Paper XXXVIII - Early-Universe Boundary Conditions under Empirically Constrained Operational Spacetime

DOI: 10.5281/zenodo.18010400 Early-Universe Boundary Conditions under Empirically Constrained Operational Spacetime Paper XXXVIII of the Ordered-Dynamics Reconstruction Program Paul Cooneya aIndependent Researcher, Innisfil, Ontario, Canada E-mail: paul.co[email protected]to.ca Abstract. We examine early-universe boundary conditions within the Ordered-Dynamics Reconstruction Program (ODRP), conditioned on empirically constrained operational time scaling, distance structure, baryon acoustic oscillations, and growth of structure. Rather than assuming a specific early-universe dynamical model, we classify admissible boundary conditions compatible with late-time operational spacetime and growth observables. By separating boundary conditions from dynamics, we demonstrate that multiple classes of early-time states remain viable without invoking inflation, dark energy, or a specific metric expansion history. This work establishes a controlled and falsifiable interface between late-time empirical reconstruction and early-universe physics. Contents 1 Program context 1 2 Boundary conditions versus dynamics 1 3 Operational early-time limit 2 4 Classification of admissible boundary conditions 2 4.1 Smooth continuation boundary conditions 2 4.2 Asymptotically static boundary conditions 2 4.3 Rapid-transition boundary conditions 2 4.4 Excluded boundary conditions 2 5 Observable consequences of boundary-condition classes 3 6 Relation to inflation and alternatives 3 7 Falsifiability and future probes 3 8 Conclusion 3 Contents 1 Program context The Ordered-Dynamics Reconstruction Program (ODRP) proceeds by reconstructing spacetime observables empirically before introducing dynamical assumptions. Papers XXXII– XXXVII complete the first empirical cycle: operational time scaling, distance structure, baryon acoustic oscillations, and growth of structure have been constrained sequentially and shown to be mutually compatible. The present paper extends the program to early-universe physics. Its purpose is not to infer a specific early-universe mechanism, but to identify which classes of boundary conditions are compatible with the empirically constrained late-time operational spacetime and growth behavior. No new observational fits are introduced, and no previously established operators are modified. 2 Boundary conditions versus dynamics In standard cosmological treatments, early-universe physics is often encoded through specific dynamical mechanisms (e.g. inflation) that simultaneously set initial conditions and drive evolution. Within the ODRP, we separate these concepts. Definition 1 (Boundary condition).A boundary condition specifies the allowed initial state of observables or operators at an early reference time without prescribing their subsequent dynamical evolution. – 1 – Definition 2 (Dynamics).Dynamics specifies evolution laws that propagate boundary conditions forward in time. This paper concerns boundary conditions only. 3 Operational early-time limit We consider the operational early-time limit z→zmax, defined as the upper redshift boundary of reliable empirical constraints. The quantity zmax is not assumed to correspond to recombination, a physical singularity, or a preferred cosmological epoch. Operational time scaling g(z), distance operators Dop(z), and growth functions Gop(z) are empirically constrained over a finite redshift range. Early-universe boundary conditions must match onto these operators smoothly at the highest redshifts probed, but need not specify behavior beyond that interface. No assumption is made regarding the existence of a metric time coordinate or a unique origin of cosmic time. 4 Classification of admissible boundary conditions We classify early-universe boundary conditions by their compatibility with the empirically admissible operator space defined in earlier ODRP papers. 4.1 Smooth continuation boundary conditions Boundary conditions in which operational time, distance, and growth operators approach finite, smooth limits as z→zmax. These conditions do not require rapid early-time evolution or horizon-crossing mechanisms. 4.2 Asymptotically static boundary conditions Boundary conditions in which operational time scaling saturates at early times, leading to an effectively static early universe from the operational perspective, without implying a globally static spacetime. 4.3 Rapid-transition boundary conditions Boundary conditions permitting sharp but finite transitions in operational scaling prior to the observational window, provided these transitions do not induce inconsistencies with late-time BAO or growth constraints. 4.4 Excluded boundary conditions Boundary conditions that require divergent operational distances, discontinuous time scaling, or growth behavior incompatible with empirically constrained late-time observables are excluded. – 2 – 5 Observable consequences of boundary-condition classes Although this paper does not introduce new observational fits, different classes of earlyuniverse boundary conditions imply qualitatively distinct observational signatures as empirical reach expands. Smooth continuation boundary conditions predict no enhanced horizon-scale phase correlations beyond those already constrained by late-time BAO and growth data. Asymptotically static boundary conditions generically suppress early-time growth normalization, leading to reduced high-redshift clustering amplitudes relative to late-time extrapolation. Rapid-transition boundary conditions may imprint scale-dependent correlations or phase features that could become detectable through high-redshift structure or horizon-scale probes. These distinctions render early-universe boundary conditions empirically meaningful rather than purely classificatory. 6 Relation to inflation and alternatives Inflationary models represent one class of dynamical mechanisms capable of producing admissible boundary conditions. However, the ODRP framework does not privilege inflation. Previous work questioning inflation typically proposes alternative early-time dynamics. The present analysis differs by conditioning early-universe boundary conditions on late-time operational spacetime and growth constraints derived independently of any early-universe assumptions. Inflation is therefore sufficient but not necessary within the broader space of admissible boundary conditions. 7 Falsifiability and future probes Early-universe boundary conditions become falsifiable through: •extension of growth measurements to higher redshift, •improved BAO measurements approaching the early universe, •horizon-scale probes sensitive to early-time causal structure. A boundary-condition class is falsified if it cannot be matched smoothly onto the empirically constrained late-time operators without inducing inconsistency in clocks, distances, or growth behavior. In this way, early-universe physics becomes progressively testable without retroactive modification of established empirical results. 8 Conclusion We have classified early-universe boundary conditions compatible with the empirically constrained operational spacetime and growth structure established by the Ordered-Dynamics Reconstruction Program. By separating boundary conditions from dynamics, the ODRP permits a broad class of viable early-universe states without committing to a specific inflationary or expansion-driven model. – 3 – This paper establishes a controlled and falsifiable interface between late-time empirical reconstruction and early-universe physics, enabling future data to progressively constrain boundary conditions without circular inference. References [1] G. F. R. Ellis, Issues in the Philosophy of Cosmology,Handbook of the Philosophy of Science (2014), arXiv:1303.7132. [2] S. Hollands and R. M. Wald, An alternative to inflation,Gen. Rel. Grav. 34 (2002) 2043–2055, arXiv:gr-qc/0205058. [3] I. M. H. Etherington, On the Definition of Distance in General Relativity,Philos. Mag. 15 (1933) 761–773. [4] P. Cooney, Synthesis of Operational Time and Distance Constraints, Zenodo (2025). [5] P. Cooney, Baryon Acoustic Oscillations and Operational Distance Scales, Zenodo (2025). [6] P. Cooney, Growth of Structure under Operational Time–Distance Constraints, Zenodo (2025). [7] P. Cooney, Early-Universe Boundary Conditions under Empirically Constrained Operational Spacetime, Zenodo (2025). – 4 –