The Universe Is in a Low Entropy State, Right?

In his books, Roger penrose points out that am the the big bang, the past hypothesis u going back in time. That's where the whole idea of the big bang comes from. The universe started off in an incredibly low enthropy state and is still in a very low entropy state. Symmetries only make sense when you talk about the subseneistion of space,. So your experiments shouldn't really be determined by these symmetries.