Gemara

15a (Mishnah): If one said Keri'as Shema inaudibly (to his own ears), he was Yotzei;

R. Yosi says, he was not Yotzei.

15b (Beraisa #1): One may not say Birkas ha'Mazon silently. If he did, he was Yotzei.

24b (Beraisa): One who prays audibly has little Emunah;

(Rav Huna): This is only if he could concentrate quietly. If not, it is permitted.

This is only when praying in private, but not b'Tzibur, lest he disturb others.

(Beraisa): One who raises his voice in prayer is like a false prophet.

31a (Beraisa) Suggestion: Perhaps one may pray audibly!

Rejection: Chanah prayed, and "v'Kolah Lo Yishame'a."

Rishonim

Rosh (3:40): If one cannot concentrate quietly, he may even raise his voice. The Yerushalmi says that R. Aba bar Zavda used to pray loudly. When Rebbi Yonah would pray in the Beis ha'Keneses, he would pray quietly. When he prayed in his house, he prayed aloud so that his household learned prayer from him. I.e. he prayed so loudly to arouse intent that his household heard and learned prayer from him. This refers to praying alone. One may not pray aloud in b'Tzibur, lest he disturb others.

Rashba (31a DH v'Kolah): Presumably, one should not be audible to others, i.e. not say it aloud, like it says above that one who prays audibly has little Emunah. One may be audible to himself, and this is the Mitzvah l'Chatchilah. The Yerushalmi says so. One who was not audible to himself was Yotzei b'Di'eved. This is a Chidush according to R. Yosi, who says regarding Keri'as Shema that even b'Di'eved he was not Yotzei. However, a Tosefta (3:9) says oppositely. It learns from Chanah that one should not be audible to himself. However, if he raises his voice for a need, it is permitted, e.g. if he cannot concentrate quietly, like it says on 24b. This refers to praying not b'Tzibur. Alternatively, if he raises his voice in order that others will learn to pray from him, it is permitted, like the Yerushalmi says.

Poskim

Shulchan Aruch (OC 101:2): One may not pray only in his heart. Rather, he must articulate the words with his lips and make them quietly audible to his ears, but not make his voice heard.

Beis Yosef (DH u'Mah she'Chasav Yesh): The Tur rejected the Tosefta due to the Yerushalmi and the connotation of the Bavli. Hagahos Maimoniyos 5:50 says so, and this is the Halachah.

Bedek ha'Bayis: The Zohar is like the Tosefta. One should be concerned for it.

Rebuttal (Magen Avraham 3): There is no proof from the Zohar. Perhaps the Zohar means that no one else should hear him, like the Rema says (141:2, regarding Tefilah and one who receives an Aliyah). Surely, if he was not audible to his ears, he was Yotzei. The Bach says that Chazanim should not raise their voices more than needed to be audible to the Tzibur. One need not say so. The Ari Zal would not make his voice audible even in Pesukei d'Zimra, just on Shabbos he raised his voice a little.

Gra (DH u'Mashmi'a): The Yerushalmi (says to be audible to his ears). If he was not, he was Yotzei (b'Di'eved). The Bavli connotes similarly. It forbids being audible to others. The Zohar agrees, unlike the Tosefta that the Rashba brings, which learns from Chanah that one should not be audible to his ears. This (the words 'to his ears') is a printing mistake. It says so also in Tana d'vei Eliyahu. Perhaps also there it is a printing mistake, for the Gemara brought the Tosefta, and it did not say 'to his ears.' This is like our text of the Tosefta. Also the Yerushalmi said 'one might have thought that he should raise his voice... (i.e. only this is forbidden - PF).

Magen Avraham (2): It is not clear whether one who prayed in his heart was Yotzei. Seemingly, he was Yotzei. Even though we hold that Hirhur is not like speech (for Keri'as Shema and Birkas ha'Mazon - 62:3, 185:2), Tefilah is different. Tefilah is the Avodah of the heart - "u'Le'avdo b'Chol Levavchem." I.e. it is primarily intent in the heart. Hash-m knows intents. However, the Gemara connotes that he was not Yotzei. If not, they should have enacted that a Ba'al Keri think the Tefilah in his heart. He may think it, for we hold that Hirhur is not like speech. Rather, one is not Yotzei through Hirhur. One must articulate the words with his lips, for the voice arouses above. A Choleh (sick person) thinks it in his heart (94:6). This is better than nothing, but he is not Yotzei. The Poskim connote like this. One who blessed Birkas ha'Mazon in his heart was Yotzei (15b), and the same applies to other Berachos. The Rosh (3:14) explains that he said the words with his lips, for Hirhur is not like speech. (The Shulchan Aruch) rules like this in 185:2. We equate everything. If not, we could say that Keri'as Shema is different, for it says "v'Shinantam" (i.e. audibly), but regarding Birkas ha'Mazon it says only "u'Verachta". One can bless Hash-m also through Hirhur, for He knows thoughts. Rather, we do not distinguish. The Gemara connotes like this. This requires investigation.

Bi'ur Halachah (DH b'Libo): Also Nefesh ha'Chayim (Sha'ar 2, Perek 20) says that if he prayed in his heart he was not Yotzei.

