  We analyze the model of a self-interacting $\phi^4_{\star}$ scalar field
theory in Snyder-de Sitter space. After analytically computing the one-loop
beta functions {in the small noncommutativity and curvature limit}, we solve
numerically the corresponding system of differential equations, showing that in
this limit the model possesses at least one regime in which the theory is
asymptotically free. Moreover, in a given region of the parameter space we also
observe a peculiar running of the parameter associated to the curvature, which
changes its sign and therefore can be interpreted as a transition from an IR
de-Sitter space to and UV anti-de Sitter one.
