The double ramification cycle and the theta divisor

We compute the classes of universal theta divisors of degrees zero and g−1 over the Deligne-Mumford compactification M_g,n of the moduli space of curves, with various integer weights on the points, in particular reproving a recent result of Müller. We also obtain a formula for the class in CH^g (M^ct_g,n) (moduli of stable curves of compact type) of the double ramification cycle, given by the condition that a fixed linear combination of the marked points is a principal divisor, reproving a recent result of Hain. Our approach for computing the theta divisor is more direct, via test curves and the geometry of the theta divisor, and works easily over all of M_g,n. We used our extended result in another paper to study the partial compactification of the double ramification cycle.