Kaf ha'Chayim (6): Eliyahu Rabah, Aruch ha'Shulchan, Shulchan Aruch ha'Rav say that he was not Yotzei. It seems that Eshel Avraham (2) and R. Chaim Vital, Yafeh l'Lev and the Mabit agree. The Zohar connotes like this. If one does not articulate the words with his lips, it is not considered Tefilah. The Poskim say only that a Choleh who cannot pray should think in his heart.

Mishnah Berurah (5): Some say to be concerned for the Zohar, so l'Chatchilah one should not be audible to his ears. The Magen Avraham rejects the proof from the Zohar. The Gra says that the Zohar is like the Shulchan Aruch! The other Acharonim agree that l'Chatchilah, one should be audible to his ears. B'Di'eved, if he was not, all agree that he was Yotzei, since he articulated the words with his lips.

Kaf ha'Chayim (8,9): One must be careful not to be audible even to his own ears. However, if one cannot have intent this way, it suffices that others cannot hear him.

Kaf ha'Chayim (10): Machazik Berachah says that perhaps even one who prays for a personal affliction should not be audible to his ears. The Zohar connotes unlike this. One should do in the way that he will have best intent.

Shulchan Aruch (ibid.): If he cannot concentrate quietly, he may raise his voice. This is when praying alone. One may not do so b'Tzibur, for he will disturb the Tzibur.

Mishnah Berurah (6): One who raises his voice in Tefilah is like one who does not believe that Hash-m hears silent prayer. The false prophets used to scream to their idolatry. L'Chatchilah one must pray so quietly that someone standing next to him cannot hear. If one cannot have intent this way, he should pray in a way that enables intent, but he must be careful not to disturb others.

Kaf ha'Chayim (7): If one raises his voice, Chitzonim (shells of Tum'ah) cling to his prayer. Chazaras ha'Shatz is on a higher level, so Chitzonim cannot cling to it. Some have the custom that if they missed Kedushah, he prays the first three Berachos aloud so the Tzibur will hear and answer Kedushah with him, and finishes his Tefilah quietly. This is permitted, for he does so so that he and others will be able to answer Kedushah. The merit of this Mitzvah will protect his Tefilah from Chitzonim.

Mishnah Berurah (7): Even in Pesukei d'Zimra it is good not to raise his voice, for Hash-m hears silent (prayer), unlike those who raise their voices too much. However, on Shabbos, the custom is that one says Pesukei d'Zimra aloud, so it is fine.

Mishnah Berurah (10): B'Tzibur one may not be audible (to others) even a little, and all the more so one may not raise his voice.

Bi'ur Halachah (DH d'Asi): Nowadays we do not teach that one may pray alone in order to arouse intent, lest others learn from this, unlike he is a Gadol ha'Dor and it is known that all his actions are l'Shem Shamayim.

Rema: If he raises his voice in his house when he prays in order that his household learn from him, it is permitted.

Beis Yosef (DH v'Im): In the Mordechai's text of the Yerushalmi, Rebbi Yonah prayed aloud in order that his household will learn from him. Mahari Avuhav says 'we must say so. Raising his voice without this intent is despised.' Why must we say so? Perhaps he just happened to be loud enough for them to learn from him! One who raises his voice in Tefilah is like the false prophets, but if he cannot concentrate quietly, it is permitted, if he prays alone. The Rosh and R. Yonah (15b DH Aval) explain like this.

Prishah (7): We must say like the Tur and Mahari Avuhav. If not, why did it say that he raised his voice until his household could learn from him? Surely, sometimes he was louder or quieter than this, based on what he needed to arouse intent! Also, if so why the Yerushalmi omit that he did so for Kavanah, i.e. the primary matter it comes to teach about?! Also, for what Chidush did the Tur mention Rebbi Yonah, since the Tur previously brought Rav Huna, who permits to raise one's voice for the sake of intent!

Taz (1): Do not say that Rebbi Yonah could not concentrate quietly. If so, whenever he prayed b'Tzibur, he did not have intent, since he had to pray quietly! This is improper. Rather, he intended to teach his family.

Rebuttal (Prishah 7): We can say that when his mind was clear, he prayed b'Tzibur. When his mind was not clear, he prayed in his house alone, aloud, to arouse intent.

Taz (1): The Mordechai explains like I said. The Rosh says that he prayed aloud to arouse intent, so much that his household heard and learned from him. He holds that even if one can have intent quietly, if he can have more intent aloud, he is like one who cannot have intent, and he may pray aloud when alone. This answers the Tur's question. We hold like this.

Gra (DH Lehagbiha): The Rosh wrote so (one may raise his voice for the sake of intent), even though the Gemara mentioned only being audible. However, the Yerushalmi says that Rebbi Yonah was so loud that his household learned Tefilah from him. The Rosh and R. Yonah explain that he did so to arouse intent. The Rashba, Tur and Mordechai say that he intended to teach them, like the Rema brings.

Bi'ur Halachah (DH v'Im): The Zohar says that if one raises his voice so much that someone else can hear, his Tefilah is not heard above. It seems that one should not rely on the Taz' leniency. The Prishah answered his question against the Rosh, especially based on the Gra, who says that according to the Rashba and Tur there is no Heter from the Gemara to raise his voice where he cannot have intent (quietly). However, the Gra is difficult, for the Tur explicitly permits raising his voice! The Gra must mean that (even though the Tur permits,) the Tur agrees that there is no source in the Gemara for this.

Kaf ha'Chayim (14): The Mechaber omitted this because R. Yonah and the Rosh explained the Yerushalmi differently.