A Generalized Framework for Constraining Temporal Screening Mechanisms: Detectability Thresholds and Model Discrimination with DESI

Abstract We introduce and investigate a generalized methodological framework for constraining a class of modified gravity theories characterized by temporal screening mechanisms. These mechanisms implement scale-independent, redshift-dependent coupling evolution, resulting in constant modifications across all cosmological scales at fixed redshift, while evolving sharply across cosmic time. This approach is designed to test the class of theories that employ temporal screening rather than environment-dependent (chameleon, Vainshtein) screening. We demonstrate this methodology using several alternative functional forms, including exponential suppression as a primary worked example. The parameterizations generate distinctive observational signatures including µ(k, z) = µ(z) independent of wavenumber, vanishing gravitational slip Σ ≈ 0, and minimal background expansion modifications ∆H/H ≲ 1%.Fisher forecasts using DESI Year 1 specifications establish a critical detectability threshold (null-boundary) for this entire class of models. We show that a coupling strength of β 0 ≳ 0.2 is required for detection with 2σ -3σ sensitivity using a multi-probe combination. For our fiducial exponential model with β 0 = 0.3 and z tr = 1.5, redshiftspace distortions alone yield σ(β 0 ) = 0.162 (54% uncertainty), while * Independent Researcher, Nice, France. E-mail: