I have a question about Proof of Stake.

Are there any protections against a user just creating an entirely new chain, since there is no computational penalty for creating a really long chain, couldn't a malicious actor create a chain larger than the one most nodes agree on with a completely different history?
Or remove past transactions easily? Does Casper or other PoS implementations just have nodes check against their existing chains to check that they haven't been fully altered?

Because the proof of work protects against this by making it extremely time confusing to change one block because you have to redo all the proofs for each block in front of it, but if you don't need to do a large amount of CPU work to change history, couldn't nodes give new nodes a blockchain missing a block or transaction?