Evidence for increasing dark energy in the Late Universe

TL;DR

The paper investigates whether dynamical dark energy exhibits an increasing trend in the late Universe and whether linearization biases in $w(a)$ analyses can spuriously produce thawing behavior. It introduces and exploits a symmetry in $w(a)$CDM, $dw(a) ∝ dc_M$, and contrasts two linearization schemes—late and early—applied to $H(z)$ data with BAO constraint $c_M$. Using Monte Carlo analyses of Local Distance Ladder data and mock datasets, it shows that late linearization yields $w_0<-1$, $w_a>0$ (increasing DE) consistent with LDL, while early linearization yields $-1<w_0<0$, $w_a<0$ (thawing) in tension with LDL by several sigma. The results suggest DESI's reported thawing could be a methodological artifact of symmetry violation in CPL-like linearization, with Euclid providing an independent test.

Abstract

Context. A comprehensive survey of Baryon Acoustic Oscillation (BAO) in the Large Scale Structure (LSS), in stratified data covering a finite redshift range is provided by the Dark Energy Spectroscopic Instrument (DESI). Extracting cosmological parameters in a joint analysis of LSS-CMB data is hereby inherently a nonlinear problem. Aims. In particular, this nonlinearity may concern the unknown equation of state of dark energy w(a), defined in the general w(a)CDM framework. Nevertheless, a common approach is the linearized approximation hereto notably w0waCDM, also applied by DESI. Here, we consider a potential source of a systematic uncertainty in this linearization due to non-commutativity between w0waCDM and a posteriori linearization of w(a)CDM, identified with an intrinsic symmetry in the latter, which is violated in the former. We shall refer to these as early and late linearization, respectively. Methods. Observational consequences of symmetry violation is inherent to early linearization regardless of choice of data, here elucidated in the analysis of the Hubble expansion in the Local Distance Ladder (LDL) using cosmic chronometer data. Results. Strikingly, opposite results are found for the evolution of dark energy by early versus late linearization, indicating a thawing or respectively, increasing dark energy. This is further confirmed by mock data experiments. Accordingly, it is unlikely that the DESI pipeline is immune to the same contradiction. Conclusions. Our results show rather than thawing, claimed by DESI, dark energy may in fact be increasing upon preserving the underlying symmetry. Further confirmation is expected from Euclid.

Figures (6)

• Figure 1: Posterior plot for $w_0$ and $w_a$ in the $w_0w_a$-plane in two distinct late and early (§ \ref{['Sec:Data1']} and \ref{['Sec:Data2']}) implementations of \ref{['EQN_w0wa']}, respectively in green and red islands. This result strikingly shows a switch in quadrant from IV to II in fallback to the fully nonlinear expression \ref{['EQN_wcdm']} equivalent to the change in the slope and $y$-intercept of the linear approximations in Fig. \ref{['fig:TwoLines']}. According to \ref{['EQN_dw']}, this is due to the violation of an underlying symmetry in red and non-commutativity between linearization and fit.
• Figure 2: ( Upper panel.) Flowchart of the late (I) and early (II) implementation of linearization $l$ according to \ref{['EQN_w0wa']} in the $w(a)$CDM formalism, starting from the Farooq data of the LDL, and the Planck-BAO constraint supplemented with the control parameter $\Omega_{m,0}$ (§ \ref{['Sec:Data']}). As shown in § \ref{['Sec:results']}, the results of these two implementations appear in different quadrants of $w_0w_a$-plane. ( Lower panel.) Schematic of the implementations of early and late linearization in estimating $w_0$ and $w_a$where $M$ refers to \ref{['EQN_wcdm']}: early linearization minimizes $\chi^2$ in $H(z)$-space according to the scatter $\delta_E$, while late linearization minimizes $\chi^2$ in $w(z)$-space according to the scatter $\delta_L$ following the nonlinear map \ref{['EQN_wcdm']}. The question is to what extent the output of these two implementations agree ceteris paribus, including their sensitivities to $\Omega_{m,0}$.
• Figure 3: ( Upper panels.) PDFs of $w_0$ and $w_a$ derived from our MC in late linearization (§ \ref{['Sec:Data1']}) which are invariant under the choice of $\Omega_{m,0}$ satisfying the constraint \ref{['EQN_anchor']}(§ \ref{['Sec:model']}). ( Lower panels.) PDFs of $w_0$ and $w_a$ derived from our MC in early linearization (§ \ref{['Sec:Data2']}) which is not invariant under the choice of $\Omega_{m,0}$ satisfying the constraint \ref{['EQN_anchor']}. In these examples, $\Omega_{m,0}=0.265$ is associated with $H_0=73.3$ km s$^{-1}$ Mpc$^{-1}$ by \ref{['EQN_anchor']}. The peak of the skewed Gaussian fit shows the nominal values of $w_0$ and $w_a$. Paradoxically, early linearization (lower panels) gives rise to nonlinear propagation of uncertainties seen in the non-Gaussian PDFs of ($w_0,\, w_a$), more so than in late linearization (upper panels). Although the peak value may be slightly different, the discrepancy between the two implementations persist for the entire ensemble covering the whole range $\Omega_{m,0} \in [0.22,0.36]$.
• Figure 4: The evolution of $w(a)$ in \ref{['EQN_wcdm']} and its linearization \ref{['EQN_w0wa']} in late and early implementations following Fig. \ref{['fig:implementation']}. The green shaded region shows $w(z_i)$ following the application of the map\ref{['EQN_wcdm']} on Farooq data including an MC process. The blue dotted line is the result from late linearization \ref{['EQN_w0wa']} on $w(z_i)$ (§ \ref{['Sec:Data1']}), clearly showing a negative slope indicative for $w_a>0$. The red dotted line, on the other hand, is the result of early linearization by application of \ref{['EQN_HL']}on the Farooq data showing a positive slope. The distinct slopes of the two demonstrate that the implementation of the linearization \ref{['EQN_w0wa']} is non-commutative with the fitting process, answering the question raised in Fig. \ref{['fig:implementation']}.
• Figure 5: Results of early and late linearization in estimating $w_0$ and $w_a$. ( Four upper panels). $w_0w_a$-estimate on $\Lambda$CDM mock data created using the injection $\Omega_{{m,0}_i}=0.27$, carrying $w_0=-1$ and $w_a=0$. This figure is a snapshot of the results when the control parameter is $\Omega_{m,0}=0.35$. While green (late linearization) gives consistent results with the underlying data regardless of $\Omega_{m,0}$, as per (5), red (early linearization), in contrast, exhibits parasitic sensitivity to the control parameter $\Omega_{m,0}$ (see also \ref{['EQN_sensitivity']}), and is consistent with green only when $\Omega_{m,0} = \Omega_{{m,0}_{i}}$. ( Four lower pannels). The same using data produced by CPL where $w_0=-1.5$ and $w_a=2$. Clearly green gives results consistent with initial injections for $w_0$ and $w_a$, but it is absent for red.