Interacting quantum scalar field theories in $dS_Dtimes M_d$ spacetime can be reduced to Euclidean field theories in $M_d$ space in the vicinity of $I_+$ infinity of $dS_D$ spacetime. Using this non-perturbative mapping, we analyze the critical behavior of Euclidean $lambdaphi_4^4$ theory in the symmetric phase and find the asymptotic behavior $beta(lambda)sim lambda$ of the beta function at strong coupling. Scaling violating contributions to the beta function are also estimated in this regime.
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