Viscosity-Driven Accelerated Expansion

Updated 15 October 2025

Viscosity-driven accelerated expansion is a cosmological approach that uses bulk viscous pressure in cosmic fluids to mimic dark energy.
Causal and nonlinear hydrodynamic models yield modified evolution equations with stable de Sitter, quintessence, or phantom attractors.
Observational constraints from SNe Ia, BAO, and CMB fine-tune viscosity parameters, supporting an alternative fluid-dynamical explanation for accelerated expansion.

Viscosity-driven accelerated expansion refers to the class of cosmological models in which bulk viscous effects in the cosmic medium generate an effective negative pressure, sufficient to cause the late-time or early-universe accelerated expansion observed in cosmological data. In these approaches, the cosmic fluid—comprising either ordinary matter, dark matter, unified dark sectors, or modified dark energy—is treated as non-ideal, acquiring a bulk viscous stress in its stress-energy tensor. When the viscosity is sufficiently large or suitably parameterized, this contribution can mimic or even replace the effect typically attributed to a cosmological constant or exotic dark energy, providing a fluid-dynamical mechanism for cosmic acceleration.

1. Theoretical Background and Model Construction

Viscous cosmologies are based on modifying the energy-momentum tensor to incorporate non-vanishing bulk viscosity. For a perfect fluid, the pressure is specified solely by the equation of state p = wρ. An imperfect fluid, however, receives an additional viscous pressure term, leading to an effective pressure of the form

$P^* = P - 3\zeta H,$

where $\zeta$ is the bulk viscosity coefficient and $H$ is the Hubble parameter.

Multiple parameterizations are employed for $\zeta$ :

Linear (e.g., $\zeta = \zeta_0 + \zeta_1 H$ ) (Avelino et al., 2010)
Power-law in the matter density ( $\zeta = \xi_0 \rho_m^s$ ) (Palma et al., 13 Oct 2025)
Terms involving $\ddot{a}/\dot{a}$ or combinations of $\rho$ and $H$ (Sasidharan et al., 2014, Rana et al., 5 Jul 2024)

The physical content varies: some models consider pressureless (dust) fluids modeling the whole dark sector (Avelino et al., 2010), others separate out baryons and a viscous dark matter/energy (Palma et al., 13 Oct 2025), or incorporate nonlinear extensions including electromagnetic sectors, coupling to curvature scalars, or modifications to gravity (such as f(R, T), f(Q), or f(Q,L_m) gravities) (Tarai et al., 2021, Rana et al., 5 Jul 2024, Myrzakulov et al., 11 Jul 2024).

The generalized Friedmann and Raychaudhuri equations and the evolution of the scale factor are determined by these modified stress-energy tensors.

2. Causal Formulations and Nonlinear Israel-Stewart Theory

Causal formulations of relativistic viscous hydrodynamics are essential for physical consistency. The full Müller-Israel-Stewart (MIS) theory modifies the transport equations for the bulk viscous pressure $\Pi$ according to

$\tau\,\dot{\Pi} + \Pi = -3\xi H - \text{nonlinear terms},$

where $\tau$ is a relaxation time. Nonlinear causal extensions, such as that of Maartens et al., introduce terms allowing the fluid to remain far from equilibrium (Palma et al., 13 Oct 2025, Acquaviva et al., 2014, Lahiri et al., 2023). For instance, a prototypical nonlinear law is

$\Pi = -\frac{\zeta \chi}{1+\tau_* \chi},$

where $\chi$ is a thermodynamic force (e.g., expansion scalar or derivatives of ρ) and $\tau_*$ encodes far-from-equilibrium timescales (Acquaviva et al., 2014, Sharif et al., 2017, Lahiri et al., 2023).

Causality is preserved by incorporating time derivatives (not just spatial gradients), as in the first-order BDNK framework (Bemfica et al., 2022). This feature is critical for obtaining stable, well-posed solutions—especially significant for high-energy inflationary models and for consistent entropy production.

3. Dynamical System Analysis and Cosmological Attractors

Reformulation of the cosmological equations in terms of autonomous dynamical systems is essential for identifying asymptotic behaviors and attractors. Dimensionless variables encode the matter density, Hubble rate, and viscous pressure, reducing the evolution equations to closed systems (Palma et al., 13 Oct 2025, Acquaviva et al., 2014, Sharif et al., 2017). Fixed points (critical points) are classified by evaluating where derivatives vanish, leading to possible attractor solutions:

De Sitter–like (w_eff = –1, q = –1) for s < 1/2 (Palma et al., 13 Oct 2025)
Generic quintessence (–1 < w_eff < –1/3) for s around 1/2
Phantom regimes (w_eff < –1) for s > 1/2
Coexistence of de Sitter and phantom attractors in the critical s = 1/2 regime
Radiation and stiff-fluid fixed points at early times

Transitions among these regimes correspond to the observed evolution: early deceleration, smooth transition, and late-time acceleration. For nonlinear viscosity, phase space analysis confirms the existence and stability of these attractors (Acquaviva et al., 2014, Sharif et al., 2017, Palma et al., 13 Oct 2025).

