I have read the paper and discuss it with colleagues earlier today. I think that the wording 'pre-big-bang' has just been used to get a buzz. Cosmic inflation is actually right after the big bang and not before it. At least to my knowledge on how it is usually used.
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This is correct. Strictly speaking, the "before big bang" is undefined. Note that there are as well alternative cosmologies without a big bang.
Dwarf galaxy problem
The dwarf galaxy problem, also known as the missing satellites problem, arises from a mismatch between observed dwarf galaxy numbers and numerical cosmological simulations that predict the evolution of the distribution of matter in the universe. In simulations, Dark matter clusters hierarchically, in ever increasing numbers of halo "blobs" as halos' components' sizes become smaller-and-smaller. However, although there seem to be enough observed normal-sized galaxies to match the simulated size distribution, the number of dwarf galaxies is orders of magnitude lower than expected from simulation.