We give an explicit formula for the second variation of the logarithm of the Selberg zeta function, Z(s), on Teichmüller space. We then use this formula to determine the asymptotic behavior as s → ∞ of the second variation. As a consequence, we determine the signature of the Hessian of log Z(s) for sufficiently large s. As a further consequence, the asymptotic behavior of the second variation of log Z(s) shows that the Ricci curvature of the Hodge bundle H 0 (K m t ) → t over Teichmüller space agrees with the Quillen curvature up to a term of exponential decay, O(s 2 e −l 0 s ), where l 0 is the length of the shortest closed hyperbolic geodesic.