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We suggest a crucial direct-observational test for measuring distinctionbetween the standard $\Lambda$CDM model and recently proposed phantom darkenergy positive curvature cosmological model. The test is based on thefundamental distance--flux--redshift relation for general Friedmann models. Itdoes not depend on the CMBR data, on the large-scale structure growth models,and also on the value of the Hubble constant $H_0$. Our crucial test can beperformed by future gamma-ray burst observations with THESEUS space mission andby using gravitational-wave standard siren observations with modern advancedLIGO--Virgo and also forthcoming LISA detectors.

A crucial test of the phantom closed cosmological model