Non-singular cyclic cosmology: A noncommutative f(R) approach

The present work investigates the implications of incorporating noncommutativity into [Formula: see text] gravity. In particular, we explore the proposed framework in a flat Friedmann–Robertson–Lamaître–Walker background. We introduced the noncommutativity between the coordinates and the momenta, in a [Formula: see text]-dimensional phase space. Applying the machinery of canonical quantization we obtain the noncommutative version of the Wheeler–DeWitt equation, and using a WKB-type approximation we can get analytical solutions for the model examining two cases for the leading noncommutative coefficient. In the first, solutions for the scale factor present a structure similar to previous solutions reported in the literature. The second one, in contrast to its commutative counterpart, the solutions obtained for the scale factor show that its evolution has the behavior of a non-singular cyclic universe. Also, we present the demeanor of the Hubble parameter and the effective equation of state parameter, where the latter crosses the “[Formula: see text]” divide line.