GeNeSyS — An Emergent Geometric Framework for the Late-Time Cosmological Background

GeNeSyS — An Emergent Geometric Framework for the Late-Time Cosmological Background Updated release including Supernovae and BAO confrontation General description This repository presents the current consolidated state of the GeNeSyS framework (Geometric Nonlocal System with causal memory), an effective cosmological model in which the phenomena commonly attributed to dark matter and dark energy emerge from the causal, nonlocal response of spacetime geometry itself, without introducing new fundamental particles, fields, or a cosmological constant. GeNeSyS is formulated as a late-time, post-primordial effective framework, defined at the level of the homogeneous and isotropic Friedmann–Robertson–Walker (FRW) background. It preserves local general relativity and standard baryonic and radiative sectors, while allowing the cosmological dynamics to depend on the causal history of curvature through well-defined, covariant memory operators. The central hypothesis is that gravity does not necessarily respond instantaneously to curvature variations on cosmological timescales. Instead, part of the expansion dynamics can arise from retarded geometric memory effects, encoded through causal Volterra-type operators acting on geometric scalars. These effects are finite, causal, regular, and saturating, and do not introduce propagating microphysical degrees of freedom. Within this framework, the large-scale expansion of the Universe is driven exclusively by spacetime geometry and ordinary matter. No non-baryonic dark matter particles, no fundamental dark energy component, and no cosmological constant are postulated. The standard Friedmann structure is preserved, while the effective dark sectors arise dynamically as emergent geometric contributions. Emergent geometric structure Two distinct effective geometric contributions are identified at the background level: A fast gravitational condensate (MC) Generated by the rapid response of a causal kernel, this contribution produces an effective matter-like behavior at late times, diluting asymptotically as a−3a^-3a−3. It reproduces the kinematic role of dark matter at the background level without introducing additional matter species. A slow gravitational memory (MM) Defined through a strictly causal Volterra integral of the curvature history, this contribution generates an effective negative pressure once it saturates, driving late-time acceleration in a dynamical and bounded manner. Its effective equation of state naturally approaches w≃−1w -1w≃−1 without invoking a cosmological constant. Both sectors are constrained by construction to be negligible at early times, ensuring radiation and matter domination, and guaranteeing compatibility with primordial physics at the background level. New in this release: Supernovae and BAO confrontation This updated release includes a dedicated quantitative confrontation of the GeNeSyS background dynamics with low-redshift cosmological observations. The analysis focuses on: Type Ia supernova luminosity distancesPantheon+SH0ES compilation, using the full covariance matrix and analytical marginalization over the absolute magnitude. Baryon Acoustic Oscillation geometric constraintsBOSS DR12 measurements, using the compressed observables DM/rdDM/rdDM/rd and DH/rdDH/rdDH/rd with their full covariance matrix. The acoustic scale rdrdrd is treated as a nuisance parameter and analytically marginalized, without any primordial calibration. The confrontation is performed through a fully reproducible numerical pipeline, with no dataset-specific tuning and no introduction of additional parameters beyond those defining the geometric memory structure. The results show that the emergent GeNeSyS expansion history provides a statistically consistent description of both supernova and BAO data, with χ2/dof≃1. 03²/dof 1. 03χ2/dof≃1. 03, across a range of external Hubble normalizations (H0=67, 70, 73H₀ = 67, \;70, \;73H0=67, 70, 73 km s−1^-1−1 Mpc−1^-1−1). These results demonstrate that the empirical success of the standard cosmological model at the background level does not uniquely fix the underlying physical interpretation of cosmic acceleration. Contents of this deposit This repository provides the complete reference material corresponding to the current operational and validated state of the GeNeSyS framework. Main documents GeNeSyS Model v10. 1 (EN / FR) Core theoretical document presenting the full causal nonlocal formulation, the gravitational memory kernels, the emergence of the MC and MM sectors, and the complete background equations. GeNeSyS Technical Documentation — Perturbative Closure and Solver Interface (EN / FR) Technical reference specifying the linear perturbation framework, effective stress–energy decomposition, gauge conventions, and Einstein–Boltzmann closure. This document defines a closed perturbative structure but does not present CMB results. GeNeSyS — Supernovae and BAO Analysis (EN / FR) Quantitative SN Ia and BAO confrontation at the background level, including methodology, numerical pipeline, figures, tables, robustness tests, and explicit limitations. For public people: X_GeNeSyS Model v10₆ Public EN. pdf or X_GeNeSyS Model v10₆ Public FR. pdf Numerical implementation and pipelines Background reconstruction and parameter scans Deterministic SN Ia + BAO likelihood pipeline with full covariance treatment Reproducible numerical outputs (CSV, JSON summaries, diagnostic figures) Data archives Pantheon+SH0ES supernova data and covariance matrices BOSS DR12 BAO summary data and covariances Derived background quantities and diagnostic products Scientific status and scope In its present state, GeNeSyS provides: a coherent and well-defined effective description of the late-time cosmological background, a fully specified perturbative framework ready for numerical implementation, and a quantitative validation of its background behavior against supernova and BAO observations. CMB anisotropies, lensing, and structure formation are explicitly outside the validated scope of this release. The framework is therefore to be interpreted strictly as post-primordial and effective. The absence of a successful CMB angular scale reproduction is documented and interpreted as a clear boundary of validity, not as an unresolved inconsistency. This release marks the closure of the background-level validation phase of the GeNeSyS project. Further developments, if any, would necessarily involve independent primordial or perturbative extensions beyond the scope of the present work. Repository and authorship GitHub repository: GeNeSyS / GeNeSyS Model — https: //github. com/eliotchimpel/GeNeSyS Author: Eliot Chimpel / MPI