Comment by whalesalad

The valid_range with a gist index is quite fast.

    SELECT COUNT(DISTINCT domain)
    FROM time_travel
    WHERE (CURRENT_DATE - INTERVAL '90 days')::timestamptz <@ valid_range
    AND owned;

This is asking, "how many domains did we own 90 days ago"

Instead of finding records where the start is less than, end is greater than, you can just say find me rows that will cover this point in time. The GiST index on valid_range does the heavy lifting.

Lots of handy range-specific query tools available: https://www.postgresql.org/docs/17/functions-range.html