The Time-Symmetric Parity Constraint I : the Twin-Time Theory of Cosmology – on the loss and recovery of constraint in modern cosmology; a compendium of papers

Summary — 

This compendium (Papers 1–21) defines and develops the Time-Symmetric Parity Constraint (TSPC): a geometric framework in which the universe’s observed anomalies are re-expressed as structural consequences of a fixed algebraic condition imposed on the spacetime metric. The proposal is not an extension of the standard model, but a radical separation from it. Dark energy, particulate dark matter, and inflation are not adjusted; they are rendered unnecessary by geometric admissibility.

Papers 2–10 establish the constraint and derive its consequences. Papers 11–16 move from derivation to falsifiability, testing whether lensing, void geometry, gravitational waves, dipoles, and cosmic chronometers conform to the imposed symmetry. Papers 18–21 confront specific high-profile claims in contemporary cosmology, asking directly whether they survive once parametric flexibility is removed.

Additional standalone papers, listed separately, extend this programme beyond the present volume. They apply the same restriction to further datasets and to the methodological architecture of survey-era cosmology itself. The compendium sets the boundary; the extended papers force the theory up against it. If the geometry fails, it fails outright. If it holds, the standard cosmological narrative does not.

Recent substantive updates — 

v.9 (2025-11-27) - Corrections to Paper 14: The Galactic-Centre Gamma Excess Reconsidered, clarifying the findings of Muru et al. (2025) on the morphology of the Galactic-centre γ-ray excess, together with the addition of a footnote noting recent claims by Tomonori Totani (2025) of a high-latitude annihilation signal. Explaining why these claims do not affect the analysis presented.

v.10  (2025-12-04) Paper 2, Sections 2–3 updated to state Π as fixed and primitive, and to clarify the resulting exclusions for admissible metrics (e.g. Gödel, anisotropic cases).

v.11 (2025-12-05) Paper 8 updated with ACT DR6 constraints on early-Universe models; Paper 14 adds recent mid-IR flare and extinction results, further tightening the astrophysical interpretation of the Galactic-Centre excess. No changes have been made to the core TSPC framework.

v.13 (2025-12-11) Minor revisions: added rebuttal of the ΛCDM timing argument in Paper 9 and clarified the Bullet Cluster discussion in Paper 10, removing dark-halo assumptions.

v.20  Brief illustrative example inserted into Section 4 of Paper 9 of a recent high-redshift Sunyaev–Zeldovich detection, cited cautiously as additional pressure on permissible structure-growth histories. No effect on the paper’s core H₀–S₈ argument.

v.21  Clarifications and refinements to Papers 2 and 3, tightening the algebraic formulation of TSPC and its enforcement at the level of the action. Paper 17 updated to include a brief abstract and minor editorial revisions to the concluding discussion. No change in any substantive result or empirical claim.

v.24  Paper 9 corrected to show the H₀ and S₈ tensions arise as linked inference effects, reflecting a bias in the mapping between early-time calibration and late-time observables imposed by the parity constraint, rather than from a physical suppression or enhancement of growth. No changes have been made to the algebraic framework, the definition of the structural parameter α_λ, the field equations, or the core Time-Symmetric Parity Constraint. All other papers in the compendium remain unaffected.

v.27  Section 3 of Paper 9 has been revised to clarify the distinction between structural and parameter-based responses to the H₀ and S₈ tensions. Recent work invoking dynamical dark energy and dark-sector interactions is briefly discussed as representative explainaway strategies within a fixed geometric framework, sharpening the contrast with the correlated expansion–growth shifts predicted by the Time-Symmetric Parity Constraint. The same section also now distinguishes early-time sound-horizon recalibration from the gravity-sector modification implied by TSPC. The discriminator is clarified: models that elevate H₀ through rₛ reduction without a correlated shift in growth favour early-ruler explanations; TSPC predicts linked departures in H(z) and fσ₈(z) once α_λ is fixed. This strengthens the falsifiability statement and situates the framework explicitly against current Nature-level proposals.

v.28  Paper 3 subsection 6.1. Added contextual reference to Jedamzik, Pogosian and Abel (2025) on primordial magnetic-field effects on recombination and sound-horizon calibration.

Paper 13 section 3. Clarified that strong-lensing reconstructions are model-dependent and subject to degeneracies (following Falco, Gorenstein & Shapiro 1985), meaning that multiple mass distributions can reproduce the same image configuration. At subsection 3.6 added a recent comparative example of complex image multiplicity from the strongly lensed supernova SN 2025wny. No change to the core argument or conclusions.

Paper 21 Section 3.  Revised to include a brief reference to Zhang, Zonoozi and Kroupa (2026) on MOND cluster mass estimates, illustrating how discrepancies in cluster dynamics may be mitigated through revised baryonic modelling while the underlying FLRW geometric framework remains unchanged. Minor editorial tightening; no change to the argument or conclusions.