Gravitomagnetic-Hydrodynamics and Turbulence in Early Universe

TL;DR

The paper introduces Gravitomagnetic-Hydrodynamics (GMHD), a GEM-based extension of relativistic fluid dynamics that couples spacetime geometry to relativistic plasmas via a generalized Ohm's law and a gravitomagnetic diffusivity $\eta_g$, defining the gravitomagnetic Reynolds number $R_g=\frac{uL}{\eta_g}$. It argues that in the hot early Universe, $R_g\gg1$ leads to a strongly coupled, nearly ideal GMHD regime with GM flux freezing and gravitational Alfvén waves, potentially driving GMHD turbulence. The authors predict an Iroshnikov–Kraichnan-type isotropic energy spectrum $E(k)\propto k^{-3/2}$ for GMHD turbulence and discuss possible enhancements of density perturbations, linking these dynamics to the stochastic gravitational wave background via $\rho_{GW}=\dfrac{|B_g|^2}{16\pi G}$. The framework provides a new lens on nonlinear spacetime-matter dynamics and suggests observational avenues through SGWB constraints, while outlining future work on nonlinear GEM effects and implications for phase transitions and inflation.

Abstract

The nonlinear coupling between spacetime geometry and matter in the early Universe remains a frontier in theoretical cosmology. By introducing a novel gravitomagnetic-hydrodynamic framework, we reveal a fundamental analogy between magnetohydrodynamics and the co-evolution of spacetime geometry and relativistic plasma. We demonstrate that, in high-energy environments such as the electroweak phase transition, the (newly defined) gravitomagnetic Reynolds number becomes large, signifying a strongly coupled system where the gravitomagnetic field could be frozen into the fluid. This coupling inevitably leads to the emergence of gravitational Alfvén waves and could drive a transition to turbulence involving the dynamics of spacetime itself. Our findings suggest that gravitomagnetic-hydrodynamic turbulence may leave imprints on the stochastic gravitational wave background, offering a new window into the nonlinear dynamics of the primordial Universe.