On the relation between mass of a pion, fundamental physical constants and cosmological parameters

We reconsider the old, mysterious relation between the mass of pion, the fundamental constants and the Hubble parameter. Firstly, we show how, by introducing the energy density of the Universe; the old rude approximation transforms into an excelant one. After that, we have argued how the new relation can be justified assuming that quantum vacuum is dominated by a gas of virtual pions which have zero gravitational mass, at a very low temperature caused by gravitation. Identification of such a gas of virtual pions with dark energy, leads to a surprisingly good numerical result for the energy density of the vacuum.