Part of cyclic event.
Matter from stars and galaxies pulled into the condensate core and expelled out.
It's a regeneration process.
In the Emergent scenario, the Universe should evolve from a non-singular state replacing the typical singularity of General Relativity, for any initial condition. For the scalar field model in [1] we show that only a set of measure zero of trajectories leads to emergence, either from a static state (an Einstein model), or from a de Sitter state.
Assuming a scenario based on CDM interacting with a Dark Energy fluid, we show that in general flat and open models expand from a non-singular unstable de Sitter state at high energies; for some closed models this state is a transition phase with a bounce, other closed models are cyclic. A subset of these models are qualitatively in agreement with the observable Universe, accelerating at high energies, going through a matter-dominated decelerated era, then accelerating toward a de Sitter phase.
The origins of the elements and isotopes of cosmic material is a critical aspect of understanding the evolution of the universe. Nucleosynthesis typically requires physical conditions of high temperatures and densities. These are found in the Big Bang, in the interiors of stars, and in explosions with their compressional shocks and high neutrino and neutron fluxes. Many different tools are available to disentangle the composition of cosmic matter, in material of extraterrestrial origins such as cosmic rays, meteorites, stardust grains, lunar and terrestrial sediments, and through astronomical observations across the electromagnetic spectrum. Understanding cosmic abundances and their evolution requires combining such measurements with approaches of astrophysical, nuclear theories and laboratory experiments, and exploiting additional cosmic messengers, such as neutrinos and gravitational waves. Recent years have seen significant progress in almost all these fields; they are presented in this review. Models are required to explore nuclear fusion of heavier elements. These have been confirmed by observations of nucleosynthesis products in the ejecta of stars and supernovae, as captured by stardust grains and by characteristic lines in spectra seen from these objects, and also by ejecta material captured by Earth over millions of years in sediments. All these help to piece together how cosmic materials are transported in interstellar space and re-cycled into and between generations of stars. Our description of cosmic compositional evolution needs observational support, as it rests on several assumptions that appear challenged. This overview presents the flow of cosmic matter and the various sites of nucleosynthesis, as understood from combining many techniques and observations, towards the current knowledge of how the universe is enriched with elements.
We propose and analyze an efficient and accurate numerical method for computing ground states of spin-2 Bose-Einstein condensates (BECs) by using the normalized gradient flow (NGF). In order to successfully extend the NGF to spin-2 BECs which has five components in the vector wave function but with only two physical constraints on total mass conservation and magnetization conservation, two important techniques are introduced for designing the proposed numerical method. The first one is to systematically investigate the ground state structure and property of spin-2 BECs within a spatially uniform system, which can be used on how to properly choose initial data in the NGF for computing ground states of spin-2 BECs. The second one is to introduce three additional projection conditions based on the relations between the chemical potentials, together with the two existing physical constraints, such that the five projection parameters used in the projection step of the NGF can be uniquely determined. Then a backward-forward Euler finite difference method is adapted to discretize the NGF. We prove rigorously that there exists a unique solution of the nonlinear system for determining the five projection parameters in the full discretization of the NGF under a mild condition on the time step size. Extensive numerical results on ground states of spin-2 BECs with ferromagnetic/nematic/cyclic phase and harmonic/optical lattice/box potential in one/two dimensions are reported to show the efficiency and accuracy of the proposed numerical method and to demonstrate several interesting physical phenomena on ground states of spin-2 BECs.
We discuss the discrete as well as the continuous symmetry transformations for a three (2+1)-dimensional (3D) combined system of the free Abelian 1-form and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism and establish their relevance in the context of the algebraic structures that are obeyed by the de Rham cohomological operators of differential geometry. In fact, our present field-theoretic system respects six continuous symmetry transformations and a couple of very useful discrete duality symmetry transformations. Out of the above six continuous symmetry transformations four are off-shell nilpotent (i.e. fermionic) in nature and two are bosonic. The algebraic structures, obeyed by the symmetry operators, are reminiscent of the algebra satisfied by the de Rham cohomological operators. Hence, our present 3D field-theoretic system provides a perfect example for Hodge theory where there is convergence of ideas from the physical aspects of the BRST formalism and mathematical ingredients that are connected with the cohomological operators of differential geometry at the algebraic level. One of the highlights of our present investigation is the appearance of a pseudo-scalar field in our theory (on the symmetry ground alone) which carries the negative kinetic term. Thus, it is one of the possible candidates for the ``phantom" fields of the cyclic, bouncing and self-accelerated cosmological models of the Universe.