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Without the inflation Even there's CC I think the universe cannot be stable.

I don't understand what you mean by "stable".

The general answer to the question you ask in the OP is that we can model such a universe using the standard FRW models without inflation. The two key characteristics of those models are the universe's spatial geometry (sphere, flat, or hyperbolic), and whether the universe expands forever or recollapses to a Big Crunch.

Without a cosmological constant, these two key characteristics are correlated: spherical spatial geometry == universe recollapses, flat or hyperbolic spatial geometry == universe expands forever.

With a cosmological constant, however, all combinations of the two key characteristics are possible, by tuning the value of the cosmological constant appropriately. Also, it becomes possible to have a static universe (the Einstein static universe) which neither expands nor collapses. However, the static universe is like a pencil balanced on its point: a small perturbation will cause it to either expand forever or collapse to a Big Crunch.