I've been idly speculating about what would be the largest number to have any meaning, and I figured it would be the number of universes created via the "many worlds hypothesis" since the dawn of time.
I'm not a physicist, but there are some thoughts I'd had on sketching it out:
The number of elementary particles created in the big bang (1088?)
The number of ways in which they can interact. (based on the laws of physics)
The total number of initial interactions within the first planck time after creation
The number of possible conseqences to those interactions
The number of possible consequences to those consequences, consequences to the consequences to those consequences, consequences to the consequences to the consequences to those consequences etc. in each planck time from the Big Bang until now.
The number of planck times since the Big Bang. (8 x 1060)
Have I missed anything?