equation of state $w_x(a)$. Two realizations, iEdS(1) and iEdS(2), are fitted to Planck 2018 CMB, DESI DR2 BAO, and Pantheon+ SN Ia data, yielding competitive fits to CMB and SN data and offering partial to full relief of the $H_0$ tension (with varying Bayesian support across datasets). The study finds $t_0 \approx 13.6$ Gyr for both iEdS variants and $S_8$ values compatible with Planck LCDM, suggesting that dark energy may be unnecessary if a realistic structure-formation model under the iEdS framework is developed. Overall, the results motivate further simulations and observations to test whether inhomogeneity-driven curvature can reproduce precision cosmology without invoking a cosmological constant.

Abstract

In our local-to-global cosmological framework, cosmic acceleration arises from local dynamics in an inhomogeneous Einstein-de Sitter (iEdS) universe without invoking dark energy. An iEdS universe follows a quasilinear coasting evolution from an Einstein-de Sitter to a Milne state, as an effective negative curvature emerges from growing inhomogeneities without breaking spatial flatness. Acceleration can arise from structure formation amplifying this effect. We test two realizations, iEdS(1) and iEdS(2), with $H_0=\{70.24,74.00\}\ \mathrm{km\ s^{-1}\ Mpc^{-1}}$ and $Ω_{\mathrm{m},0}=\{0.290,0.261\}$, against CMB, BAO, and SN Ia data. iEdS(1) fits better than $Λ$CDM and alleviates the $H_0$ tension, whereas iEdS(2) fully resolves it while remaining broadly consistent with the data. Both models yield ${t_0\simeq13.64\ \mathrm{Gyr}}$, consistent with globular-cluster estimates.

Figures (6)

• Figure 1: Planck 2018 CMB temperature power spectrum compared with best-fit iEdS and $\Lambda$CDM predictions, both calibrated to $\Omega_{\mathrm{m},0}H_0^2=1431.354\ \mathrm{km^2\ s^{-2}\ Mpc^{-2}}$ and matched in $\theta_\mathrm{MC}$. Only the iEdS(1) spectrum and residuals are shown, as they are visually indistinguishable from iEdS(2); both models fit the data comparably to $\Lambda$CDM (see Table \ref{['tab:table1']}), with minor deviations between the model spectra at the lowest multipoles.
• Figure 2: Posterior distributions of $H_0$ from DESI DR2 BAO fits for the two iEdS and the flat $\Lambda$CDM models. $H_0$ is in $\mathrm{km\ s^{-1}\ Mpc^{-1}}$. Green dashed lines show the best-fit (posterior median) $H_0$ values with 16th–84th percentile errors listed above each plot, and red vertical lines (where visible) mark the reference $H_0^\mathrm{CMB}$ values (Table \ref{['tab:table1']}).
• Figure 3: $\dot{a}(z)\equiv H(z)/(1+z)$ from DESI DR2 $D_\mathrm{H}=c/H(z)$ measurements and from the three models fitted to DESI DR2 BAO data. The iEdS curves include 16th–84th percentile contours, while only the best-fit $\Lambda$CDM curve is shown. The LRG1 point at $z=0.51$, excluded from the fits, is shown for visualization only. The transition from decelerated to accelerated expansion occurs at $z_\mathrm{t}=0.85$, $z_\mathrm{t}=0.844$, and $z_\mathrm{t}=0.672$ for the iEdS(1), iEdS(2), and flat $\Lambda$CDM models, respectively.
• Figure 4: $H_0$ posterior distributions from Pantheon+ SNe Ia fits for the two iEdS and flat $\Lambda$CDM models. Blue dashed lines show the posterior medians with 16th–84th percentile errors (given above each plot), and red lines (where visible) mark the reference $H_0^\mathrm{CMB}$ values (Table \ref{['tab:table1']}). All $H_0$ values are in $\mathrm{km\ s^{-1}\ Mpc^{-1}}$. $H_0$ was fitted jointly with the nuisance parameters $\alpha$, $\beta$, $\gamma$, and $M_B$; the corresponding posterior distributions are available in our code repository Zenodo_repo.
• Figure 5: Distance moduli for $1701$ Pantheon+ SN Ia observations (shown at $z=z_\mathrm{HD}$) and for the best-fit iEdS(1) model (see Table \ref{['tab:table2']}). The lower panel shows the residuals relative to the model $\mu(z)$ curve.