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The simplest model of inflation involves a hypothetical, yet undiscovered, single scalar field $\phi$ called \emph{inflaton}. The action of this scalar field minimally coupled to gravity is given by $$S[\phi,g]=\int d^4x\sqrt{-g}[\frac{1}{2}\mathcal{R}+\frac{1}{2}g_{\mu\nu}\partial^\mu\phi \partial^\nu\phi-V(\phi)-\mathcal{L}_{\phi-\text{matter}}]$$ $$=S_{EH}+S_{\phi}+S_{\phi-matter}$$ Why is it that in the discussion of inflation, one often neglects the coupling of the matter field with $\phi$ i.e., $S_{\phi-matter}$?

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Coupling to matter is neglected during the inflation because there is no matter. All matter is produced after inflation, during the reheating (and preheating) phase, when inflaton oscillates around the minimum of the potential and decays into the matter particles.

I suggest this review of the topic. Although you can find it in other standard cosmology textbooks and lecture notes.

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