The Integrated Sachs–Wolfe Effect without Dark Energy: A Causal Gradient Prediction

We present a first-principles, analytic explanation of the late-time Integrated Sachs–Wolfe (ISW) effect within the Spacetime Flow Hypothesis (SFH) — a Lorentz-invariant field-theoretic framework in which gravity and cosmological redshift arise from spatial and temporal variations in the flow of proper time, encoded in a scalar resistance field α(x), rather than from metric expansion or dark energy. Recent high-precision stacking analyses of supervoids, superclusters, and filaments using Planck, DESI, and SDSS data reveal a coherent ISW pattern that is opposite to ΛCDM predictions: hot void cores, cold clusters and filaments, sign-reversing rings, and a universal three-zone radial morphology. These features now reach a combined significance of approximately 6σ across independent void, cluster, and filament analyses (e.g. Kovács et al. 2022; Hung et al. 2024; Planck 2024 legacy stacks) and constitute a multi-sign crisis for potential-decay–based cosmology. Building on the Phase-I (linear, analytic) limit of SFH, we derive the ISW temperature shift as a line-of-sight projection of gradients in the α-field. In this formulation: The sign of the ISW signal is fixed by geometry and is not tunable. The ring structures and three-zone morphology arise automatically from α-gradient sign reversals at void and cluster boundaries. No ISW-specific parameters or normalizations are introduced. Crucially, the amplitude and angular scale of the ISW signal follow from the same α-field parameters independently required to explain supernova redshift evolution and the local H₀ tension, establishing ISW as a cross-domain prediction rather than a fit. Because ISW relies solely on CMB temperature anisotropies, the cleanest dataset in cosmology, this result provides one of the most direct observational probes of late-time gravitational physics currently available. Within SFH, the ISW anomaly is transformed from a statistical tension into direct empirical evidence for gradient-driven gravity. This work is explicitly limited to the analytic, weak-field regime and motivates Phase-II development of a full nonlinear α-field cosmology solver, enabling map-level predictions and α-field reconstruction from large-scale structure. Foundational Theory Spacetime Flow Hypothesis — Core Field-Theoretic Framework. DOI : https://doi.org/10.5281/zenodo.17626069 Defines the flow-field, scalar resistance α(x), drift law, energy conservation, and Lagrangian. Empirical Validation Gravitational Wave Orbital Decay — Binary pulsars (leading-order agreement with GR from first principles). DOI: https://doi.org/10.5281/zenodo.18214948 SN1a — Luminosity distance + time dilation (χ²/dof = 0.934). DOI: https://doi.org/10.5281/zenodo.18217479 Galaxy Rotation Curves — 20/20 fits without dark matter. DOI: https://doi.org/10.5281/zenodo.17014960 Gravitational Lensing Time Delays — 10 strong-lens delays from baryons only. DOI : https://doi.org/10.5281/zenodo.17849232 Predictive Frontier (New V2) Fast-Flow Bubble — Local void explains Hubble tension (11σ match to Pantheon+ residuals). DOI : https://doi.org/10.5281/zenodo.18136251 (New) Filament Rotation — Cosmic filaments rotate only when ∇α is asymmetric. DOI : https://doi.org/10.5281/zenodo.18452749 Together with prior empirical validations of SFH across binary pulsars, supernova time dilation, galaxy rotation curves, gravitational lensing delays, and large-scale ISW correlations, the present filament-rotation result supports a unified, causal interpretation of gravity based on gradients in the flow of proper time. Version 2 (January 2026). This revision incorporates clarifications in Sections 4–6, adds explicit comparisons with recent (2024–2025) ISW stacking analyses, expands the reference list, and improves figure placement and internal consistency. No scientific conclusions are changed relative to Version 1.