3000 ft-pds of muzzle energy is one measure many "experts" on bear defense recommend. That sets the 30-06 and other rifles in that neighborhood as minimum bear guns. My .444 Marlin is in that range.
Most guides recommend .338 magnum as the minimum rifle and go up from there but some will accept the 30-06 as a minimum as well. Since out of state hunters in Alaska must have a guide, securing the guide and then getting their advice/recommendations is probably the place you should go first to answer your question. For me in Northern Idaho, I feel secure with my .444 and Buffalo Bore 335 gr ammo. The .444 has stopped large grizzlies in at least two documented cases in the last few years. Anything smaller than these calibers is not likely to have any support from your guide.
Lastly, another rule a lot of "experts" go with is to take the largest rifle you can confidently and accurately shoot well. If you are recoil shy, hunting grizzlies is probably not a wise hobby to consider.