Can I make a large purchase after I filed for divorce without sharing the purchase with my husband?

After separation what you buy is your separate property if you use money earned after separation. You are also responsible for the debt.

In Utah, the answer is: maybe, maybe not. In Utah, all property acquired by purchase during the marriage by either spouse is presumed to be marital property. That means that even if you made a purchase intended for yourself and made that purchase after you filed for divorce, the court could still consider it to be marital property when dividing marital property between you and your spouse. To ensure that a big purchase that you intend to make after you have filed for divorce is treated as your separate property, you will need your spouse to agree to treat the purchase at your separate property and get a court order acknowledging that. If your spouse will not agree to you making the purchase and keeping it is your separate property, then you will need to file a motion with the court in advance of making the purchase and getting a court order recognizing the purchase to be your separate property. If you have already made the major purchase without court approval, that's riskier, but you should still file a motion with the court asking the court to acknowledge the property to be your separate property.

Will you use assets acquired during the course of the marriage to make the purchase?