Conceptual problem for noncommutative inflation and the new approach for nonrelativistic inflationary equation of state

In a previous paper, we connected the phenomenological noncommutative inflation of Alexander, Brandenberger and Magueijo [ Phys. Rev. D 67 081301 (2003)] and Koh and Brandenberger [ J. Cosmol. Astropart Phys. 2007 21 ()] with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group-like procedure in which even Hopf algebras (roughly the symmetries of noncommutative spaces) could lead to the equation of state of inflationary radiation. Nevertheless, in this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons being bounded from above) and the Fock-space structure of the representation which leads to the fundamental inflationary equations of state. We show that the Fock structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like leading to a problematic scattering theory, for example. We suggest replacing the Fock space by one of two possible structures that we propose. One of them relates to the general theory of Hopf algebras (here explained at an elementary level) while the other is based on a representation theorem of von Neumann algebras (a generalization of the Clebsch-Gordan coefficients), a proposal already suggested by us to take into account interactions in the inflationary equation of state.

From inflation to dark energy through a dynamical Λ: an attempt at alleviating fundamental cosmic puzzles

After decades of successful hot big-bang paradigm, cosmology still lacks a framework in which the early inflationary phase of the universe smoothly matches the radiation epoch and evolves to the present “quasi” de Sitter spacetime. No less intriguing is that the current value of the effective vacuum energy density is vastly smaller than the value that triggered inflation. In this paper, we propose a new class of cosmologies capable of overcoming, or highly alleviating, some of these acute cosmic puzzles. Powered by a decaying vacuum energy density, the spacetime emerges from a pure nonsingular de Sitter vacuum stage, “gracefully” exits from inflation to a radiation phase followed by dark matter and vacuum regimes, and, finally, evolves to a late-time de Sitter phase.

Inhibitors of Trypanosoma brucei trypanothione reductase: comparative molecular field analysis modeling and structural basis for selective inhibition

Background: Sleeping sickness is a major cause of death in Africa. Since no secure treatment is available, the development of novel therapeutic agents is urgent. In this context, the enzyme trypanothione reductase (TR) is a prominent molecular target that has been investigated in drug design for sleeping sickness. Results: In this study, comparative molecular field analysis models were generated for a series of Trypanosoma brucei TR inhibitors. Statistically significant results were obtained and the models were applied to predict the activity of external test sets, with good correlation between predicted and experimental results. We have also investigated the structural requirements for the selective inhibition of the parasite's enzyme over the human glutathione reductase. Conclusion: The quantitative structure-activity relationship models provided valuable information regarding the essential molecular requirements for the inhibitory activity upon the target protein, providing important insights into the design of more potent and selective TR inhibitors.