Why should we care about the top quark Yukawa coupling?

In the cosmological context, for the Standard Model to be valid up to the scale of inflation, the top quark Yukawa coupling y_t should not exceed the critical value y_t ^crit, coinciding with good precision (about 0.2‰) with the requirement of the stability of the electroweak vacuum. So, the exact measurements of y_t may give an insight on the possible existence and the energy scale of new physics above 100 GeV, which is extremely sensitive to y_t. We overview the most recent theoretical computations of and the experimental measurements of y_t ^crit and the experimental measurements of y_t. Within the theoretical and experimental uncertainties in y_t, the required scale of new physics varies from 10⁷ GeV to the Planck scale, urging for precise determination of the top quark Yukawa coupling.