The Talmud Yerushalmi states that one who sleeps on Rosh Hashonah will have “sleepy mazel” throughout the year. Based on this concept, Rema quotes a custom not to sleep on the day of Rosh Hashonah. Some Achronim qualify that the custom only applies to lying down to go to sleep, and not to falling asleep while sitting on a chair. The poskim disagree about whether one must arise at daybreak to fulfill this custom. Some say that although it is not necessary to get up at that time, if one does, he may not go back to asleep. According to the Arizal, a person may go to sleep after midday, since by that time mercy has already been aroused through the tefillos and tekiyos. A person who is feeling weak and cannot focus on the tefillos may take a rest in order to strengthen himself.
[שו"ע תקפג, ב, משנ"ב ט, ושעה"צ י; ביאורים ומוספים דרשו, 16-14]