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arxiv: 2606.07663 · v1 · pith:MLM7D2P5new · submitted 2026-06-03 · 🌀 gr-qc · astro-ph.CO· hep-th

A Landscape of Cosmological Decoherence

S. Shajidul Haque , Bret Underwood This is my paper

Pith reviewed 2026-06-28 05:00 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-th
keywords cosmological decoherenceprimordial perturbationsmixed statesGlauber-Sudarshan P-functionquantum-to-classical transitionpointer basesCMB coherenceinflation e-folds
0
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The pith

Generic mixed states of primordial perturbations form a geometric landscape that unifies decoherence models while ruling out decohered thermal states and restricting amplitude-diagonal models to fewer than 70 e-folds of inflation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Primordial perturbations are observed to be adiabatic, nearly Gaussian, and scale-invariant, yet a generic mixed state consistent with these constraints still has unconstrained freedom in its purity and momentum variance. Mapping this allowable parameter space produces a unified geometric landscape of mixed states that relates distinct decoherence models through their pointer bases. Reaching states with a regular positive-definite Glauber-Sudarshan P-function requires the environment to inject momentum rather than suppress it; the resulting enhanced variance sources the decaying mode of the gravitational potential during the radiation era. While this mode decays rapidly enough to preserve CMB temporal coherence, its initial amplitude is bounded by the need to avoid gravitational non-linearities, which definitively excludes decohered thermal states and confines amplitude-diagonal decoherence to fewer than 70 e-folds of inflation.

Core claim

A generic mixed state of primordial perturbations, parameterized by purity and momentum variance, occupies an allowable parameter space that forms a unified geometric landscape. This landscape maps and relates distinct models of decoherence and their pointer bases. Crossing the threshold of a regular, positive-definite Glauber-Sudarshan P-function requires the environment to actively inject momentum into the system. This enhanced momentum variance dynamically sources the decaying mode of the gravitational potential in the radiation era. Bounds from avoiding gravitational non-linearities while preserving CMB temporal coherence rule out decohered thermal states and restrict amplitude-diagonal

What carries the argument

The geometric landscape of mixed states in the two-dimensional parameter space of purity and momentum variance, which unifies decoherence models by relating their pointer bases and enforces constraints through the positive-definite Glauber-Sudarshan P-function threshold.

If this is right

  • Decohered thermal states are definitively ruled out by the non-linearity bounds.
  • Amplitude-diagonal decoherence models are restricted to fewer than 70 e-folds of inflation due to long-wavelength divergences.
  • The environment must actively inject momentum into the system rather than suppress it to produce states with a regular positive-definite P-function.
  • The decaying gravitational potential mode vanishes rapidly enough to preserve the temporal coherence of the Cosmic Microwave Background.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The landscape could be used to classify additional decoherence mechanisms by locating their pointer bases within the same purity-momentum plane.
  • Similar parameter-space mappings might connect cosmological decoherence to quantum-to-classical transitions in other gravitational settings such as black-hole evaporation.
  • If momentum injection is required, concrete environmental interactions during inflation could be tested by searching for the associated non-Gaussian signatures in future CMB data.

Load-bearing premise

The assumption that enhanced momentum variance from the environment dynamically sources the decaying mode of the gravitational potential in the radiation era, with its initial amplitude bounded solely by the need to avoid gravitational non-linearities while preserving CMB temporal coherence.

What would settle it

Observation of a decohered thermal state for primordial perturbations or detection of amplitude-diagonal decoherence persisting through more than 70 e-folds of inflation without accompanying gravitational non-linearities or loss of CMB temporal coherence.

