Exploring Quantum Cosmology within the Framework of Teleparallel $f(T)$-gravity

TL;DR

This paper develops a quantum cosmology framework within teleparallel $f(T)$-gravity, deriving the universe's wave function and exploring its potential to resolve classical singularities.

Contribution

It formulates the Hamiltonian and quantum description of $f(T)$-gravity cosmology using the Dirac-Bergmann algorithm, a novel approach in this context.

Findings

Derived the universe's wave function in $f(T)$-gravity

Compared quantum solutions with classical singularities

Proposed a probabilistic interpretation of the wave function

Abstract

We investigate quantum cosmology in teleparallel $f(T)$-gravity. We delve extensively into the minisuperspace description within the context of teleparallelism. The $f(T)$-theory constitutes a second-order theory of gravity, whose cosmological counterpart is delineated by a degenerate point-like Lagrangian. To formulate the Hamiltonian function encompassing all constraints and degrees of freedom inherent to $f(T)$ cosmology, we employ the Dirac-Bergmann algorithm. Subsequently, we determine the wave function of the universe and introduce a ``probabilistic'' interpretation. We perform comparisons to some classical solutions to see to what extent the quantum approach can cure classical singularities.