My wife is due to give birth on succot and could go into labor any moment. She is worried that she will go into labor when I am at shul and will have no way to contact me. On Rosh Hashana, can I carry a phone in my talis bag so she can call me in case of emergency?
Also this will be an even more of an issue for Yom Kippur.
You should not carry a phone in the Tallis bag.
Under the circumstances I would perhaps drop in at home every hour or so (if this is possible) to make sure that everything is okay. Also, you can make an arrangement with a neighbor or child of a neighbor that he/she will be available in case of emergency to go to shul and call you.
The birth should be be’shaa tovah, and best wishes.