The Unified Recursive Cosmological Model (URCM): An Operator-Driven Cyclic Framework for Bounded Entropy and Predicting CMB Anomalies

Note: This is a speculative, but highly mathematically refined new model, based on ΛCDM. These results are based on a reduced-dimensional toy pipeline and are not derived from a likelihood analysis in data space; future forward-modelling with CAMB/CLASS will be required for quantitative validation

The Unified Recursive Cosmological Model (URCM) proposes a cyclic, operator-based framework for cosmology in which entropy is actively bounded and reset each cycle while preserving large-scale structural information. Using a discrete operator stack—comprising Recursive propagation (R′), Projection (P′), Bounce (B′), and Temporal modulation (T^{m′})—URCM generates specific, testable predictions for five cosmic microwave background (CMB) observables: entropy skewness (Sₑ), low-ℓ suppression magnitude (LℓSM), phase-normalised recurrence correlation (PNRC), mid-band spectral divergence (ΔCℓ²), and recursion autocorrelation (RAC). Predictions are initially derived from a simplified toy-spectrum simulation, serving as a proof-of-concept for the model’s predictive framework. Comparisons with Planck PR4 show alignment in key features, with extended discussion including ACT DR6 and WMAP for broader observational grounding. URCM offers a falsifiable, reproducible approach to addressing entropy growth, recurrence, and unexplained CMB anomalies, with a forward path toward full-physics modelling and empirical testing by missions such as LiteBIRD and CMB-S4.