The cosmological constant vs adiabatic invariance

TL;DR

This paper explores how adiabatic invariance in a generalized gravitational potential, including a cosmological constant term, can explain galactic dynamics and the Hubble tension, revealing differences from classical Keplerian orbits.

Contribution

It introduces a novel approach using adiabatic invariance with a potential that incorporates the cosmological constant, deriving orbital parameters with explicit differences from Kepler's laws.

Findings

Derived orbital parameters using Weierstrass functions.

Revealed explicit differences from Kepler problem.

Provided insights into galaxy group dynamics and Hubble tension.

Abstract

The property of adiabatic invariance is studied for the generalized potential satisfying the condition of identity of sphere's and point mass's gravity. That function contains a second term corresponding to the cosmological constant as weak-field General Relativity and enables to describe the dynamics of groups and clusters of galaxies and the Hubble tension as a result of two flows, local and global ones. Using the adiabatic invariance approach we derive the orbital parameters via Weierstrass functions, including the formula for the eccentricity which explicitly reveals the differences from the Kepler problem.