The Recognition Dynamics Framework: Recognition Deepening, the Cosmological Bounce, and the Intertwiner CMB Signature (Paper 23 of the LQG–LQC Intertwiner Series)

Abstract

1. Introduction1.1 Two motivating problemsClassical general relativity predicts its own breakdown. In a contracting Friedmann–Lemaître–Robertson–Walker(FLRW) universe the scale factor a(t) reaches zero and the energy density diverges at finite time; the field equationsbecome undefined at the big-bang singularity. A quantum theory of gravity is required to resolve it. Independently, therole of observation in quantum mechanics — the measurement problem — has resisted resolution for a century, withmost interpretations treating observation as external to physics.The Recognitive Consciousness (RC) framework (Papers 12–13) addresses the second problem algebraically: it derivesrecognition from the closure properties of operator algebras, identifying the recognition coefficient κ as a state’s proximity to the unique KMS equilibrium, with κ = 0 far from equilibrium and κ = 1 at equilibrium. That the KMS stateis canonical (not chosen) is what gives the identification its force. This paper supplies the dynamics that Papers 12–13left implicit and couples those dynamics to spacetime geometry, connecting the recognition program to the LQG–LQCintertwiner spectral theory of Papers 1–17.1.2 Loop quantum cosmology as the established benchmarkLoop quantum cosmology implements the discrete geometry of loop quantum gravity at the homogeneous level, replacing the classical singularity with a quantum bounce at a critical density ρ_crit ≈ 0.41 ρ_Planck (Ashtekar–PawlowskiSingh; Ashtekar–Singh). LQC is mature, published, and observationally testable, and we adopt its bounce as the cosmological setting for the present work. The intertwiner spectral program (Papers 1–17) builds on LQC a parameter-freewindow function W(κ) governing the primordial spectrum, from which the CMB predictions used here are derived.1.3 Contribution and roadmapThis paper contributes: (i) explicit macroscopic and microscopic evolution equations for κ, with proved existence, globalattractivity, an exact deepening-rate law, and an exact protocol-linearity theorem (§3), numerically validated (§4); (ii)a demonstration that κ couples to the LQC bounce as a gauge-invariant spectator, receiving a localized excitation therewhile the singularity is resolved by the LQC mechanism (§5); and (iii) identification of the framework’s CMB signatureas a discrete higher-spin comb, a consequence of the linear intertwiner spectral map (§6). Section 7 discusses relationsto other approaches and open questions; §8 summarizes epistemic status; appendices give the protocol specification,proofs, numerical methods, and cosmological supporting calculations.Conventions. Planck units = c = 1, G = 1/(16π), M_Planck = G^{−1/2}; signature (−,+,+,+); ADM 3-metric γ_ij;recognition-time τ and thermal-time t related by dτ/dt = 1; κ [0,1] throughout.