The classical and quantum implications of the Raychaudhuri equation in f(T)-gravity

The present work deals with the classical and quantum aspects of the Raychaudhuri equation (RE) in the framework of f ( T )-gravity theory. In the background of homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker space-time, the RE has been formulated and used to examine the focusing theorem and convergence condition for different choices of f ( T ). Finally in quantum cosmology, the wave function of the Universe has been shown to be the energy eigen function of the time-independent Schrödinger equation of a particle. Also probability measure on the minisuperspace has been examined at zero volume for singularity analysis in the quantum regime. Lastly, the Bohmian trajectory for the present quantum system has been explicitly determined for some particular choices.