Under FAR Part 91 operations what course of action should a pilot take if radio communication is lost after being cleared for an instrument approach in IMC and then a missed approach becomes necessary due to inadequate visibility?
In the event a balked (rejected) landing occurs at a position other than the published missed approach point, the pilot should contact ATC as soon as possible to obtain an amended clearance.
If unable to contact ATC for any reason, the pilot should attempt to re−intercept a published segment of the missed approach and comply with route and altitude instructions.
If unable to contact ATC, and in the pilot’s judgment it is no longer appropriate to fly the published missed approach procedure, then consider either maintaining visual conditions if practicable and reattempt a landing, or a circle−climb over the airport.
That indicates that ATC expects you to fly the published (or instructed) missed approach procedure if possible, or climb over the airport if not.
As for what happens after going missed and climbing to a safe altitude, that's up to you. Even if you were in contact with ATC, they would ask for your intentions because they don't know why you went missed and whether you want to try the same approach again or divert. ATC also doesn't know your filed alternate airport (see the AIM p. 5-1-24) and there's no requirement to go there anyway. It's up to you as PIC to determine the best course of action; ATC will help by keeping other aircraft away from you as far as they can.