Evolving and interacting dark energy: photometric and spectroscopic synergy with DES Y3 and DESI DR2

Technical Summary: Evolving and Interacting Dark Energy: Photometric and Spectroscopic Synergy with DES Y3 and DESI DR2

Problem Statement
The current concordance cosmological model, $\Lambda$CDM, faces emerging tensions, including indications of time-evolving dark energy from DESI measurements and the $S_8$ discrepancy between late-time Large-Scale Structure (LSS) observations and early-time Cosmic Microwave Background (CMB) predictions. Interacting Dark Energy (IDE) models, specifically those involving pure momentum exchange (Type III models) between dark matter and dark energy, offer a theoretical extension to address these issues. The "Dark Scattering" (DS) model is a prominent candidate where dark energy and cold dark matter exchange momentum via elastic scattering, suppressing structure growth without altering the background expansion history. However, constraints on DS have been weak, particularly when combined with evolving dark energy equations of state. This study investigates an extended DS scenario where the dark energy equation of state evolves according to the Chevallier–Polarski–Linder (CPL) parametrisation, aiming to constrain the interaction strength and dark energy dynamics using a synergy of photometric and spectroscopic data.

Methodology
The authors perform a joint analysis combining three datasets:

1. DES Y3: Three two-point correlation functions (3$\times$2pt) including cosmic shear, galaxy clustering, and galaxy–galaxy lensing.
2. DESI DR2: Baryon Acoustic Oscillation (BAO) measurements.
3. Additional Probes: Type Ia supernovae from DES Year 5 (Y5) and CMB data from Planck 2018.

To model the nonlinear structure formation in the DS+CPL framework, the authors employ the halo model reaction formalism. This approach calculates the nonlinear matter power spectrum $P_{NL}$ as a product of a standard $\Lambda$CDM nonlinear spectrum and a "boost" function $B(k,a)$, which accounts for the interaction effects.

• Emulation: A neural network emulator for the boost function $B(k,a)$ was constructed using the Cosmopower platform. The emulator was trained on $1.4 \times 10^6$ spectra generated by the ReACT code, covering wavenumbers $k \in [10^{-2}, 5] h/\text{Mpc}$ and redshifts $z \in [0, 2.5]$. The emulator achieves $\sim 1\%$ accuracy in the relevant regime.
• Parameterisation: The model introduces the CPL parameters $\{w_0, w_a\}$ and the interaction strength. While previous works used a parameter $\xi$ (cross-section per mass), this study utilizes the parameter $A_{ds} \equiv (1+w)\xi$ to define the interaction at a pivot redshift ($z_{piv} \approx 0.4$), alongside the value at $z=0$.
• Analysis: The analysis utilizes the CosmoSIS pipeline. Chains without CMB data use Polychord, while those including CMB use Nautilus for improved convergence. Priors are defined in Table 1, including flat priors on cosmological parameters and specific constraints on the interaction parameter.

Key Contributions

1. First Combined Constraints: This work provides the most stringent pre-Euclid constraints on the Dark Scattering model by combining photometric (DES) and spectroscopic (DESI) data with CMB and Supernovae.
2. Nonlinear Modeling: The study extends the application of the halo model reaction formalism to a DS model with a time-evolving equation of state (CPL), utilizing a custom neural network emulator to efficiently compute nonlinear power spectra.
3. Synergy Analysis: The paper explicitly quantifies the added value of photometric data (DES Y3) in constraining interacting dark energy models compared to spectroscopic data (DESI) and CMB alone.

Results

• Interaction Constraints: For all data combinations, the interaction parameter $A_{ds}$ is consistent with zero within $1\sigma$. The only exception is the DESI+SN+CMB combination, which shows a $\sim 2\sigma$ preference for non-zero interaction; however, the authors attribute this to projection effects and the fact that background probes (SN, BAO) and CMB alone are weakly constraining on the interaction term.
• Model Preference: The CPL model (non-interacting, evolving dark energy) is statistically preferred over the DS model. The Bayes factor analysis indicates "moderate" to "strong" evidence for CPL over DS when DES photometric data is included.
• Parameter Constraints (Full Combination):
  • CPL: $w_0 = -0.76 \pm 0.06$, $w_a = -0.77^{+0.23}_{-0.20}$.
  • DS: $w_0 = -0.79^{+0.05}_{-0.06}$, $w_a = -0.56^{+0.24}_{-0.15}$, $A_{ds} = 9.8^{+2.8}_{-9.5} \text{ bn/GeV}$.
• Impact of Photometric Data: Including DES Y3 data improves the Figure-of-Merit (FoM) on the $(w_0, w_a)$ plane by $\sim 12\%$ for CPL and $\sim 25\%$ for DS relative to DESI+SN+CMB alone. The larger improvement for DS highlights the necessity of structure growth data (like weak lensing) to constrain the interaction amplitude.
• $S_8$ Tension: The study finds no evidence for an $S_8$ discrepancy between low-redshift measurements and high-redshift CMB extrapolations in either the CPL or DS models. In the DS model, the CMB-derived $S_8$ constraints are significantly broadened due to degeneracies with dark energy parameters, rendering them consistent with low-redshift measurements.

Significance
The paper claims that these results represent the most rigorous pre-Euclid constraints on Dark Scattering derived from a combined photometric and spectroscopic analysis. The findings suggest that while the DS model is theoretically viable, current data does not support a detection of dark sector interactions. The study emphasizes that structure formation data is critical for breaking degeneracies in interacting models; without the photometric constraints from DES, the preference for CPL over DS is negligible. The authors conclude that the observed trends (preference for CPL and lack of $S_8$ tension) are robust, though they note that future recalibrations of supernova data or new surveys (Euclid, Rubin) may refine these constraints further.