Turbulence Inhibits Planetesimal Formation in Class 0/I Disks Subject to Infall

There is growing evidence that planet formation begins early, within the $\lesssim 1$Myr Class 0/I phase, when infall dominates disk dynamics. Our goal is to determine if Class 0/I disks reach the conditions needed to form planetesimals ($\sim 100$km planet building blocks) by the streaming instability (SI). We focus on a recent suggestion that early infall causes an ``inflationary'' phase in which dust grains are advected outward. We modified the \texttt{DustPy} code to build a 1D disk that includes dust evolution, infall, and heating and cooling sources. We ran six models and examined the implications for the SI, taking into account recent works on how the SI responds to external turbulence. In line with other works, we find that grains are advected outward, which leads to ``advection-condensation-drift'' loop that greatly enhances the dust density at the water snowline. However, we do not see this process at the silicate line. Instead, we find a new pile up at the edge of the expanding disk. However, despite these localized enhancements, even a modest amount of turbulence ($\alpha = 10^{-3}$) leaves planetesimal formation far out of reach. The midplane dust-to-gas ratio is at least an order of magnitude below the SI threshold, even taking into account recent results on how dust coagulation boosts the SI. For planetesimals to form in the Class 0/I phase may require a way to transport angular momentum without turbulence (e.g., disk winds) or a non-SI mechanism to form planetesimals.