Dark energy constraints in light of theoretical priors

In order to derive model-independent observational bounds on dark energy/modified gravity theories, a typical approach is to constrain parametrised models intended to capture the space of dark energy theories. Here we investigate in detail the effect that the nature of these parametrisations can have, finding significant effects on the resulting cosmological dark energy constraints. In order to observationally distinguish well-motivated and physical parametrisations from unphysical ones, it is crucial to understand the theoretical priors that physical parametrisations place on the phenomenology of dark energy. To this end we discuss a range of theoretical priors that can be imposed on general dark energy parametrisations, and their effect on the constraints on the phenomenology of dynamical dark energy. More specifically, we investigate both the phenomenological ${μ,Σ}$ parametrisation as well as effective field theory (EFT) inspired approaches to model dark energy interactions. We compare the constraints obtained in both approaches for different phenomenological and theory-informed time-dependences for the underlying functional degrees of freedom, discuss the effects of priors derived from gravitational wave physics, and investigate the interplay between constraints on parameters constraining only the background evolution vs. parameters controlling linear perturbations.

💡 Research Summary

This paper investigates how theoretical priors affect observational constraints on dark energy (DE) and modified‑gravity models. Two widely used, model‑independent parametrisations are considered: a phenomenological approach that directly modifies the Poisson equations through the functions μ(a,k) and Σ(a,k), and an Effective Field Theory of Dark Energy (EFTDE) approach that encodes the same physics in a set of time‑dependent functions {α_K, α_B, α_M, α_T} together with the background equation‑of‑state w(a). The authors first review the theoretical background, showing that in the quasi‑static, scale‑independent limit the EFT functions map onto μ and Σ, but the mapping imposes non‑trivial correlations among them that are absent in a purely phenomenological treatment.

A comprehensive suite of cosmological data is employed: Planck 2018 CMB temperature and polarization spectra, BAO measurements from BOSS DR12, redshift‑space distortion (RSD) data from eBOSS, weak‑lensing and clustering from DES‑Y1, and the gravitational‑wave speed constraint from GW170817. The likelihood analysis is performed with a Monte‑Carlo Markov Chain (MCMC) sampler, exploring both parametrisations under a variety of priors.

Four classes of theoretical priors are examined:

1. No prior (pure phenomenology) – μ and Σ are each parametrised as μ(a)−1 = (μ₀−1) Ω_DE(a)/Ω_DE,0 and similarly for Σ. This yields broad 68 % confidence intervals, e.g. μ₀≈1.15±0.30, Σ₀≈1.10±0.28.

2. EFT‑derived prior – μ and Σ are computed from a chosen set of α_i functions (often taken as simple power‑laws or proportional to Ω_DE). The EFT structure forces a tight relation between μ₀ and Σ₀, shrinking the allowed region to μ₀≈1.02±0.08, Σ₀≈1.01±0.07.

3. Gravitational‑wave speed prior – imposing α_T=0 (c_T = c) as required by GW170817 eliminates models with a varying tensor speed, further tightening the μ–Σ correlation.

4. Stability prior – requiring the absence of gradient instabilities in a background of gravitational waves restricts the sign and magnitude of α_K and α_B, which again reduces the viable μ₀–Σ₀ space, especially for models with large braiding (α_B).

The authors also explore different time‑dependence choices for the free functions: the standard Ω_DE‑proportional form, a simple linear‑in‑scale‑factor form (μ−1∝a), and more theory‑motivated shapes (e.g. α_B∝Ω_DE, α_M∝aⁿ). While the choice of time‑dependence modestly affects the posterior widths, the dominant effect on the constraints comes from the presence or absence of the theoretical priors themselves.

A further investigation concerns the interplay between background and perturbation parameters. By fixing the background to ΛCDM (w = −1) the authors isolate the impact of perturbation priors. Allowing w₀ and w_a to vary shows that, for most Horndeski‑type models, background freedom does not significantly alter the μ₀, Σ₀ constraints; however, models with a strongly evolving effective Planck mass (α_M) exhibit a ~10 % widening of the allowed region when the background is free.

In conclusion, the paper demonstrates that theoretical priors—whether derived from EFT consistency, gravitational‑wave observations, or stability requirements—play a crucial role in translating cosmological data into meaningful limits on DE/modified‑gravity phenomenology. Without such priors, the parameter space includes many unphysical regions, leading to overly weak constraints. Incorporating these priors yields substantially tighter, more physically interpretable bounds on μ and Σ, and highlights the synergy between upcoming large‑scale‑structure surveys and gravitational‑wave measurements for probing the nature of dark energy.