It is from the Sunnah to recite the tashahhud quietly.
حدثنا أبو سعيد الأشج حدثنا يونس بن بكير عن محمد بن إسحق عن عبد الرحمن بن الأسود عن أبيه
من السنة أن يخفي التشهد
No references are available.
[Sahih]. Abu Dawud narrated it in the Book of Prayer, chapter on concealing the tashahhud, no. 986, from the hadith of Yunus bin Bukayr with this wording. Ibn Khuzayma graded it sahih, no. 706, and Hakim (1/267) said it meets the standard of Muslim, and Dhahabi agreed with him.Hasan bin Ubaydullah also narrated it from Abdul-Rahman bin Aswad with this wording. Hakim narrated it (1/230) and graded it sahih according to the standard of the two sheikhs, and Dhahabi agreed with him.