f(T) Quantum Cosmology

We quantize a flat cosmological model in the context of $f(T)$ theory of modified gravity using the Dirac’s quantization approach for Hamiltonian constraint systems. In this regard, first we obtain the Wheeler-DeWitt equation as the operator equation of the Hamiltonian constraint and solve it for some typical cosmological models of $f(T)=T-2\mathrm{\Lambda }$, $f(T)=\beta \sqrt{-2T}$ and $f(T)=\gamma T^2$. Then, in the context of classical-quantum correspondence, we interpret the obtained wavefunctions of the universe to describe an accelerating de Sitter universe which is found to be in good agreement with $f(T)=T-2\mathrm{\Lambda }$ model. Finally, we study Bohm–de Broglie interpretation of the quantum model for $f(T)=T-2\mathrm{\Lambda }$ model.