Cosmological Instantaneous Classicalisation

Cosmological Instantaneous Classicalisation Stefan-Alexandru Gheorghe Arboros Research Aberdeen [email protected] October 28, 2025 Abstract We introduce a promising, albeit speculative design, that peers through the spectrum of Cosmological Instantaneous Classicalisation by integrating the microphysics of Loop Quantum Gravity (LQG) with the entropic framework of the Event Driven First Passage Model (EDFPM) [7] and by extension the Entropic Bridge Model (EBM) [7]. We adopt three core axioms: (1) The microphysical stochasticity of quantum geometry, driven by a fundamental Poisson process on spin network edges [9], defines a universal frequency ω≈1043 Hz. This value is shown to be consistent with the Loop Quantum Cosmology (LQC) bounce timescale tb∼lPl/c [1,2]. (2) The EBM’s entropic instability governs collapse via a hazard rate α=ωln N(t), where N(t) counts the combinatorial degrees of freedom in the spin network boundary. (3) Cosmological N(t) scales holographically as N(t)∝ (RH(t)/lPl)2, with horizon radius RH(t)≈ct. The unified model yields a mean collapse time ⟨T0⟩= 1/α(t)≪10−32 s during inflation, enforcing instantaneous classicalisation. This mechanism delivers the classical, thermal universe essential for Big Bang Nucleosynthesis (BBN) [4], addressing a central dilemma in cosmology. 1 1 Introduction Standard cosmology posits that the early universe had transitioned to a classical, thermal state by the epoch of Big Bang Nucleosynthesis (BBN), at t≈10 s [4], yet the underlying mechanism for this quantum to classical transition remains an open dilemma. Extending prior syntheses of entropic collapse models (EDFPM, EBM) [7] and objective collapse theories (SUV, CSL) [5,6], this work incorporates Loop Quantum Cosmology (LQC) [1,2] and emergent quantum geometry models [9] to furnish a physically grounded mechanism for cosmological classicalisation, deriving the entropic hazard rate α∝ln Nfrom spin network combinatorics [10]. We leverage this LQC framework, integrated with recent models of emergent quantum geometry [9], to ground the classicalisation mechanism. We posit that the fundamental frequency ω≈1043 Hz required by collapse models [5–7] is not an ad hoc parameter, but emerges directly from a microphysical Poisson process on spin network edges [9]. This frequency is shown to be consistent with the characteristic timescale tbof the LQC bounce [1,2], setting the cadence for stochastic collapse. Augmenting the EBM’s entropic axiom with this ωand a holographic N(t)∝t2, we derive a time dependent hazard rate α(t)=ωln N(t). This formalism predicts near instantaneous collapse (⟨T0⟩≪10−32 s), pointing to a mechanism that yields the classical universe demanded by BBN [4] without ad hoc assumptions. 2 2 Microphysical Stochasticity We posit that the stochasticity required by entropic collapse models [7] is not an external process, but is intrinsic to the emergence of quantum geometry itself. Following the work of Nandi et. al. [9], we identify a fundamental Poisson driven stochastic process on the edges of the spin network. This process, linked to the spinning of quantum geometry, yields a characteristic frequency ωfor the stochastic updates. Nandi et. al.