What have electrons, black holes and Clifford Algebra ever done for us?

Dark Energy as a Viscoelastic Stochastic Medium The cosmological dark sector can be understood as a relativistic viscoelastic medium coupled to gravity via a stochastic Einstein–Langevin equation. ΛCDM emerges as a special limit of this more general framework.   1. Emergent Gravity, Elasticity, and Dissipation 1.1 Elasticity of Spacetime Gravity may be emergent rather than fundamental: Jacobson (1995) : Einstein equations as a thermodynamic equation of state, $\delta Q = T dS$. Padmanabhan : Spacetime behaves like an elastic solid; diffeomorphisms are deformations; horizons are defects carrying area entropy. Sakharov : Einstein–Hilbert action arises from induced metrical elasticity of quantum vacuum fluctuations. In this view, as we previously  discussed, spacetime is elastic at long wavelengths, with an effective modulus set by vacuum energy: $$Y_\Lambda = \frac{\Lambda c^4}{8\pi G} = \rho_\Lambda c^2.$$ This modulus corresponds to a "cosmic Young's modulus," g...

The idea that bulk viscosity  could be an alternative to dark energy has been around for a while. For example, see the dark goo  paper, or viscous universe . The 2025  paper , Origin of bulk viscosity in cosmology and its thermodynamic implications , takes a kinetic/thermodynamic slant.  The paper establishes four facts: $$p_{\text{vis}}=-3\zeta H, \qquad \dot S_h>0, \qquad \dot S_m<0, \qquad T_m\neq T_h$$ and hence $$\boxed{\dot S_{\text{tot}}>0 ;\text{always}}$$ These are consequences of: Hubble expansion producing velocity gradients, The apparent horizon behaving as a thermodynamic boundary, The fluid inside the horizon being an open system.     So, let us complete, self-contained derivation synthesising the kinetic, fluid dynamics, EFT, and thermodynamic/irreversibility perspectives on bulk viscosity of the vacuum in an expanding FLRW universe. 1. Kinetic Derivation: Momentum Flux Across Layers Step 1: Setup As per the paper, con...

  Yes , you can define an effective Poisson ratio for the horizon—but only in a very specific, emergent, hydrodynamic sense—and it takes its extremal value. The value you get is not arbitrary; it is forced on you by horizon incompressibility, maximal entropy, and diffusion physics. 1. What a Poisson ratio really measures The Poisson ratio (ν) is defined (in ordinary elasticity) as $$\nu = - \frac{\text{transverse strain}}{\text{longitudinal strain}}.$$ Equivalently, in terms of elastic moduli: $$\nu = \frac{3K - 2\mu}{2(3K + \mu)} \quad \text{(3D bulk)},$$ or $$\nu_{2D} = \frac{K_{2D} - \mu_{2D}}{K_{2D} + \mu_{2D}} \quad \text{(membrane)}.$$ So to even ask for a Poisson ratio, we need: a bulk (or area) modulus (K), a shear modulus (μ). This is where horizons are special. 2. Horizon fluids: what moduli exist? From the membrane paradigm, AdS/CFT, and your own derivations: Horizons have: finite shear viscosity (η), no elastic shear modulus ((μ = 0)), negative bulk ...

  De Sitter space as a thermodynamic equilibrium During both inflation and late-time cosmic acceleration, the Universe is well-approximated by a de Sitter (dS) spacetime with nearly constant curvature radius ($\ell_\Lambda $). Our present Universe may therefore be regarded as a quasi–de Sitter state , possessing a cosmic event horizon (CEH) associated with its vacuum energy density (cosmological constant). A defining feature of de Sitter space is that the cosmological horizon is not merely a causal boundary but a thermodynamic object, endowed with temperature, entropy, and energy. In this context, the total bare (rest) energy associated with the horizon, defined via the Brown–York quasilocal energy, can be written as: \begin{equation} E_0 = 2\, k_B T_{dS} S_{dS} = 2\, m_{CEH} c^2 = 2E_H  \end{equation} This relation is a horizon version of the entanglement first law , from which the Einstein equations themselves can be derived. Here: $S_{dS}$ is the de Sitter entropy (d...

  In general relativity, defining "energy" is notoriously difficult. A specific point of confusion often arises in de Sitter space: Why is the quasi-local energy of the horizon exactly double the effective gravitational mass? By imposing a fundamental consistency condition— Horizon Uncertainty—we can re-derive the thermodynamics of the de Sitter horizon. We find that the horizon behaves exactly like a quantum-stretched membrane, where the "factor of two" is simply the result of the Virial Theorem applied to spacetime itself. Horizon Position Uncertainty Whether through holographic arguments, diffusion models, or entanglement entropy, a causal horizon is never sharp. Its position fluctuates. The variance of the horizon position $\Delta x^2$  scales with the geometric mean of the Planck length $L_p$ ​ and the horizon radius $l_{\Lambda}$ ​ :  \begin{equation}     \Delta x^2 = L_P \, l_\Lambda, \qquad L_P = \sqrt{\frac{G\hbar}{c^3}} \end{equation}    W...