The Hyperbolic Vacuum: A Zero-Parameter Cosmology and an Exact Solution of Einstein's Field Equations
Year: 2026
Type: preprint
Abstract: Einstein's spacetime interval metric describes a universe with negatively curved (hyperbolic) geometry, and is itself an exact solution of his field equations. Taking it at face value gives a cosmology with no fitted parameters: the luminosity distance to redshift z is d_L(z) = (c/H0)(1+z)sinh(ln(1+z)), and from the age of the universe alone, the Hubble constant follows as H0 = 1/t0 = 71.9 km/s/Mpc. The model reproduces the Pantheon+ and DES-SN5YR supernova distances across 3,400 objects with zero free parameters and no dark energy, and produces the 1998 dimming that dark energy was introduced to explain as a consequence of the geometry. The concordance model appears to be a heuristic fit to the underlying hyperbolic manifold, its two density parameters the coordinate freedom needed to write negative spatial curvature in flat-space language. The paper states plainly the three early-universe constraints the strict late-time geometry does not meet — the CMB acoustic angle, structure formation, and nucleosynthesis — as explicit requirements on any completion rather than as solved problems.
Author: TURNER, L.K.
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169718381
Cites:
Cited by:
Related to: