  We show that the f(T) gravitational paradigm, in which gravity is described
by an arbitrary function of the torsion scalar, can provide a mechanism for
realizing bouncing cosmologies, thereby avoiding the Big Bang singularity.
After constructing the simplest version of an f(T) matter bounce, we
investigate the scalar and tensor modes of cosmological perturbations. Our
results show that metric perturbations in the scalar sector lead to a
background-dependent sound speed, which is a distinguishable feature from
Einstein gravity. Additionally, we obtain a scale-invariant primordial power
spectrum, which is consistent with cosmological observations, but suffers from
the problem of a large tensor-to-scalar ratio. However, this can be avoided by
introducing extra fields, such as a matter bounce curvaton.
