How Dark is Dark Energy? A Lightcones Comparison Approach

We present a geometrical approach that provides a non-perturbative technique, allowing the standard FLRW observer to evaluate a measurable, scale-dependent distance functional between her idealized FLRW past light cone and the actual physical past light cone. From the point of view of the FLRW observer, gathering data from sources at cosmological redshift $\widehat{z}$, this functional generates a geometry–structure–growth contribution ${Ω_Λ(\widehat{z})}$ to the FLRW cosmological constant ${\widehatΩ_Λ}$. This redshift–dependent contribution erodes the interpretation of ${\widehatΩ_Λ}$ as representing constant dark energy. In particular, ${Ω_Λ(\widehat{z})}$ becomes significantly large at very low $\widehat{z}$, where structures dominate the cosmological landscape. At the pivotal galaxy cluster scale, where cosmological expansion decouples from the local gravitation dynamics, we get ${Ω_Λ(\widehat{z})/\widehatΩ_Λ},=,\mathscr{O}(1)$, showing that late–epoch structures provide an effective field contribution to the FLRW cosmological constant that is of the same order of magnitude as its assumed value. We prove that ${Ω_Λ(\widehat{z})}$ is generated by a scale-dependent effective field governed by structure formation and related to the comparison between the idealized FLRW past light cone and the actual physical past light cone. These results are naturally framed in the mainstream FLRW cosmology; they do not require exotic fields and provide a natural setting for analyzing the coincidence problem, leading to an interpretative shift in the current understanding of constant dark energy.

💡 Research Summary

The paper proposes a novel, non‑perturbative geometric framework to assess how late‑time cosmic structures affect the interpretation of the cosmological constant Λ in the standard FLRW (Friedmann‑Lemaître‑Robertson‑Walker) model. The authors introduce two observers: an ideal FLRW observer who lives in a perfectly homogeneous‑isotropic background, and a “physical” observer who inhabits the actual, inhomogeneous universe where galaxy clusters, filaments and voids dominate on scales below ~100 h⁻¹ Mpc. Each observer possesses a past light‑cone; the ideal observer’s light‑cone is described by the exact FLRW metric, while the physical observer’s light‑cone is embedded in a generic Lorentzian manifold (M,g).

The core of the analysis is a scale‑dependent distance functional Δ(ẑ) that measures the mean‑square deviation between the celestial sphere of the ideal light‑cone and that of the physical light‑cone at a given redshift ẑ. This functional is constructed using Lipschitz and bi‑Lipschitz mappings, and can be expressed in terms of the quadratic fluctuations of the physical angular‑diameter distance D_A^phys(ẑ,Ω) relative to the FLRW reference distance D_A^FLRW(ẑ). Mathematically,

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