The time it takes for a rat to decompose under a deck is around 3 to 4 weeks.
So if you have a dead rat under your deck and cannot get to the dead rat and remove the dead rats body then the rats body will decompose completely within 3 weeks to 4 weeks.
After 4 weeks the rat should be fully decomposed but after a few days the smell of the dead rats body should be gone.
Sometimes I'll have dead rats or mice under my house or deck and although there's a bad smell it's not worth it to go under the house or deck to get to the dead rat.
The smell of the decomposing rats body should go away within a few days and the body of the rat should be fully decomposed within 1 month.