4. Observational Constraints and Physical Viability

Confrontation with observational data is a defining step:

Type Ia Supernovae (SNe Ia) luminosity distances constrain viscous model parameters ( $\zeta_0, \zeta_1, s$ ), often yielding expansion histories nearly degenerate with ΛCDM (Avelino et al., 2010, Sasidharan et al., 2014, D et al., 2020).
Combined datasets (Pantheon, CC, SH0ES, BAO, CMB) improve Bayesian parameter estimation in modified gravity + viscous fluid contexts (Rana et al., 5 Jul 2024, Myrzakulov et al., 11 Jul 2024).
Late-time transition redshift ( $z_t$ ), deceleration-to-acceleration epochs, and present equation of state ( $\omega_\text{eff}$ ) are fitted, with best estimates usually in the quintessence regime ( $-1 < \omega_\text{eff} < -1/3$ ) and transition redshifts around $z \sim 0.5-1$ (Sasidharan et al., 2014, Myrzakulov et al., 11 Jul 2024).
The effective negative pressure from viscosity yields ages of the Universe in reasonable agreement with globular cluster data, though some models with extra viscosity coefficients may predict slightly lower ages (Avelino et al., 2010, D et al., 2020).
Diagnostic tools: Statefinder (r, s) reveals approach to de Sitter behavior or deviation from ΛCDM at present epoch; Om(z) tests typically confirm the quintessence nature (Sasidharan et al., 2014, Rana et al., 5 Jul 2024, Myrzakulov et al., 11 Jul 2024).

5. Thermodynamic Consistency and Entropy Production

Consistency with the second law of thermodynamics is a non-trivial requirement:

The local entropy production rate obeys $T\nabla_\nu s^\nu = 9H^2 \zeta$ . For physical viability, $\zeta \ge 0$ is required (Avelino et al., 2010, Sasidharan et al., 2014, D et al., 2020).
Some parameterizations (e.g., two-parameter models with $\zeta_0$ and $\zeta_1$ ) violate local entropy increase at early times (high z), while constant viscosity ( $\zeta_1 = 0$ ) may satisfy it globally (Avelino et al., 2010).
The generalized second law (matter + horizon entropy) can remain valid even if local violations occur, as in scenarios where the total entropy (including apparent horizon contributions) remains non-decreasing (Sasidharan et al., 2014).
Nonlinear causal models systematically respect non-negative entropy production for all identified attractors, with the entropy always increasing toward equilibrium (Palma et al., 13 Oct 2025, D et al., 2020).

6. Extensions: Modified Gravity, Coupled Fluids, and Unified Models

Viscous accelerated expansion can be realized in frameworks extending beyond standard GR:

f(Q) gravity and its extensions (e.g., f(Q, L_m)) supplement geometric modifications with viscous matter, yielding analytical late-time solutions and EOS parameters compatible with acceleration. Bulk viscosity is incorporated as $\zeta = \zeta_0 \rho H^{-1} + \zeta_1 H$ (Rana et al., 5 Jul 2024, Myrzakulov et al., 11 Jul 2024).
In f(R, T) scenarios, viscous pressure is essential to obtain negative effective pressure and match the observed quintessence-like expansion (Tarai et al., 2021).
Coupled two-fluid models (e.g., viscous van der Waals fluid plus pressureless matter) allow fine-tuning of inflationary observables such as n_s and r, and naturally accommodate early inflation and late acceleration, with phase transitions in viscosity handling graceful exit from inflation (Astashenok et al., 2021, Brevik et al., 2017, Brevik et al., 2018).
In unified dark matter models, non-linear causal viscosity can be the sole mechanism producing both dark matter–like and dark energy–like eras within a single dissipative fluid (Palma et al., 13 Oct 2025).
In generalized inhomogeneous EoS fluids, bulk viscosity yields extra negative pressure, and logarithmic or quadratic corrections can model late-time acceleration without a cosmological constant (Brevik et al., 2019).

7. Physical Implications and Distinction from Shear Viscosity

Theoretical analysis distinguishes bulk viscosity from shear viscosity in cosmological dynamics. Bulk viscosity directly modifies the homogeneous expansion and can fundamentally change the global deceleration parameter, enabling cosmic acceleration at Hubble scales (Giovannini, 2015). By contrast, shear viscosity acts only at higher orders in spatial gradients and is relevant only for sub-Hubble scale inhomogeneities, without the capacity to drive global acceleration (Floerchinger et al., 2014, Giovannini, 2015).

Causal, nonlinear bulk viscosity models relax the requirement for large viscous coefficients as in Eckart-based, non-causal approaches. Accelerated expansion emerges robustly across a range of viscosity strengths, tied to the non-equilibrium structure and dynamical attractors of the system (Palma et al., 13 Oct 2025).

In summary, viscosity-driven accelerated expansion frameworks provide a robust, fluid-dynamical alternative to scalar dark energy or a cosmological constant by leveraging the physically motivated mechanism of bulk viscous dissipation. The approach is supported by causal relativistic hydrodynamics, yields cosmological observables consistent with current data, and is compatible with thermodynamic laws when properly formulated. The models admit a spectrum of dynamical outcomes—including de Sitter, quintessence, and phantom attractors—governed by the power-law index and strength of the bulk viscosity, and can be realized in both standard and modified gravitational frameworks.