  High-frequency multi-messenger observations provide a powerful probe of
gamma-ray bursts (GRBs), pioneered by {\em BeppoSAX} in gamma-rays and
LIGO-Virgo in gravitational waves. Identifying the central engines - magnetars
or black holes - also promises to improve on GRBs as probes of cosmological
evolution. THESEUS' design is ideally suited to pursue both science objectives.
Here, we present a general-purpose {\em graphics processor units}
(GPU)-accelerated broadband search algorithm for long duration ascending and
descending chirps, post-merger or from core-collapse of massive stars, in
electromagnetic and gravitational radiation. It implements butterfly filtering
using banks of up to 8 million templates of 1 second duration at over one
million correlations per second by heterogeneous computing using a dozen
high-end GPUs. We demonstrate its application with the identification of
broadband Kolmogorov spectra in long GRBs and the long duration ascending chirp
in the merger GW170817. The first shows a noticeable absence of a high
frequency bump, otherwise expected from newly formed magnetar central engines.
The second illustrates the need for deep searches to identify GRB central
engines in descending chirps in gravitational waves, post-merger or from nearby
energetic core-collapse supernovae. A future catalogue of THESEUS' GRBs
covering a broad range of redshifts may probe the nature of the cosmological
vacuum and establish the de Sitter limit as a turning point in cosmological
evolution.
