Exploring the low redshift universe: two parametric models for effective pressure

Astrophysical observations have put unprecedentedly tight constraints on cosmological theories. The $\Lambda$CDM model, mathematically simple and fits observational data-sets well, is preferred for explaining the behavior of universe. But many basic features of the dark sectors are still unknown, which leaves rooms for various nonstandard cosmological hypotheses. As the pressure of cosmological constant dark energy is unvarying, ignoring contributions from radiation and curvature terms at low redshift, the effective pressure keeps constant. In this paper, we propose two parametric models for non-constant effective pressure in order to study the tiny deviation from $\Lambda$CDM at low redshift. We recover our phenomenological models in the scenarios of quintessence and phantom fields, and explore the behavior of scalar field and potential. We constrain our model parameters with SNe Ia and BAO observations, and detect subtle hints of $\omega_{de}<-1$ from the data fitting results of both models, which indicates possibly a phantom dark energy scenario at present.Comment: 11 pages, 24 figure

Continuity of Calderón-Zygmund Operators on the Space BMO

David and Journé discovered a criterion for the continuity on L2 of Calder´on- Zygmund operators defined by singular integrals. In their approach the distributional kernel of the given operator is locally H¨older continuous outside the diagonal. The aim of this paper is to prove a David-Journ´e theorem where this smoothness assumption is replaced by a weaker one. Our approach strongly relies on an algorithm developed by Beylkin, Coifman, and Rokhlin