Writing during Davening:
Initially, one may not make an interval during Davening [past Baruch Sheamar] for the sake of writing, even if he will not be saying the words. However, in a time of need, one may write during Davening.
 Salmas Chaim 49; Yagel Yaakov 10; Betzel Hachochma 4:88; Beir Moshe 2:7; Yabia Omer 9:10; Teshuvos Vehanhagos 2:40; Shevet Hakehasi 1:77; Piskeiy Teshuvos 55:8; 66:1
 The reason: As although writing is not like talking regarding its quality of interval [See Admur 47:3 regarding Birchas Hatorah], and thus does not receive the same level of severity, nevertheless, initially, one is not to make any interval during Davening, even if it does not involve speech, just as is the law regarding Shema. [Beis Oved 51:3; Makor Chaim 51; Kaf Hachaim 51:17; See Admur 63:7]
 The reason: As one may stop to make non-speech intervals even during Kerias Shema, after the first Parsha, if it is for the sake of a Mitzvah. [Admur ibid] Certainly then this applies during Pesukei Dezimra. [Beis Oveid ibid] Likewise, this allowance also applies in a time of need. [Poskim ibid]