Future dynamics in f(R) theories

The $f(R)$ gravity theories provide an alternative way to explain the current cosmic acceleration without invoking dark energy matter component. However, the freedom in the choice of the functional forms of $f(R)$ gives rise to the problem of how to constrain and break the degeneracy among these gravity theories on theoretical and/or observational grounds. In this paper to proceed further with the investigation on the potentialities, difficulties and limitations of $f(R)$ gravity, we examine the question as to whether the future dynamics can be used to break the degeneracy between $f(R)$ gravity theories by investigating the future dynamics of spatially homogeneous and isotropic dust flat models in two $f(R)$ gravity theories, namely the well known $f(R) = R + \alpha R^{n}$ gravity and another by A. Aviles et al., whose motivation comes from the cosmographic approach to $f(R)$ gravity. To this end we perform a detailed numerical study of the future dynamic of these flat model in these theories taking into account the recent constraints on the cosmological parameters made by the Planck team. We show that besides being powerful for discriminating between $f(R)$ gravity theories, the future dynamics technique can also be used to determine the fate of the Universe in the framework of these $f(R)$ gravity theories. Moreover, there emerges from our numerical analysis that if we do not invoke a dark energy component with equation-of-state parameter $\omega < -1$ one still has dust flat FLRW solution with a big rip, if gravity deviates from general relativity via $f(R) = R + \alpha R^n$. We also show that FLRW dust solutions with $f''<0$ do not necessarily lead to singularity.Comment: 12 pages, 8 figures. V2: Generality and implications of the results are emphasized, connection with the recent literature improved, typos corrected, references adde

Structural and functional stabilization of glycomacropeptide via encapsulation within multiple emulsions

Bovine glycomacropeptide (GMP), derived from whey proteins, has been demonstrated to possess an interesting bioactivity that has attracted a lot of attention over the last few years. In particular, its ability to bind Vibrio cholerae and Escherichia coli enterotoxins, inhibit bacterial and viral adhesion, suppress gastric secretions, promote bifidobacterial growth and modulate immune system responses. Of these, protection against toxins, bacteria and viruses, and modulation of the immune system, are the most promising applications for this bioactive dairy macropeptide. The development of strategies that may allow its structural and functional stabilization via nanoencapsulation within multiple emulsions may increase its food and biopharmaceutical applicabilities. In this research effort, bovine GMP was (thermodynamically) stabilized via entrapment within water-in-oil-in-water (W/O/W) multiple emulsions aiming at mimicking the multifunctional design of biology, with several lipid matrices, and stabilizing layer compositions. Due to their compartimentalized internal structure, multiple emulsions are ideal for encapsulation since they can carry both polar and non-polar (bio)molecules. The composition of the stabilizing layer of the nanosystem was changed by using different poloxamers and proportions of lecithin. Physicochemical characterization of the optimized GMP-encasing nanovesicle formulations encompassed determination of Zeta potential and particle hydrodynamic size over storage time, surface morphology via CRYO-SEM, and microcalorimetric analysis via DSC