My husband's aorta is also dilated, currently at 4.1. He's been being watched with an annual echo, and occasional CT scan. At that measurement, that's really all they'll do for now.
You're below the surgical threshold of 5.0 cm. Some docs set the threshold at 6.0 cm, but considering that's about the diameter of a Coke can, personally, I'd get it done before it gets to that size (a normal aorta is about 2.5 to 2.8 cm in diameter). You'll be monitored yearly with either CT or MRA to see if it progresses, and your doctor may put you on a beta blocker to reduce peak aterial stress. Other monitoring you may receive can include echo, they'll be looking to see if your aortic valve is being affected by the dilation. You'll also be told to avoid lifting very heavy weights (anything hard enough for you to close your glottis while lifting). Your doctor may evaluate you to see if you have a related genetic condition, such as Marfan's or Ehler-Danlos.
If it progresses to the surgical threshold, the surgery replaces the damaged portion of the aorta with a Dacron. If your arch is involved, the surgery can become more complicated. If your aortic valve is compromised, the aorta and valve may be replaced with a combination valve and artieral graft. While any type of aortic surgery is complex and risky, in the hands of an experienced surgeon, this surgery has come a long way in the last 20 years.
Typical progression rates are on the order of 0.12 cm/yr, with significant variation from case to case.