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We consider the CANNEX (Casimir And Non-Newtonian force EXperiment) test ofthe quantum vacuum intended for measuring the gradient of the Casimir pressurebetween two flat parallel plates at large separations and constrainingparameters of the chameleon model of dark energy in cosmology. A modificationof the measurement scheme is proposed that allows simultaneous measurements ofboth the Casimir pressure and its gradient in one experiment. It is shown thatwith several improvements the CANNEX test will be capable to strengthen theconstraints on the parameters of the Yukawa-type interaction by up to an orderof magnitude over a wide interaction range. The constraints on the couplingconstants between nucleons and axion-like particles, which are considered asthe most probable constituents of dark matter, could also be strengthened overa region of axion masses from 1 to 100 meV.

Prospects for Searching Thermal Effects, Non-Newtonian Gravity and Axion-Like Particles: Cannex Test of the Quantum Vacuum