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Structural Limitations on Constraining the Time Evolution of Dark Energy

Seokcheon Lee

TL;DR

The paper addresses why distance-based cosmological probes struggle to constrain the time evolution of the dark energy equation of state $\omega(z)$. It develops a linear-response framework demonstrating that mapping $\omega(z)$ to distance observables involves a double integration, yielding a broad, low-pass kernel in redshift that suppresses high-frequency features independent of parametrization. A toy Fisher analysis reveals a steep eigenvalue hierarchy, showing only the first ~1–3 Fisher modes are constrained, highlighting a fundamental, kernel-imposed limit rather than a statistical artifact. The results imply that to access rapid or localized time variation in $\omega(z)$ one must rely on observables with different kernels, such as direct expansion-rate or growth probes, or perform joint analyses to mitigate the non-locality in redshift.

Abstract

Cosmological constraints on a time-varying dark energy equation of state are often interpreted as evidence for a dynamical dark energy. In this Letter, we show that such interpretations are fundamentally limited by the integral structure through which the equation of state enters cosmological observables. The mapping from ω(z) to distances involves successive integrations, which act as an intrinsic low-pass filter in redshift space. As a result, only a small number of slowly varying modes of ω(z) are observationally accessible, while rapid or localized temporal variations are irretrievably suppressed. This limitation is independent of any specific parametrization and represents a structural property of Friedmann--Lemaitre--Robertson--Walker cosmology with distance-based probes.

Structural Limitations on Constraining the Time Evolution of Dark Energy

TL;DR

The paper addresses why distance-based cosmological probes struggle to constrain the time evolution of the dark energy equation of state . It develops a linear-response framework demonstrating that mapping to distance observables involves a double integration, yielding a broad, low-pass kernel in redshift that suppresses high-frequency features independent of parametrization. A toy Fisher analysis reveals a steep eigenvalue hierarchy, showing only the first ~1–3 Fisher modes are constrained, highlighting a fundamental, kernel-imposed limit rather than a statistical artifact. The results imply that to access rapid or localized time variation in one must rely on observables with different kernels, such as direct expansion-rate or growth probes, or perform joint analyses to mitigate the non-locality in redshift.

Abstract

Cosmological constraints on a time-varying dark energy equation of state are often interpreted as evidence for a dynamical dark energy. In this Letter, we show that such interpretations are fundamentally limited by the integral structure through which the equation of state enters cosmological observables. The mapping from ω(z) to distances involves successive integrations, which act as an intrinsic low-pass filter in redshift space. As a result, only a small number of slowly varying modes of ω(z) are observationally accessible, while rapid or localized temporal variations are irretrievably suppressed. This limitation is independent of any specific parametrization and represents a structural property of Friedmann--Lemaitre--Robertson--Walker cosmology with distance-based probes.

Paper Structure

This paper contains 5 sections, 13 equations, 2 figures.

Table of Contents

  1. Introduction.
  2. Linearized response of cosmological observables.
  3. Low-pass filtering and effective modes.
  4. Role of direct expansion-rate probes.
  5. Implications and conclusions.

Figures (2)

  • Figure 1: Conceptual schematic of intrinsic low-pass filtering. Successive integrations map $\omega(z)$ onto a broad kernel, suppressing localized or high-frequency features. In a principal-component description, only the first few smooth eigenmodes are well constrained.
  • Figure 2: Quantitative illustration of kernel-induced information loss using a toy Fisher analysis. The Fisher eigenvalues for the mode amplitudes $c_k$ decrease rapidly with mode index, indicating that only the first few smooth combinations of $\omega(z)$ significantly affect distance observables.