What is the Optimal block size based on 90 percentile block propogation delay? We can have pruned nodes that can verify blocks and transactions so the block size can be increased without leading to the centralization of block verification.
But if we increase block size then block verification time and propagation delay will increase. It will increase the probability of two miners mining a block simultaneously and also delay the competing blockchain branches to resolve the dispute. Probably any increase in block propagation delay will increase the time to resolve disputes exponentially.
Based on a website (Can't remember) currently, block propagation delay is 5 seconds to reach 90% nodes which may increase to 15-20 seconds if all transactions were Segwit.
I think block propagation delay is the only limiting factor in increasing block size.
Has anyone done an investigation to find out the relationship between block propagation delay and optimal block size?
I think block propagation delay is the only limiting factor in increasing block size.

This assumption is not accurate. While block propagation time is an important parameter for fair competition among miners, the block size also affects initial synchronization times of new nodes, disk space for archival nodes, and bandwidth (especially upload) requirements for all node operators.
Block propagation between miners should preferably take less than a second, but I don't think the block size and propagation are as related as the question surmises and thus consider the main question to be unanswerable.