Where Focusing Fails: The Density and Time Interval of Raychaudhuri Defocusing Around a Torsion Bounce
Year: 2026
Type: article
Abstract: For dust, focusing fails above a density ratio of 0.250, and the defocusing interval lasts 2.308 bounce timescales across both branches. For radiation the interval lasts 1.413 bounce timescales. For stiff matter the critical ratio rises to 0.400. The depth of the violation, measured by the minimum of rho_eff + 3 p_eff in units of the bounce density, is -1.00 for dust and -2.00 for stiff matter, both attained exactly at the bounce point where the effective density passes through zero while the effective pressure remains finite and negative. The identity of this interval with the accelerating window is exact in this description, which is expected: cosmic acceleration and geodesic defocusing are two readings of the same sign change. The study is a computation from stated assumptions, performed by the accompanying script; it is simulated, not measured.
Author: Aldred, William Alexander
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225821056
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