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The "$\phi^2$" slow roll inflation combined with General Relativity islargely excluded by Planck data. In this paper, we consider the same potentialcombined with the $R+C^2$ gravity of purely virtual particles (or fakeons),where the would-be ghost introduced by the Weyl tensor term, $C^2$, isquantized with the fakeon prescription. We compute the tensor power spectrum inthe full theory by means of the Cosmic Renormalization Group formalism andcritically examine its physical meaning. In particular, we show that it is notpossible to retrieve the power spectrum of the fakeon free-theory byconsidering the decoupling limit of the purely virtual particles. We provide aphysical explanation in terms of the causal structure of the theory to inferthat a model of quadratic inflation from purely virtual particles is alsodiscarded from a phenomenological point of view.

Causality Bounds in Quadratic Inflation from Purely Virtual Particles