Dynamical Dark Energy or Simply Cosmic Curvature?

TL;DR

This study shows that the common flatness assumption can severely bias the inferred dynamics of dark energy, especially for $z>0.9$, because the curvature term $\Omega_k (1+z)^2$ and curved geodesics mimic evolving $w(z)$. By reconstructing $w(z)$ from both $H(z)$ and $d_L(z)$, the authors demonstrate opposite systematic trends depending on the observable and highlight that ignoring $\Omega_k$ leads to phantom-like or divergent behavior. They derive explicit flat-universe reconstructions that fail to reproduce the curved background unless $\Omega_k$ is accounted for, and they propose a curvature estimator from joint $H(z)$ and $d_L(z)$. The work argues for including $\Omega_k$ as a fitted parameter and emphasizes that achieving precise $w(z)$ measurements at moderate/high redshift requires tight curvature constraints, with implications for planning future BAO and weak-lensing surveys.

Abstract

We show that the assumption of a flat universe induces critically large errors in reconstructing the dark energy equation of state at z>~0.9 even if the true cosmic curvature is very small, O(1%) or less. The spuriously reconstructed w(z) shows a range of unusual behaviour, including crossing of the phantom divide and mimicking of standard tracking quintessence models. For 1% curvature and LCDM, the error in w grows rapidly above z~0.9 reaching (50%,100%) by redshifts of (2.5,2.9) respectively, due to the long cosmological lever arm. Interestingly, the w(z) reconstructed from distance data and Hubble rate measurements have opposite trends due to the asymmetric influence of the curved geodesics. These results show that including curvature as a free parameter is imperative in any future analyses attempting to pin down the dynamics of dark energy, especially at moderate or high redshifts.

Figures (2)

• Figure 1: Reconstructing the dark energy equation of state assuming zero curvature when the true curvature is 2% in a closed $\Lambda$CDM universe. The $w(z)$ reconstructed from $H(z)$ is phantom ($w < -1$) and rapidly acquires an error of order 50% and more at redshift $z\gtrsim2$, and diverges at finite redshift. The reconstructed $w(z)$ from $d_L(z)$ for $\Omega_k<0$ is phantom until $z\approx0.86$, where it crosses the true value of $-1$ and then crosses 0 at high redshift, where the bending of geodesics takes over from dynamical behavior, producing errors in opposite direction to the DE reconstructed from $H(z)$. In order to make up for the missing curvature, the reconstructed DE is behaving like a scalar field with a tracking behavior. These effects arise even if the curvature is extremely small $<0.1\%$.
• Figure 2: The accuracy with which we must know $\Omega_k$ in order to measure $w(z)$ to within a given error.