Here, within the Scale-Symmetric Theory (SST), we calculated the positron fraction in primary cosmic rays as a function of energy and we described positron flux. Obtained results are consistent with the data from the Alpha Magnetic Spectrometer (AMS) on the International Space Station (ISS). These data lead to the internal structure of the core of baryons and to phenomena characteristic for regions in the Universe filled with baryonic plasma described within SST. Here as well we described new cosmological problems which lead to new cosmology. They are as follows. There are not in existence the B-modes associated with gravitational waves - it leads to conclusion that there was a separation in time of the inflation (the big bang) and the expansion of the Universe (the “soft” big bang) or/and that gravitational waves do not exist (SST shows that both conclusions are correct). In the Universe there is too small number of dwarf galaxies - there should be about 10 times more dwarf galaxies than we observe. In the very distant Universe there are numerous massive elliptical galaxies which do not significantly evolve so a time for their formation was too short. In the very distant Universe there are too many barred galaxies - it is inconsistent with simulations grounded on the Cosmological Standard Model (CSM). There is a substantial asymmetry in the CMB signal observed in the two opposite hemispheres of the sky. These new problems suggest that CSM starts from wrong initial conditions.