After my bypass surgery
I was told not to sleep on my stomach until I got approval from my surgeon.
I was told the reason for this was to protect the sternum
(breastbone) until it had a chance to mend after the surgery. Similarly I was not allowed to lift more than five pounds per hand or drive until cleared by the surgeon.
Five weeks after my surgery my surgeon lifted all these restrictions.
I have read that some bypass surgeries are now done without using a heart-lung machine, which I think may mean that the sternum is not damaged as it is when using a heart-lung machine.
In any case, ask your surgeon and follow his orders.