Is our world in free fall? A kinematic reinterpretation of cosmic expansion

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Abstract
Based on entropy considerations, Boltzmann proposed that our universe might be a fluctuation within an eternal background. Combined with gravitation, this idea leads to an alternative cosmological model, the Boltzmann Universe (BU), in which expansion and its apparent acceleration arise from gravitational free fall on hyperbolic trajectories. This collective inertial dispersion, in which cosmological redshift results from relativistic Doppler shifts along a geodesic congruence, reproduces key cosmological signatures such as the Hubble law, large-scale homogeneity and effective spatial flatness. Although its theoretical foundations differ from those of the standard cosmological model (Standard Universe, SU), the BU exhibits formal similarities with the SU, including analogous expansion descriptions and geometric representations, while leading to distinct distance-redshift relations. The BU provides an alternative special-relativistic parametrization of large-scale cosmic dispersion that does not require a cosmological constant or exotic fields, in which the role attributed in the SU to dark energy, driving expansion against gravity, is instead played by gravity itself.

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