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How Dark is Dark Energy? A Lightcones Comparison Approach

Mauro Carfora, Francesca Familiari

TL;DR

This paper develops a non-perturbative geometrical framework that compares the actual past light cone with the FLRW past light cone to extract a scale-dependent contribution to the cosmological constant, $\Omega_\Lambda(\widehat{z})$. By modeling celestial spheres, null geodesic propagation, and area-distance fluctuations on a bi-Lipschitz sky, the authors derive a curvature–driven correction to $\widehat{\Lambda}^{(FLRW)}$, with the effect peaking near the cluster boundary where structure decouples from cosmic expansion. They show that late-time inhomogeneities can produce a finite-infinity–scale effective field of the same order as the nominal cosmological constant, linking geometry and growth to dark energy and offering a natural lens to address the coincidence problem. The framework yields a redshift-dependent splitting of the FLRW cosmological constant into a physical part and a structure-induced part, compatible with current constraints and potentially aligned with observational hints of evolving dark energy (e.g., DESI). These results motivate quantitative comparisons with data and extensions to a broader range of structures, potentially reshaping interpretations of dark energy within standard cosmology.

Abstract

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.

How Dark is Dark Energy? A Lightcones Comparison Approach

TL;DR

This paper develops a non-perturbative geometrical framework that compares the actual past light cone with the FLRW past light cone to extract a scale-dependent contribution to the cosmological constant, . By modeling celestial spheres, null geodesic propagation, and area-distance fluctuations on a bi-Lipschitz sky, the authors derive a curvature–driven correction to , with the effect peaking near the cluster boundary where structure decouples from cosmic expansion. They show that late-time inhomogeneities can produce a finite-infinity–scale effective field of the same order as the nominal cosmological constant, linking geometry and growth to dark energy and offering a natural lens to address the coincidence problem. The framework yields a redshift-dependent splitting of the FLRW cosmological constant into a physical part and a structure-induced part, compatible with current constraints and potentially aligned with observational hints of evolving dark energy (e.g., DESI). These results motivate quantitative comparisons with data and extensions to a broader range of structures, potentially reshaping interpretations of dark energy within standard cosmology.

Abstract

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 , this functional generates a geometry--structure--growth contribution to the FLRW cosmological constant . This redshift--dependent contribution erodes the interpretation of as representing constant dark energy. In particular, becomes significantly large at very low , where structures dominate the cosmological landscape. At the pivotal galaxy cluster scale, where cosmological expansion decouples from the local gravitation dynamics, we get , 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 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.

Paper Structure

This paper contains 27 sections, 21 theorems, 371 equations.

Table of Contents

  1. Introduction
  2. Motivation and a new best fit FLRW strategy
  3. A tale of two observers
  4. Celestial spheres and celestial cartography
  5. The Method: Comparing celestial spheres
  6. The coupling with spacetime scalar curvature
  7. Memories of late epoch inhomogeneities
  8. Structures and the FLRW cosmological constant
  9. An example: Galaxy Clusters
  10. Discussion
  11. A Geometrical Analysis Appendix
  12. The standard FLRW model in a nutshell
  13. The physical spacetime and its FLRW avatar
  14. The directional Celestial Spheres
  15. The reference cosmological redshift
  16. ...and 12 more sections

Key Result

Proposition 3.1

As $n(\theta, \phi)$ varies over the celestial sphere $\mathbb{C\,S}(p)$, the corresponding set of null rays in $C^-\left(T_pM, \{E_{(i)}\} \right)$ parametrizes the null geodesic generators of the physical past lightcone The geometrical structure of $\mathscr{C}^-(p,g)$ is characterized by its terminal points, the last–points on the null geodesic generators that lie on the boundary $\partial\ma

Theorems & Definitions (56)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Remark 2.1
  • Definition 3.1
  • Proposition 3.1
  • proof
  • Definition 3.2
  • Definition 4.1
  • Remark 4.1
  • ...and 46 more