Peas and carrots use different root zones and make use of different above ground space. Peas also make their own nitrogen from symbiotic organisms so they shouldn't compete with the carrots for it. You should be able to plant them rather close.

In my mind the pattern would be like this [ :o:o:o: ] or [ #o#o#o# ] where ":" is 2 carrots, "#" is a block of carrots 9 or 16 per square foot, and "o" is peas. The carrot/peas/carrot planting will make the best use of space but the carrot-block/peas/carrot-block planting will give more carrots and give the carrots more light. I don't think the carrots will need more light though so it's really up to how many of each you want. Why not try both and see what you like better?

I'm moving and have packed my books already so I can't give any book answer. It should be pretty easy to use your best judgment as well as plant them in a way that gradually changes the spacing along the length of your row. For the spacing of 2 carrots between pea plants though I suspect that no change in pea plant spacing would be required at all. I'm sure it will be fine anyway you do it but gradually changing the spacing over the length of the row will give you feedback on which spacings work best.

Have fun!