If an individual recites Musaf on Rosh Hashanah in his home, he should not do so during the first three hours of the day, for that is a period of Divine judgment, when God is angered by the idolaters who engage in their idolatry at this time.

The Talmud (Avodah Zarah 4b) relates:

It was taught in the name of R. Meir: At the time when the [gentile] kings place their crowns upon their heads (at the third hour o f the day, when kings arise) and bow down to the sun, God immediately becomes angry.

R. Yosef taught: An individual should not recite Musaf during the first three hours of the day on Rosh Hashanah, for during those hours the Divine judgment is stern and it is possible that an individual's actions might be scrutinized then and severe judgment passed. If so [one may ask], then should a congregation also refrain from praying Musaf at this time? No; the congregation is not rejected, for it has many sources of merit.