The production of quantum field excitations or particles in cosmological spacetimes is a hallmark prediction of curved quantum field theory. The generation of cosmological perturbations from quantum fluctuations in the early Universe constitutes an important application. The problem can be quantum-simulated in terms of structure formation in an interacting Bose-Einstein condensate (BEC) with time-dependent s-wave scattering length. Here, we explore a mapping between cosmological particle production in general (
D+1)-dimensional spacetimes and scattering problems described by the nonrelativistic stationary Schr\"odinger equation in one dimension. Through this mapping, intuitive explanations for emergent spatial structures in both the BEC and the cosmological system can be obtained for analogue cosmological scenarios that range from power-law expansions to periodic modulations. The investigated cosmologies and their scattering analogs are tuned to be implemented in a (
2+1)-dimensional quantum field simulator.
We consider a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise, and one irreducible representation (IR) of the symmetry algebra splits into independent IRs describing a particle an its antiparticle only in the approximation when de Sitter energies are much less than the characteristic of the field. As a consequence, the very notions of particles and antiparticles are only approximate and such additive quantum numbers as the electric, baryon and lepton charges are conserved only in this approximation. There can be no neutral elementary particles and the spin-statistics theorem can be treated simply as a requirement that standard quantum theory should be based on complex numbers.