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Bouncing solutions in Rastall's theory with a barotropic fluid

Rastall's theory is a modification of Einstein's theory of gravity where the covariant divergence of the stress-energy tensor is no more vanishing, but proportional to the gradient of the Ricci scalar. The motivation of this theory is to investigate a possible non-minimal coupling of the matter fields to geometry which, being proportional to the curvature scalar, may represent an effective description of quantum gravity effects. Non-conservation of the stress-energy tensor, via Bianchi identities, implies new field equations which have been recently used in a cosmological context, leading to some interesting results. In this paper we adopt Rastall's theory to reproduce some features of the effective Friedmann's equation emerging from loop quantum cosmology. We determine a class of bouncing cosmological solutions and comment about the possibility of employing these models as effective descriptions of the full quantum theory.