Cosmology with non-minimal coupled gravity: dynamical study of the inflationary universe in the deformed phase space scenario

Abstract

In this work, we consider a noncommutative (NC) inflationary model with a homogeneous scalar field non-minimally coupled to gravity. We propose to use a canonical deformation between momenta in a spatially flat Friedmann–Le maitre–Robertson–Walker universe. This particular choice of noncommutativity allows interesting dynamics that other NC models seem not to allow. In this approach, the dimensional parameter $$\theta $$ , which considered as the length of Planck, presents the quantum regime. But also, it is crucial to recover the standard results by taking the appropriate limits of this parameter. To note that the $$1\mathrm{st}$$ Friedmann equation remains unaffected while both the Friedmann acceleration and the Klein-Gordon equations are affected by an additional term linear in the NC parameter.