Quantum cosmology in scalar-tensor gravity

We investigate the quantum cosmology of a non-minimally coupled scalar-tensor theory of gravity of the form R + ξ R ϕ 2 within the framework of a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) Universe. Motivated by the emergence of scalar-tensor theories from the low-energy limit of string theory, we employ the canonical quantization formalism to explore the quantum dynamics of this model. Using the Arnowitt-Deser-Misner (ADM) 3+1 decomposition, we derive the Hamiltonian constraint and quantize the system within the Wheeler-DeWitt framework. Due to the non-minimal coupling, the scalar field remains non-trivially entangled with the geometric variables, precluding straightforward variable separation. To address this challenge, we adopt a perturbative approach by expanding the wave function in powers of the coupling parameter ξ . The zeroth-order Wheeler-DeWitt equation is found to be separable and analytically solvable. Although the first-order equation remains coupled and contains a source term dependent on the zeroth-order solution, it is solvable exactly giving the first order correction to the wave function. Importantly, both the zeroth- and first-order wave functions are shown to satisfy the DeWitt boundary condition at the classical singularity, confirming singularity resolution in this framework. These findings lay a promising foundation for investigating the resolution of the cosmological singularity within the broader framework of quantum scalar-tensor cosmology.