V2.96: Viscous Horizon Corrections

Objective

Compute the bulk viscous correction at the cosmological horizon from gravitational viscosity and determine its effect on the effective Lambda.

Background

Chirco-Liberati (2010) showed that horizons have gravitational viscosity eta/s = 1/(4*pi). For FRW (isotropic), the shear tensor sigma = 0, but bulk viscosity from the expansion theta = 3H can contribute. Three sources of bulk viscosity are considered:

1. Conformal fields (massless): zeta = 0 exactly
2. Massive SM fields: zeta ~ m^2*T, Boltzmann-suppressed at T_horizon
3. Trace anomaly: zeta_anom ~ delta * H^2 (Eling-Oz 2011)

Results

Phase 1: Trace Anomaly Viscosity

The Eling-Oz formula gives:

• zeta_anom = -2deltaH^2 / (36*pi) = 1.22 x 10^{-2} (H_0 units)
• This produces Delta_Lambda/Lambda ~ 0.67 in dimensionless units

However, this formula was derived for AdS/CFT fluid-gravity duality, not FRW cosmology. Its applicability to the cosmological horizon is uncertain.

Phase 2: SM Massive Field Viscosity

• Horizon temperature: T = H_0/(2*pi) = 2.4 x 10^{-34} eV
• ALL massive SM fields are Boltzmann-suppressed: m/T > 10^{30} for neutrinos, > 10^{39} for electrons
• Total SM massive bulk viscosity: exactly zero

Phase 3: Viscous Friedmann Correction

Source	zeta	Delta_Lambda/Lambda
Conformal fields	0 (exact)	0
SM massive fields	0 (Boltzmann)	0
Trace anomaly (Eling-Oz)	1.2 x 10^{-2}	0.67

The trace anomaly viscosity gives an O(1) dimensionless correction. However, this result depends on whether the Eling-Oz formula (derived for holographic fluids) applies to FRW cosmology.

Key Finding

Viscous corrections from massive fields are exactly zero. The cosmological horizon temperature (~10^{-33} eV) is 120 orders of magnitude below the lightest massive particle.

Trace anomaly viscosity is model-dependent. The Eling-Oz formula gives a potentially significant correction, but:

1. It was derived for AdS/CFT, not FRW
2. FRW has zero shear (sigma = 0) by isotropy
3. No rigorous derivation exists for the FRW bulk viscosity from trace anomaly
4. The result cannot be reliably used to close the gap

Implications

Without a first-principles derivation of bulk viscosity for FRW horizons, viscous corrections must be treated as uncertain. They do not provide a reliable path to closing the Lambda gap. The main remaining candidates are:

• Field content (V2.93): Determines R between 0.530 (full SM) and 1.205 (photon only)
• Omega_Lambda target (V2.94): Shifts target from 1.0 to 0.685

Runtime

< 0.1s