[9] demonstrate this frequency is foundational, and we identify it as the universal clock tick for all quantum processes, including collapse. For computational tractability, we adopt the Planck scale value ω≈1043 Hz. 2.1 Bounce Timescale in Loop Quantum Cosmology This microphysical frequency finds strong validation within Loop Quantum Cosmology (LQC). LQC quantizes general relativity using loop quantum gravity techniques, replacing the Big Bang singularity with a quantum bounce via holonomy flux algebra corrections to the Hamiltonian constraint [1,2]. At densities ρ∼ρPl ≈5.1×1093 g/cm3, repulsive quantum effects dominate, transitioning the universe from contraction to expansion. The bounce timescale tbemerges from the discreteness of spacetime at the Planck scale. In the effective dynamics of LQC, the bounce occurs when the scale factor asatisfies ρ(ab) = ρcrit ≈0.41ρPl, yielding tb∼r3 8πGρcrit ≈lPl c∼10−43 s,(1) with lPl =pℏG/c3≈1.616 ×10−35 m and c= 3 ×108m/s. This tbconstitutes the primordial “clock tick” of quantum cosmology [1,2,8]. The associated angular frequency, ωb= 2π/tb≈6.28 ×1043 Hz, is in direct agreement with the fundamental frequency ω≈1043 Hz derived from the underlying stochastic microphysics [9]. This consistency provides a non arbitrary, physically grounded value for the collapse parameter, aligning the LQC effective dynamics with the fundamental stochastic emergence of geometry. 2.2 Entropic Hazard Rate (Axiom, Derived from Spin Network Combinatorics): The Entropic Bridge Model (EBM) formalizes collapse as an entropic first passage process, where the hazard rate α(τ) for branch decoherence at proper time τobeys α(τ)=ωH(τ). Here, ωis the fundamental stochastic frequency [9], and H(τ)=−Pipi(τ) ln pi(τ) is the Shannon entropy of the superposition over uncollapsed branches [7]. For an equiprobable ensemble of Nmicrostates combinatorial degrees of freedom, H(τ)≈ln N[7]. In the spin foam formalism of loop quantum gravity, extended to entropic motion via random walks on spin network graphs [10], the local entropy at a boundary vertex puncture arises from the combinatorial connectivity: for a vertex of valence N(number of incident edges, proxy for holographic degrees of freedom), the Shannon entropy of transition probabilities in the stationary distribution approximates Sv≈ln Nin the high valence, uniform weight limit [10]. 3 While this serves as a robust approximation, we acknowledge that extensions for non uniform or weighted puncture distributions could introduce corrections. Identifying the collapse hazard with this entropic instability rate, the logarithmic measure of superposed geometric configurations, then yields the axiom: α(t)=ωln N(t).(2) This encapsulates growing instability: larger N(t) amplifies α(t), accelerating collapse as combinatorial complexity accrues [7,10]. The survival probability follows S(t) = exp −Rt 0α(t′)dt′, with mean first passage time ⟨T0⟩=R∞ 0S(t)dt ≈1/α(t) in the high rate limit α(t)≫1/t. 2.3 Cosmological Degrees of Freedom In loop quantum gravity (LQG), the combinatorial degrees of freedom N(t) for a cosmological horizon are counted by the effective number of punctures on the boundary spin network, scaling with the area AH(t) = 4πR2 H(t)≈4π(ct)2as N(t)≈AH(t)/l2 Pl [1]. For cosmology, RH(t)≈ct post bounce (a scaling valid after the initial Hubble regime, which neglects early superluminal expansion), yielding: N(t)≈4π(ct)2 l2 Pl .(3) This quadratic growth N(t)∝t2reflects the proliferation of boundary punctures as the observable universe expands. 2.4 The Quantum Instability Model Merging these yields the time dependent hazard rate. Substituting N(t) into Eq. (3), α(t)=ωln N(t)=ωln 4π(ct)2 l2 Pl  =ω[ln(4π) + 2 ln(ct)−2lnlPl]≈2ωln ct lPl ,(4) where the approximation drops subdominant constants (ln(4π)≈2.53, but ln(ct/lPl)∼ 120 during inflation, dominating). The mean collapse time then becomes: ⟨T0⟩(t)≈1 α(t)=1 ωln N(t).(5) 4 3 The Collapse and Cosmological Classicalisation We begin by calculating the hazard rate during the inflationary epoch (t≈10−32 s): 1. Degrees of Freedom at t= 10−32 s: N(10−32s) ≈4π(3 ×108·10−32)2 (1.6×10−35)2≈10−46 10−69 ≈1023.1(6) 2. Hazard Rate at t= 10−32 s: α(10−32s) ≈ω·ln(N)≈(1043 Hz) ·ln(1023)≈53 ×1043 Hz.(7) 3. Mean Collapse Time: ⟨T0⟩ ≈ 1 α≈1 53 ×1043 ≈10−45 s.