Making the block reward dependent on the difficulty?

Question

I am looking for papers which discuss, if making the block rewards dependent on the difficulty could be used to curb excessive PoW growth.

Idea is that BTC price roughly drives difficulty and energy consumption proportionaly. If the block rewards would decrease with difficulty (like in reward=(a+b/difficulty) with suitable constant values for aand b) then it would become much faster unprofitable to add more hash power, thus curbing the growth of total hash power and energy consumption.

This must have been discussed somewhere before, but I can not find anything related.

Answer 1

Your approach is interesting however to have a significant energy-consumption decrease you need to have a signficiant reward decrease which will involve a significant hash power decrease since then the security would have a significant decrease (because any old high hash power organization like current mining pool could "easily" reach 51 % of hash power of the total network hash power cf https://en.wikipedia.org/wiki/Double-spending#51%_attack)

Answer 2

Difficulty is proportional to hash power. If buying more hash power doesn’t increase difficulty but reduces you profit it wouldn’t make sense to invest but in a larger scale it would kind of correlate the halving with the hash power. But not every 4 years or so. And the total amount of coins would be unknown but still capped when a certain hash limit is reached.