Mishnah Berurah — משנה ברורה

During the Shema and Amidah - Meaning, at the very least during Shema and the Amidah, as can be seen below in siman 37 se'if 2. It says in the Gemara (Berakhot 14b:24) "Anyone who recites Shema without tefillin - it's as if he gives false testimony on himself", Heaven forbid. Tosofos explains that this is because the person says (Deuteronomy 6:8) "And you shall tie them as a sign [on your arm]...", but [here] he is not tying it. And even though, after the fact, one still fulfilled their obligation of reciting Shema, nevertheless, on the other hand he is sinning since he is presenting as if he does not want to fulfill the will of Hashem, and that is the false testimony that he gives on himself. See in [sefer] Levush for another explanation. Sefer Chareidim wrote "...that from this we can learn that when one says (Deuteronomy 6:5) "And you shall love Hashem...", he should see to it to enter love for Hashem into his heart, so that he shouldn't be like one speaking falsehood, Heaven forbid. You should know that they (Chazal) only said this (ie. reciting Shema without tefillin) regarding one who purposely does not put on his tefillin, for he is too lazy to put them on before reciting Shema. But one who [simply] does not have tefillin [at that moment], or is on the road and because of the cold he is not able to put them on, or any similar scenarios, certainly [in those cases] one should not delay reciting Shema in it's proper time because of that - Levush, siman 58, I quoted his words there."