Causal Viscous Fluids and Non-Singular Cosmological Bounces

We investigate the realization of non-singular bouncing cosmologies driven by causal bulk-viscous fluids within General Relativity, $f(R)$ gravity, and Loop Quantum Cosmology. Building on the no-go result of Eckart theory in spatially flat universes, we show that the Israel–Stewart formulation, which incorporates finite relaxation times, permits controlled violations of the null energy condition at the bounce while remaining consistent with thermodynamic and causality requirements. Analytical bounce solutions are constructed from parametrized scale factors, yielding explicit constraints on the viscosity coefficient and relaxation time that guarantee positive entropy production and stable perturbations. In extended gravity frameworks, we demonstrate that higher-curvature corrections in $f(R)$ models and quantum geometry effects in Loop Quantum Cosmology further enhance the robustness of viscous bounces. Our results establish a unified description in which bulk viscosity provides a physically consistent mechanism for singularity resolution across different theories of gravity, highlighting distinctive conditions under which smooth cosmological bounces can occur.

💡 Research Summary

The paper tackles the long‑standing problem of the initial cosmological singularity by proposing a physically motivated mechanism that generates a non‑singular bounce through causal bulk‑viscous fluids. The authors begin by revisiting the well‑known no‑go theorem for Eckart‑type first‑order relativistic hydrodynamics in a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) universe. In Eckart theory the bulk viscous pressure is algebraically tied to the Hubble rate, Π = −3ζH. At a bounce the Hubble parameter vanishes, forcing Π = 0, and consequently the Raychaudhuri equation reduces to ˙H = −4πG(ρ + p) ≤ 0 for ordinary matter. Hence the null energy condition (NEC) cannot be violated and a bounce is impossible, confirming the Eckart no‑go result.

To overcome this limitation the authors adopt the second‑order Israel–Stewart (MIS) formalism, which introduces a finite relaxation time τ and treats the bulk pressure Π as an independent dynamical variable. The full transport equation reads
τ ·Π + Π = −3ζH − ½τΠ