Q. I am frequently distracted during davening by others who daven audibly (during the Amidah) or who daven significantly louder than the rest of the congregation during the parts (like psukei d’zimra) that are recited out loud. It is very hard for me to focus on my own davening when this happens.
Do I have a right to ask them to daven quietly, or at least not louder than the norm in that place?
It is often otherwise very respectable people who do this, so I am really reluctant to ask them, but the alternatives – davening without proper kavanah, or going to another shul, are not appealing.

A. Shulchan Aruch (O.H. 582: 9) rules that although during the rest of the year we pray silently, on Rosh Hashana and Yom Kipur it is tradition to raise our voices. Mishna Berura (ibid. 24) explains that during Yamim Noroim it is permitted since this may be essential to raise one’s kavanah and intention.
Horav Shlomo Miller’s Shlit”a opinion is that during the rest of the year you can ask politely in a gracious and congenial way and as a favor, not a complaint. If that did not help, you may consider changing places with someone else.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a.