Hello, i have website at Hostgator and domain also with their registar.
I run an wordpress blog and after repeated WebPageTest, i see around 20 seconds Time To First byte.
Your best bet is to reach out to Hostgator or switch hosting (WPEngine can do very fast wordpress hosting). The 20 seconds is a result of slow database queries usually and W3TC can sometimes hide it but it looks like your hosting is so over provisioned that they would have to do something on their side or you need to find a better provider (not necessarily more expensive though that wouldn’t hurt).