Moving from the consideration that matter fields must be treated in terms of their fundamental quantum counterparts, we show straightforward arguments, within the framework of ordinary quantum mechanics and quantum field theory, in order to convince readers that cosmological perturbations must be addressed in term of the semiclassical limit of the expectation value of the quantum fields. We first take into account cosmological perturbations originated by a quantum scalar field, and then extend our treatment in order to account for the expectation values of bilinears of Dirac fermion fields. The latter can indeed transform as scalar quantities under diffeomorphisms, as well as all the other bilinear Dirac fermion elements of the Clifford algebra. Phenomenological consequences follow, including the possibility of generating cross-correlation spectra from fermion perturbations. We then discuss how the macroscopic state for matter we propose can be interpreted as a non-Bunch-Davies vacuum, and then generalise this construction likening it to representation theory. Phenomenological consequences of this identification are then outlined.
We study transitions of hadronic matter to three-flavour quark matter (3QM) locally both for shock-induced and diffusion-induced conversions. The former is the transition via two-flavour quark matter triggered by a rapid density rise in a shock wave and the latter is induced by diffusions of a seed 3QM. Not only the jump condition on both sides of the conversion front but the structures inside the front are also considered by taking into account what happens during the conversion processes on the time scale of weak interactions. We demonstrated that the combustion will occur in the so-called endothermic regime which has been ignored in the discussion so far. We also find that the deflagration front is unstable in the exothermic regime but stable in the endothermic regime, which is quite contrary to the ordinary combustion. It is also confirmed that strong detonation and weak deflagration are always obtained for shock-induced and diffusion-induced combustion, respectively, regardless of whether in exothermic or endothermic regime.