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The Infrared Universe

Jonathan Holland

Abstract

We develop a mesoscopic framework in which the cosmological exterior is treated as an open quantum subsystem coupled to horizon degrees of freedom. Although local conservation laws satisfy $\nabla_μ\langle J^μ\rangle=0$, transport of baryon number across horizons removes conserved charges from the observer--accessible sector, producing effective depletion in exterior densities. Global unitarity therefore requires compensating source terms in the reduced exterior continuity equations. We show that relativistic causality forces this compensation to occur through long--wavelength geometric excitations: only infrared modes can restore entropy and charge while remaining outside the causal wedge of the infalling matter. An infrared return channel thus emerges as a generic feature of horizon--coupled semiclassical gravity. The second ingredient is a Carnot--Carathéodory (CC) tangent geometry, whose mesoscopic scale $σ$ governs both infrared mode excitation and the kinematics of photon and matter propagation. In this setting, photon trajectories follow recurrent horizontal geodesics, producing an effective cosmic cavity whose stationary state is a Planck spectrum characterized by $σ$. The same scale modifies large--radius circular motion in a manner consistent with flattened galactic rotation curves. Horizon thermodynamics and mesoscopic balance laws then link $σ$ to the cosmic expansion rate, yielding $H\simσ$ and a unified infrared structure underlying photon equilibrium, baryon balance, and large--scale kinematics.

The Infrared Universe

Abstract

We develop a mesoscopic framework in which the cosmological exterior is treated as an open quantum subsystem coupled to horizon degrees of freedom. Although local conservation laws satisfy , transport of baryon number across horizons removes conserved charges from the observer--accessible sector, producing effective depletion in exterior densities. Global unitarity therefore requires compensating source terms in the reduced exterior continuity equations. We show that relativistic causality forces this compensation to occur through long--wavelength geometric excitations: only infrared modes can restore entropy and charge while remaining outside the causal wedge of the infalling matter. An infrared return channel thus emerges as a generic feature of horizon--coupled semiclassical gravity. The second ingredient is a Carnot--Carathéodory (CC) tangent geometry, whose mesoscopic scale governs both infrared mode excitation and the kinematics of photon and matter propagation. In this setting, photon trajectories follow recurrent horizontal geodesics, producing an effective cosmic cavity whose stationary state is a Planck spectrum characterized by . The same scale modifies large--radius circular motion in a manner consistent with flattened galactic rotation curves. Horizon thermodynamics and mesoscopic balance laws then link to the cosmic expansion rate, yielding and a unified infrared structure underlying photon equilibrium, baryon balance, and large--scale kinematics.

Paper Structure

This paper contains 391 sections, 4 theorems, 530 equations, 11 figures.

Table of Contents

  1. Introduction
  2. MOND as an Implicit Sub-Riemannian Theory
  3. The $\Lambda$CDM framework and its conceptual fragmentation
  4. Scope and status of the present work.
  5. Roadmap
  6. Heisenberg Kinematics and Radial Potentials
  7. Canonical one-form and horizontal momenta
  8. Free Hamiltonian in polar coordinates
  9. Adding a radial potential
  10. Circular orbits and rotational velocity
  11. Virial theorem
  12. Causal implications and a cartoon view of the model
  13. Bulk Carnot Geometry and the Origin of $\sigma$
  14. A $(3,3)$ nilpotent model
  15. Planar motions and the Heisenberg limit
  16. ...and 376 more sections

Key Result

Theorem 1

The generic geodesic for the Hamiltonian $H$ is given by where $u\in\operatorname{im}\mathbb H$, $Z_1u=uZ_1$, $Z_2u=uZ_2$, $\mu_1,\mu_2\in\mathbb R$, and where $c$ is a real constant, and $\mu_1,\mu_2,u$ are conserved along the geodesic. The limiting geodesics are great circles on $S^4$.

Figures (11)

  • Figure 1: Rotation curve, with a naive exponential (Freeman) decay matter model, for M31 galaxy. Top curve: nonzero $\sigma$; bottom curve: $\sigma=0$. This uses the following parameters: $G=2.26954\times 10^{-69}\,\mathrm{kpc}^3/\mathrm{kg\cdot s}^2$, $M=2\times 10^{42}\operatorname{kg}$ (mass of a typical galaxy like M31), $\sigma=10^{-17}\mathrm s^{-1}\approx 5 H_0$, $r_0=10\,\mathrm{kpc}$ (scale parameter).
  • Figure 2: Basic 2-dimensional Heisenberg model. A projected geodesic is shown, from an observer to the cosmological horizon. The observer's causal access is limited by the radius of curvature. The "Exterior" is the universe that the observer may observe.
  • Figure 3: A "holographic" view. Black holes nucleate in the exterior, and their entropy microstates are encoded as qubits on their horizons. As expansion drives them outward, these horizon degrees of freedom are absorbed into the microstates of the cosmological horizon.
  • Figure 4: Heisenberg--wave toy model for the angular power spectrum. We plot $D_\ell \equiv \frac{\ell(\ell+1)}{2\pi} C_\ell,$ using the form $D_\ell = \frac{\ell(\ell+1)}{2\pi}\,e^{-2\alpha \ell}\,\sin^2\!\Bigl(\beta\,\sqrt{2\ell+1}\Bigr),$ with $\alpha = 0.0025$ and $\beta = 0.25$. The exponential factor mimics slow angular diffusion on the sky with a characteristic timescale $\tau_{\mathrm{mix}}\sim (2\alpha)^{-1}H_0^{-1} \sim 10^3 H_0^{-1}$, i.e. a diffusion rate of order $\gamma \sim 10^{-3}H_0$ --- consistent with the horizon--coupled mixing rate appearing elsewhere in the model. The parameter $\beta$ controls the spacing of the oscillations and is rounded here to $1/4$, close to the value inferred from the free--energy throughput calculation. These choices produce a dominant peak near $\ell\!\sim\!200$, a secondary peak near $\ell\!\sim\!500$, and rapidly decaying high--$\ell$ structure, showing that even simple Heisenberg--wave spectra can yield qualitatively realistic acoustic behavior.
  • Figure 5: Toy two--field experiment in a one--dimensional radial surrogate. Left: evolution of the temporally averaged mesoscopic field $\bar{\sigma}(r,t)$ under the fast--$\Sigma$, slow--$\sigma$ reaction--diffusion closure. Right: corresponding effective circular--speed profiles $v_c(r,t)$ computed from $\bar{\sigma}(r,t)$ using the step--2 circular--orbit condition. The mapping from $\sigma$ to $v_c$ is diagnostic and isolates the sensitivity to radial gradients rather than asserting a literal gravitational interpretation.
  • ...and 6 more figures

Theorems & Definitions (9)

  • Theorem 1
  • proof
  • Definition 1
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Corollary 1
  • proof