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Understanding planetesimal formation is an essential first step tounderstanding planet formation. The distribution of these first solid bodieswill drive the locations where planetary embryos can grow. We seek tounderstand the parameter space of possible protoplanetary disk formation andevolution models of our Solar System. A good protoplanetary disk scenario forthe Solar System must meet at least the following three criteria: 1) anextended dust disk (at least 45 au); 2) formation of planetesimals in at leasttwo distinct locations; and 3) transport of high temperatures condensates(i.e., calcium-aluminium-rich inclusion, CAIs) to the outer disk. We explore alarge parameter space to study the effect of the disk viscosity, the timescaleof infall of material into the disk, the distance within which material isdeposited into the disk, and the fragmentation threshold of dust particles.  We find that scenarios with a large initial disk viscosity ($\alpha>0.05$),relatively short infall timescale ($T_{infall}<100-200$ kyr), and a smallcentrifugal radius ($R_C\sim0.4$~au; the distance within which material fallsinto the disk) result in disks that satisfy the criteria for a goodprotoplanetary disk of the Solar System. The large initial viscosity and shortinfall timescale result in a rapid initial expansion of the disk, which we dubthe inflationary phase of the disk. Furthermore, a temperature-dependentfragmentation threshold, which mimics that cold icy particles break moreeasily, results in larger and more massive disks. This results in more "icy"than "rocky" planetesimals. Such scenarios are also better in line with ourSolar System, which has small terrestrial planets and massive giant planetcores. Finally, we find that scenarios with large $R_C$ cannot transport CAIsto the outer disk and do not produce planetesimals at two locations within thedisk.

An inflationary disk phase to explain extended protoplanetary dust disks