Protect the sternum
Essentially after any procedure that involves cutting the sternum, one has to protect it for a while (up to three months in some cases).
It is best to support the sternum with a pillow (we give a "heart
pillow" to the patients) which is pressed against the chest when the patient is sneezing or coughing. Patient is instructed essentially to hug the pillow. No specific rest position that i know of.