When a new node connects to the network, other nodes start to share new transactions with this new node they got. But do they share their mempool, when a node disconnects from the network for some time for example? I think that the mempool size is too large and it would be difficult to share their mempool state, but maybe I'm wrong...
Think about it that way - transaction could be unconfirmed (is stored in the mempool) or confirmed (kept in block chain). Each new transaction must be populated and known to other nodes - otherwise miners would not be aware given transaction exists and will not be able to include it in their mined blocks.
Why do you think mempool is 'too large' to be synchronised?