Make no mistake, your spouse (and his or her attorney) are exploring every possible route to gain evidence for the case. If you are receiving modifiable alimony, you may not want to broadcast every detail of your swank new life. A fellow blogger writes about a recent case in which the former wife blogged about her adventures on her boyfriend's sailboat in the Caribbean. Under Connecticut law, living with a boyfriend/girlfriend justifies a change in alimony. In Maryland, it is possible to see a similar sort of circumstances if the alimony is modifiable (it is not uncommon for the couple to agree upon non-modifiable alimony). The court would take the various financial considerations into account. Even though in Maryland, living together does not per se require a change in alimony, but it would be taken into account that the former wife may now have lower expenses (reduced need) based on the cohabitation.
Lest you think this is an unusual circumstance, check out this post on the Maryland Divorce Legal Crier, describing a case in which a blogging belly dancer blew her cover.