Lowering the Horizon on Dark Energy: A Late-Time Response to Early Solutions for the Hubble Tension

Abstract

We present a model-independent null test of the late-time cosmological response to a reduced sound horizon, as typically required by early-universe solutions to the Hubble tension. In this approach, we phenomenologically impose a shorter sound horizon without modeling early-universe physics to isolate its impact on late-time dark energy inference. Using baryon acoustic oscillations (BAO), supernovae (SN), big bang nucleosynthesis (BBN), and local $H_0$ data, while explicitly avoiding CMB anisotropies, we examine how this calibration shift propagates into constraints on the dark energy equation of state. We find that lowering $r_d$ systematically drives the $w_0$-$w_a$ posterior toward less dynamical, quintessence-like behavior, bringing it closer to $Λ$CDM. This result underscores that some of the apparent evidence for evolving or phantom-like dark energy may reflect early-universe assumptions rather than genuine late-time dynamics. More broadly, our analysis highlights the importance of carefully disentangling calibration effects from physical evolution in interpreting forthcoming results from DESI and future surveys.

Figures (3)

• Figure 1: Posterior distributions of cosmological parameters with (right panel) and without (left panel) the $r_d$ prior. Each triangle plot shows the 68% and 95% confidence regions for key parameters using the baseline combinations of BAO, BBN, and SN data. Shaded bands indicate the SH0ES Riess:2021jrx confidence regions for $H_0$, and black dashed lines guide the eye to $w_0 = -1$ and $w_a = 0$. The inclusion of a reduced sound horizon prior shifts $H_0$ to higher values and induces correlated changes in the CPL parameters ($w_0$, $w_a$), reflecting the late-time response required to maintain consistency with BAO and SN observations.
• Figure 2: Evolution of the best-fit values of $H_0$, $w_0$, and $w_a$ as functions of the imposed sound horizon $r_d$, normalized to the Planck 2018 best-fit value. The results are shown for the BAO+BBN+SN+rs dataset combination. The shaded regions indicate the phantom regime ($w\le-1$), while the red dashed line marks the crossing of the phantom divide.
• Figure 3: Comparison of DE EoS constraints obtained with the CPL parameterization and a binning reconstruction approach DESI:2025fii, using BAO+BBN+SN+rs data. The solid red curve indicates the best-fit $w(z)$ derived from $w_0$ and $w_a$, with shaded regions denoting the $1\sigma$ and $2\sigma$ uncertainties. Results from the binning reconstruction are shown in blue: the horizontal bars correspond to the fixed bin size and the vertical bars correspond to $1\sigma$ uncertainties. Gray contours represent the 1D posterior for the binned parameters. The green dashed curve and band show the CPL fit using the DESI DR2 dataset (BAO+CMB+DESY5) DESI:2025zgx, reproduced for comparison. The horizontal gray dashed line denotes the $\Lambda$CDM expectation.