Am I correct in understanding that in the cosmological version of Loop quantum gravity, namely Loop quantum cosmology, the universe in all models starts with a big bounce? Are there other models, for example, the pre-big bang condition with unconnected loops?
Loop Quantum Cosmology is a finite, Symmetry reduced model of LQG, which for a layman means it arose from Loop Quantum Gravity. It predicts a Quantum bridge between the Expansion and the Contraction of the Cosmological branches. So, instead of having Big Bang, you have a Big Bounce. Loop Quantum Cosmology aims to describe a lot more than Bounce, it mathematically describes the Inflation in the Early Universe. For more, you can read the articles of Francessca Vidotto and Aurelien Barrau. The first Link is given here. https://tel.archives-ouvertes.fr/tel-01737503. They talk about some basic aspects of Loop Quantum Cosmology and the Loop Quantum Cosmology aspects of the Dark Universe