We improve the universality theorem of the Riemann zeta-function in short intervals by establishing universality for significantly shorter intervals \([T,T+H]\) . Assuming the Riemann Hypothesis, we prove that universality in such short intervals holds for \(H=(\log T)^B\) with an explicitly given \(B>0\) . Unconditionally, we show that for the same H the set of real numbers \(\tau \in [T,T+H]\) such that \(\zeta (s+i\tau )\) approximates an arbitrary given analytic function has a positive upper density.
