Scale-Invariant Cosmological Models: Resolution of the Hubble Tension, the S8 Tension, and Decreasing Dark Energy Density

The standard cosmological model, Lambda-CDM, has been very successful as a model of the cosmos, but measurements increasingly show deviations from its predictions. The Hubble tension is well known and recent measurements show increasing statistical significance for the different values of the Hubble constant derived from early versus late universe data. The S8 tension, representing differing values for the fluctuations in matter density between early and late universe measurement, is comparable in magnitude to the Hubble tension, but opposite in direction, with late universe values smaller than early universe values. This qualitative difference between the Hubble and S8 tensions is a significant challenge to models to replace Lambda-CDM. The Dark Energy Survey Instrument (DESI) Data Release 2 (DR2) finds a 3-4 σ preference for time-varying dark energy versus the constant rate in the baseline Lambda-CDM model. We show that a cosmological model based on a scale-invariant formulation of contraction of the material world, rather than expansion of space as in the Lambda-CDM model, resolves those discrepancies as well as other concerns. In particular, a model of the universe where the material world is contracting with time with respect to an unchanging fabric of spacetime resolves the Hubble and S8 tensions as well as predicts the current observed rate of decrease of the dark energy density. The vacuum energy is the leading explanation for the force of dark energy, but the vacuum energy force is ~10122 larger than that derived from the observed acceleration of the expansion of space. However, a force that large is a plausible candidate as a compression mechanism for contraction of the material world. Additionally, a scale-invariant cosmological model preserves the conservation of energy over time, and explicitly has all material objects moving at sub-luminal relative velocities, both of which are violated in the Lambda-CDM model. Scale invariance ensures the physical laws for dynamics, electromagnetism, quantum field theory, and general relativity are unchanged when the measurable quantities of length, time, mass, and charge contract synchronously, as well as ensuring the speed of light and the gravitational constant do not change with time. It is shown that a scale invariant model based on the vacuum energy as a driver of scale contraction retains the successful features of Lambda-CDM, agrees with the recent DESI measurements of the expansion rate of the universe, explains the unexpectedly large number of early galaxies observed by JWST, resolves some inconsistencies in the age of the universe and early galaxies, and resolves the Hubble tension and the S8 tension as a ~10% correction to Lambda-CDM due to a decreasing scale factor for the material world. The current scale factor is estimated to be ~70% of its value at the Big Bang.