How Dark is Dark Energy? A Lightcones Comparison Approach

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 $\hat{z}$, this functional generates a geometry--structure--growth contribution ${\Omega }_{\Lambda }(\hat{z})$ to the FLRW cosmological constant ${\hat{\Omega }}_{\Lambda }$. This redshift--dependent contribution erodes the interpretation of ${\hat{\Omega }}_{\Lambda }$ as representing constant dark energy. In particular, ${\Omega }_{\Lambda }(\hat{z})$ becomes significantly large at very low $\hat{z}$, where structures dominate the cosmological landscape. At the pivotal galaxy cluster scale, where cosmological expansion decouples from the local gravitation dynamics, we get ${\Omega }_{\Lambda }(\hat{z})/{\hat{\Omega }}_{\Lambda }=\mathcal{O}(1)$, 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 ${\Omega }_{\Lambda }(\hat{z})$ 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.

109 pages

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