Bateman dual fields and cosmological dissipation: Tachyons, born–infeld dynamics, and hubble-scale stabilization

We present a novel application of Bateman-type dissipation to relativistic scalar fields in cosmology, focusing on tachyonic and Born–Infeld (DBI) frameworks. By embedding a dual-field structure directly at the Lagrangian level with an exponential time-dependent factor, we introduce intrinsic dissipative dynamics that dynamically modify the effective mass of the field. Remarkably, this mechanism can quench tachyonic instabilities, leading to a positive effective mass related to the Hubble expansion rate, thereby stabilizing the field without introducing external friction or environmental couplings. We explore the implications of this framework for early-universe dynamics, including inflationary behavior, gravitational collapse, and gauge field back-reaction in nonlinear BI/DBI cosmologies. Furthermore, the approach suggests potential relevance for late-time cosmic acceleration and dark energy models, providing a dynamical route to slow or regulate expansion. The study also opens conceptual connections with fractional calculus and nonlocal dissipation, offering a pathway to generalized scalar-field dynamics in cosmology. Overall, our results highlight a unified and original perspective on dissipation in field theory, with broad implications for both early- and late-universe physics.