| Popis: |
While a theory calculating a cosmological generation of particles ina case of the expanding space-time is quite developed, we study here a theory of a cosmological generation of particles in a case of a space- time which is expanding and then contracting back. The simplest case of fields studied in this connection is a scalar field. We will show in our paper that the quantum scalar field has delocalized in the conformal time η particle-like modes uⁱⁿ and two localized in the conformal time modes uⁱⁿ and uⁱⁿ for our choosen scale factor C(η). The vacuum for these states | 0, out > defined through massive modes uᵒᵘᵗ and through modes uᵒᵘᵗ and uᵒᵘᵗ is the same as the vacuum | 0, in >. A detector shows that there are no mass particles and no localized states forη → +∞ for non-accelerating case. For η → −∞ a Minkowski space- time is realized, as it is realized also in the out case. The quantum field has delocalized in the conformal time η particle-like modes uᵒᵘᵗ which in the -out region have k-dependent phase shifts with respect to the quantum field delocalized in the conformal time η particle-like modes uⁱⁿ in the -in region. The phase shift of delocalized modes (k-particles) is due to scattering in the gravitational field leading toexpansion and contraction of the space. Thus while in the expansion phase there is present generation of particles, due to nonpresence of particles in η → +∞ conformal time it is clear that in the phase of contraction of the scale factor there is present annihilation of particles from their peak state, where they are occurring from the generationprocess. |