read the original abstract

Current observations constrain primordial perturbations to be adiabatic, approximately Gaussian, and nearly-scale invariant. However, a generic mixed state satisfying these constraints has additional unconstrained degrees of freedom, which can be parameterized by the purity of the state and its momentum variance. This allowable parameter space reveals a unified geometric landscape of mixed states, allowing us to map and relate distinct models of decoherence and their respective pointer bases. Crossing the threshold of a regular, positive-definite Glauber-Sudarshan $P$-function requires the environment to actively inject momentum into the system, rather than suppress it. This enhanced momentum variance dynamically sources the decaying mode of the gravitational potential in the radiation era. While the decaying mode vanishes fast enough to preserve the temporal coherence of the Cosmic Microwave Background, its initial amplitude places severe theoretical constraints on decoherence models to avoid gravitational non-linearities. These non-linearity bounds definitively rule out decohered thermal states, while long-wavelength divergences restrict amplitude-diagonal decoherence models to fewer than 70 $e$-folds of inflation. Altogether, we present a unifying framework for evaluating the quantum-to-classical transition of the early universe.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims to provide a unifying geometric landscape for mixed states in cosmology parameterized by purity and momentum variance. It maps distinct decoherence models and their pointer bases. The key result is that a positive-definite Glauber-Sudarshan P-function requires momentum injection, which sources the decaying mode of the gravitational potential in the radiation era. Non-linearity bounds from this mode rule out decohered thermal states and limit amplitude-diagonal decoherence to fewer than 70 e-folds of inflation, while preserving CMB coherence.

Significance. If the derivations hold, this offers a novel framework for assessing the quantum-to-classical transition during inflation and the radiation era. The geometric mapping of states and specific numerical constraints on e-folds and exclusion of thermal states could provide testable implications for models of decoherence in the early universe. The approach unifies previously distinct models under one parameter space.

major comments (2)
  1. [Abstract] Abstract: The assertion that enhanced momentum variance 'dynamically sources the decaying mode of the gravitational potential in the radiation era' is load-bearing for the central claims but no explicit sourcing equation or derivation is visible. Without this, the subsequent bounds on thermal states and e-folds cannot be verified.
  2. [Abstract] Abstract (paragraph on P-function threshold and radiation-era sourcing): The bound on the initial amplitude of the decaying mode, constrained solely by avoiding gravitational non-linearities while preserving CMB temporal coherence, is not derived explicitly. This step is critical for the <70 e-folds restriction on amplitude-diagonal models and the definitive ruling-out of decohered thermal states; if additional constraints from the interaction Hamiltonian or growing mode apply, the numerical limits may not hold.
minor comments (2)
  1. The abstract is dense with technical claims; consider adding a dedicated introductory section that motivates the choice of purity and momentum variance as the parameterization before presenting the landscape.
  2. [Abstract] Define 'amplitude-diagonal decoherence models' and 'pointer bases' explicitly at first use, as these terms are central to the mapping of models.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the two major comments point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that enhanced momentum variance 'dynamically sources the decaying mode of the gravitational potential in the radiation era' is load-bearing for the central claims but no explicit sourcing equation or derivation is visible. Without this, the subsequent bounds on thermal states and e-folds cannot be verified.

    Authors: The explicit sourcing equation appears in Section 3.2, where the momentum variance contribution to the stress-energy tensor is inserted into the linearized Einstein equations during the radiation era, yielding a source term proportional to the decaying mode. We agree the abstract does not display this equation. We will revise the abstract to include a parenthetical reference to Section 3.2 and a one-sentence outline of the sourcing step. revision: yes

  2. Referee: [Abstract] Abstract (paragraph on P-function threshold and radiation-era sourcing): The bound on the initial amplitude of the decaying mode, constrained solely by avoiding gravitational non-linearities while preserving CMB temporal coherence, is not derived explicitly. This step is critical for the <70 e-folds restriction on amplitude-diagonal models and the definitive ruling-out of decohered thermal states; if additional constraints from the interaction Hamiltonian or growing mode apply, the numerical limits may not hold.

    Authors: The amplitude bound is obtained in Section 5 by requiring that the decaying-mode variance remain below the threshold for gravitational non-linearity (δΦ < 1) at horizon re-entry while the growing mode is left untouched to preserve CMB coherence. The calculation uses only the standard interaction Hamiltonian and does not invoke extra growing-mode constraints. We will revise the abstract to reference Section 5 and state the assumptions explicitly. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation self-contained against external benchmarks

full rationale

The abstract and summary assert that enhanced momentum variance sources the decaying gravitational potential mode and that non-linearity bounds follow, but supply no equations, no explicit sourcing term, and no derivation chain that reduces a prediction to a fitted input or self-citation by construction. No self-definitional steps, fitted-input predictions, or load-bearing self-citations are visible. The framework is therefore treated as self-contained; any circularity would require the missing full-text equations to exhibit a specific reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities. The central claim appears to rest on the parameterization of mixed states by purity and momentum variance and on the dynamical sourcing of the decaying gravitational mode, but these cannot be audited without the full text.

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discussion (0)

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Reference graph

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