Growth factor in f(T) gravity

We derive the evolution equation of growth factor for the matter over-dense perturbation in $f(T)$ gravity. For instance, we investigate its behavior in power law model at small redshift and compare it to the prediction of $\Lambda$CDM and dark energy with the same equation of state in the framework of Einstein general relativity. We find that the perturbation in $f(T)$ gravity grows slower than that in Einstein general relativity if \p f/\p T>0 due to the effectively weakened gravity.Comment: 15 pages,1 figure; v2,typos corrected; v3, discussions added, accepted by JCA

Red or Blue Tensor Spectrum from GW170817-compatible Einstein-Gauss-Bonnet Theory: A Detailed Analysis

In this work we shall prove that the tensor spectral index of the primordial tensor perturbations for GW170817-compatible Einstein-Gauss-Bonnet theories, takes the approximate simplified form $n_{\mathcal{T}}\simeq 2\left(-1+\frac{1}{\lambda(\phi)} \right)\epsilon_1$ at leading order, with $\lambda (\phi)$ being a function of the scalar field which depends on the scalar field potential and the second derivative of the scalar-Gauss-Bonnet coupling $\xi''(\phi)$. With our analysis we aim to provide a definitive criterion for selecting Einstein-Gauss-Bonnet models that can provide a blue-tilted inflationary phenomenology, by simply looking at the scalar potential and the scalar-Gauss-Bonnet coupling. We shall prove this using two distinct approaches and as we show the tilt of the tensor spectral index is determined by the values of the potential $V(\phi)$ and of scalar-Gauss-Bonnet coupling at first horizon crossing. Specifically the blue-tilted tensor spectral index can occur when $\xi''(\phi_*)V(\phi_*)>0$ at first horizon crossing.Comment: EPL Accepte

Periodic Cosmological Evolutions of Equation of State for Dark Energy

We demonstrate two periodic or quasi-periodic generalizations of the Chaplygin gas (CG) type models to explain the origins of dark energy as well as dark matter by using the Weierstrass $\wp(t)$, $\sigma(t)$ and $\zeta(t)$ functions with two periods being infinite. If the universe can evolve periodically, a non-singular universe can be realized. Furthermore, we examine the cosmological evolution and nature of the equation of state (EoS) of dark energy in the Friedmann-Lema\^{i}tre-Robertson-Walker cosmology. It is explicitly illustrated that there exist three type models in which the universe always stays in the non-phantom (quintessence) phase, whereas it always evolves in the phantom phase, or the crossing of the phantom divide can be realized. The scalar fields and the corresponding potentials are also analyzed for different types of models.Comment: 28 pages, 6 figures, title changed, version to appear in a special issue "Modified Gravity: From Black Holes Entropy to Current Cosmology" of Entrop

Kinetic Axion Dark Matter in String Corrected f(R)f(R) Gravity

Under the main assumption that the axion scalar field mainly composes the dark matter in the Universe, in this paper we shall extend the formalism of kinetic axion $R^2$ gravity to include Gauss-Bonnet terms non-minimally coupled to the axion field. As we demonstrate, this non-trivial Gauss-Bonnet term has dramatic effects on the inflationary phenomenology and on the kinetic axion scenario. Specifically, in the context of our formalism, the kinetic axion ceases to be kinetically dominated at the end of the inflationary era, since the condition $\dot{\phi}\simeq 0$ naturally emerges in the theory. Thus, unlike the case of kinetic axion $R^2$ gravity, the Gauss-Bonnet corrected kinetic axion $R^2$ gravity leads to an inflationary era which is not further extended and the reheating era commences right after the inflationary era, driven by the $R^2$ fluctuations.Comment: Published in the Physics of the Dark Univers

Effect of hydrodynamic cavitation treatment on electrochemical indicators of tap water

Розглянуто особливості кавітаційних процесів в умовах вихрового відцентрового поля тиску при обробці рідин з метою руйнування біологічних забруднювачів низької щільності. Наведено результати дослідження впливу гідродинамічних кавітаційних ефектів на електрохімічні показники водопровідної води: кислотно-лужний баланс; окислювально-відновний потенціал; електропровідність; температуру.The article is devoted to the features of cavitation processes in the vortex centrifugal pressure field in the processing fluids to destroy biological contaminants of low density. The results of the investigation of the influence of hydrodynamic cavitation effects on the electrochemical figures of water: acid-base balance; redox potential; electrical conductivity; temperature were given.Рассмотрены особенности кавитационных процессов в условиях вихревого центробежного поля давления при обработке жидкостей с целью разрушения биологических загрязнителей низкой плотности. Приведены результаты исследования влияния гидродинамических кавитационных эффектов на електрохимические показатели водопроводной воды: кислотно-щелочной баланс; окислительно-восстановительный потенциал; електропроводность; температуру