(8) Thus, the mean time to collapse (∼10−45 s) is far shorter than the duration of the inflationary epoch itself (∼10−32 s). This model predicts a near instantaneous collapse. The universe is driven to classicality by its own immense entropic instability as soon as it begins to inflate. This provides a first principles mechanism that delivers the classical, thermal universe that BBN and all subsequent cosmology require [4]. By retaining the sound logic of the framework: the fundamental microphysical frequency (ω≈1043 Hz) [1,2,8,9] and the EBM’s entropic hazard rate (α∝ln N) [7]. Coupling this to the correct 2D holographic scaling for N, we derive a time dependent hazard rate α(t)≈ω·ln(N(t)). This predicts a near instantaneous classicalisation of the universe (⟨T0⟩≪10−32 s), driven by its own immense entropic instability. This points to a first principles physical mechanism that replaces standard cosmology’s ”just so” assumption of classicality [4], while providing the necessary conditions for BBN to occur [4].2This model’s strength lies in its grounding of the two primary parameters, ωand N(t), in the physics of quantum gravity. The identification of the fundamental frequency ωwith the Poisson driven stochasticity of emergent spin networks [9] provides a concrete microphysical origin for the collapse process. It suggests the stochasticity required by the collapse model [5–7] is the same stochasticity from which quantum geometry itself emerges.[9] 1Using more precise standard values (c≈2.998 ×108m/s, lPl ≈1.616 ×10−35 m), N(10−32s) ≈ 4.33 ×1023, yielding ln N≈52.95. The order of magnitude ln(1023)≈53 used in Eq. (7) is sufficient. 2When looking at primordial spectra, we could only speculate the lcut ≈30 Gaussian suppression for the CMB. The observed 5-10% power deficit at low-lmultipoles [3], remains an open and unexplained question, with the model cautiously suggesting its cause might not be a delayed classicalisation, but has to be due to other physics (e.g., inflationary dynamics, LQC bounce effects on P(k) [1,2]). 5 4 Conclusion This work demonstrates that a synthesis of Loop Quantum Cosmology, emergent geometry, and entropic collapse models can provide a robust, first principles mechanism for cosmological classicalisation. By identifying the fundamental frequency of the spin network’s stochastic microphysics [9] as the universal cadence (ω≈1043 Hz), a value confirmed by the LQC bounce timescale [1,2]and identifying the entropic hazard rate (α=ωln N) with spin network combinatorics [10], we derive a concrete, time dependent instability. The primary prediction is an instantaneous collapse time (⟨T0⟩ ∼ 10−45 s) during the inflationary epoch, far exceeding the inflationary timescale itself. This entropic instability mechanism naturally delivers the classical, thermal universe required for Big Bang Nucleosynthesis, resolving a foundational dilemma of standard cosmology. The model unifies the stochasticity of collapse with the emergent nature of quantum geometry itself, pointing to a coherent picture of cosmological evolution. Naturally as we have changed a fundamental parameter and discretised the path integral, a new set of completely new calculations and derivations emerges. The development of alternative models and bridges and other internally consistent theories about our cosmos is nascent and still to be explored. 6 References [1] M. Bojowald, ”Loop quantum cosmology,” Living Rev. Relativity, vol. 11, 2008. [2] A. Ashtekar, T. Pawlowski, and P. Singh, ”Quantum Nature of the Big Bang: Improved dynamics,” Phys. Rev. D, vol. 74, p. 084003, 2006. [3] Planck Collaboration, ”Planck 2018 results. VII. Isotropy and Statistics of the CMB,” Astron. 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