Non-Markovian Memory-Induced Effects in Quantum Cosmology
We study memory effects in quantum cosmology by extending the semiclassical Wheeler-DeWitt framework beyond its usual local form. The main idea is to introduce a causal memory kernel at sub leading order, rather than imposing fractional derivatives directly by hand. In this setting, fractional time evolution appears as an effective description of the underlying nonlocal dynamics. We apply the framework to cosmological perturbations in de Sitter space and find a correction to the primordial power spectrum with a characteristic $k^{3/4}$ scaling. This contribution mainly affects high $l$ CMB temperature anisotropies, in contrast with standard semiclassical quantum gravitational corrections, which are strongest at large angular scales. We also discuss how the same memory-dependent dynamics may affect primordial non-Gaussianity, producing scale dependent corrections to the bispectrum and possible deviations from the usual squeezed limit consistency relation. Since the memory coefficient controls short scale power, it may also influence structure formation and could require some tuning in order to give phenomenologically acceptable astrophysical environments. Finally, we suggest that a cyclic extension of the Hawking-Hartle no-boundary proposal may provide a setting in which the effective memory strength can evolve across successive cosmological histories. In this way, the framework gives a concrete realization of fractional quantum cosmology based on memory effects and also points to possible observational signatures of nonlocal quantum gravitational dynamics.