Stochastic Worldlines and an Emergent Frustrated String Equation of State

Abstract

We show that coarse-graining the noise-history label of a relativistic point particle subject to Gaussian multiplicative noise generates a non-degenerate effective two-dimensional worldsheet geometry, with a transverse scale set by the noise amplitude and an explicit coarse-graining scale. Varying the associated Nambu–Goto-type action with respect to the background metric and averaging over the isotropic orientation of the emergent string direction in the cosmological rest frame yields a perfect-fluid equation of state (EoS) [Formula: see text] in [Formula: see text] dimensions. This is the EoS of a frustrated network of one-dimensional defects and is incompatible with a cosmological constant. Because a fluid with this EoS dilutes as [Formula: see text], identical to spatial curvature in the Friedmann equation, current curvature constraints bound the abundance of this component directly. A joint fit to cosmic chronometers, Pantheon+SH0ES supernovae, and DESI DR2 BAO measurements yields [Formula: see text] (95%) without CMB information. Adopting the current DESI+CMB curvature constraint tightens this bound to [Formula: see text], corresponding to an energy scale [Formula: see text], a factor of four below the dark energy scale. The mechanism is not a source of dark energy but a plausible route from stochastic point-particle dynamics to an emergent frustrated-string fluid whose abundance is constrained by current curvature measurements. The exact background-level degeneracy with spatial curvature is broken at perturbation order by the presence of anisotropic stress, providing a potential observational discriminator.