Causal Field Theory IV: Quantum Gravity and the Causal Wheeler-DeWitt Equation

We present the first complete quantization of gravity within the framework of Causal Field Theory in the minisuperspace approximation, where spacetime is endowed with a dynamical causal structure described by a scalar field. Starting from the principle of causal optimality, the modified Einstein equations and the causal potential V () = (e^2-1-2) were derived in previous work (Papers I, II, and III). Using the ADM formalism, we obtain the causal Wheeler-DeWitt equation (Eq. ~14 in the main text), where a is the scale factor and is the wave function of the universe. The field is shown to be monotonic, allowing it to serve as an intrinsic quantum clock. A Hermitian time operator t is constructed with an accuracy better than 0. 03\% over the physical domain, transforming the Wheeler-DeWitt equation into a Schr\"odinger equation iₜ = H₏₇ₘₒ. The physical Hamiltonian yields a discrete energy spectrum with 24 bound states and ground state energy E₀ = -3051. 43 (in Planck units). Building on previous work (Papers I, II, and III), the same field unifies dark matter (_=0. 429 from SPARC data), dark energy (ₕ₀₂=0. 3476), the Hubble tension (0. 0786, yielding H₋₎₂₀₋/H₂₌₁ = 1. 0829), and gravitational wave propagation (satisfying the GW170817 bound with |vg-c|/c 210^-24 for LIGO-band frequencies). This work constitutes the first complete quantization of gravity within the causal field framework in minisuperspace, resolving the long-standing problem of time in quantum gravity and eliminating classical singularities. The discrete energy spectrum of the universe emerges as a new quantum prediction, potentially detectable through imprints on the cosmic microwave background.