What if gravity is not a warping of empty space, but the pressure driven flow of a dynamic, compressible vacuum medium?

A Compressible Vacuum Model of Gravity, presents a bold, mathematically rigorous alternative to General Relativity - one that bridges the physics of quantum fields, the structure of galaxies and the expansion of the cosmos itself.

Drawing on the concept of a relativistic superfluid vacuum, potentially an axion Bose–Einstein condensate, this model interprets gravity as arising from pressure gradients rather than spacetime curvature. The framework reproduces all classical gravitational tests, explains flat galaxy rotation curves without invoking dark matter, accounts for cosmic acceleration without a cosmological constant and proposes a rarefaction-wave mechanism for inflation that bypasses the need for speculative scalar fields.

From planetary systems to the large-scale cosmic web, from quantum field theory to gravitational wave dispersion, Callan weaves a coherent, cross-scale theory grounded in fluid dynamics. Along the way, readers encounter:

The barotropic equation of state and its role in unifying scales.

Parameter variations (e.g., polytropic index γ, ALP mass) as natural regime-specific adaptations.

Predictive signatures in CMB anisotropies, galaxy surveys, and gravitational wave data.

A pathway for laboratory-scale analogue gravity experiments to probe the vacuum's structure.

For physicists, cosmologists and scientifically curious readers alike, this work offers not only a shift in understanding gravity, but also a roadmap for testing it against the universe itself.