  Understanding planetesimal formation is an essential first step to
understanding planet formation. The distribution of these first solid bodies
will drive the locations where planetary embryos can grow. We seek to
understand the parameter space of possible protoplanetary disk formation and
evolution models of our Solar System. A good protoplanetary disk scenario for
the Solar System must meet at least the following three criteria: 1) an
extended dust disk (at least 45 au); 2) formation of planetesimals in at least
two distinct locations; and 3) transport of high temperatures condensates
(i.e., calcium-aluminium-rich inclusion, CAIs) to the outer disk. We explore a
large parameter space to study the effect of the disk viscosity, the timescale
of infall of material into the disk, the distance within which material is
deposited 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 small
centrifugal radius ($R_C\sim0.4$~au; the distance within which material falls
into the disk) result in disks that satisfy the criteria for a good
protoplanetary disk of the Solar System. The large initial viscosity and short
infall timescale result in a rapid initial expansion of the disk, which we dub
the inflationary phase of the disk. Furthermore, a temperature-dependent
fragmentation threshold, which mimics that cold icy particles break more
easily, results in larger and more massive disks. This results in more "icy"
than "rocky" planetesimals. Such scenarios are also better in line with our
Solar System, which has small terrestrial planets and massive giant planet
cores. Finally, we find that scenarios with large $R_C$ cannot transport CAIs
to the outer disk and do not produce planetesimals at two locations within the
disk.
