Here we present several remarkable irregularities at chemical freeze-out which are found using an advanced version of the hadron resonance gas model. The most prominent of them are the sharp peak of the trace anomaly existing at chemical freeze-out at the center of mass energy 4.9 GeV and two sets of highly correlated quasi-plateaus in the collision energy dependence of the entropy per baryon, total pion number per baryon, and thermal pion number per baryon which we found at the center of mass energies 3.8-4.9 GeV and 7.6-10 GeV. The low energy set of quasi-plateaus was predicted a long time ago. On the basis of the generalized shock-adiabat model we demonstrate that the low energy correlated quasi-plateaus give evidence for the anomalous thermodynamic properties inside the quark-gluon-hadron mixed phase. It is also shown that the trace anomaly sharp peak at chemical freeze-out corresponds to the trace anomaly peak at the boundary between the mixed phase and quark gluon plasma. We argue that the high energy correlated quasi-plateaus may correspond to a second phase transition and discuss its possible origin and location. Besides we suggest two new observables which may serve as clear signals of these phase transformations.

We study the feebly interacting dark matter with the Standard Model fields, where the preceding and the latter ones are the constituents of the bosonic cosmological objects, the scalar boson stars (BS). The scalar dark matter (SDM) massive fields can form the macroscopic scalar bound state when minimally coupled to gravity (GR). The star may have approximately a stationary form with an asymptotically flat geometry, and the maximal mass of the BS is larger than the solar mass. We consider an effective description of a more complete model with the (thermo)dynamic potential of the BS at finite temperature. The formation of the BS may also be explained in terms of the electric fluxes of the hidden vector field under the influence of the SDM field as the cosmological dynamical quantity minimally coupled to GR. The SDM fields may fluctuate with the temperature and is established around the equilibrium state at some weak background scale.