Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | [email protected]

August 10, 2025

The cosmological constant Λ, originally introduced by Einstein to allow for a static universe, is retained in modern cosmology to account for the observed acceleration of cosmic expansion, commonly attributed to “dark energy.” In the ΛCDM model, Λ manifests as a constant energy density filling space homogeneously, producing a repulsive gravitational effect at very large scales. However, this effect is inherently rooted in General Relativity’s (GR) curved spacetime framework—a purely geometric interpretation that lacks a direct force-based physical mechanism observable in laboratory or local astrophysical contexts.

The application of the cosmological constant Λ within Newtonian dynamics—as demonstrated in the paper "Dark energy and the structure of the Coma cluster of galaxies"—relies on incorporating a Λ-term adapted from General Relativity’s curved spacetime model. This reliance on the Λ-term transpired the need for a repulsive effect on gravity at large cosmic scales, yet remains inapplicable to real-world observations due to relativity’s dependence on the abstract concept of curved spacetime. Consequently, the referenced research resorted to force-based Newtonian dynamics to address the Λ-term in a physically interpretable framework.

From an observational standpoint, the repulsive effect ascribed to Λ cannot be measured directly in local systems such as planetary or stellar dynamics. For instance, the gravitational acceleration produced by Λ at solar system scales is negligibly small—many orders of magnitude weaker than the already minuscule influence of galactic tides. Furthermore, attributing cosmic acceleration to Λ presumes that the same constant applies uniformly across all scales, an assumption unsupported by empirical evidence outside of large-scale cosmological fits.

Alternative frameworks, such as Extended Classical Mechanics (ECM), instead treat such large-scale accelerations without invoking an unmeasurable constant. ECM models can describe galaxy cluster dynamics or large-scale structure formation through field–mass interactions that preserve physical measurability and avoid dependence on GR’s curvature formalism. These approaches offer a testable, force-based interpretation of phenomena that Λ in GR can only model abstractly, without physical grounding in local experiments.