Ask HN: How to warm up a domain for email

I send out ~40k emails every morning through mailchimp to our subscribers and for the past three years or so have fairly regularly gotten low 40's% open rates every weekday. Then last Wednesday, it dropped to low 30's. Our format hasn't changed, our content hasn't changed. Mailchimp doesn't see anything wrong. We can't figure out what might have caused the drop. (Did anything happen that I don't know about in Mailchimp, gmail, etc?)

We never authenticated our domain (so our sender shows as 'via' mailchimps servers) and I think perhaps that's the next step to take. I'm worried about our open rates/deliverability taking a huge dip since our domain isn't 'warmed up' with sending that many emails out every day. Does that happen? Anything I need to do or anything else I should think about?