Implications of the Conformal Higgs Model

The postulate of universal local Weyl scaling (conformal) symmetry modifies both general relativity and the Higgs scalar field model. The conformal Higgs model (CHM) acquires a cosmological effect that fits the observed accelerating Hubble expansion for redshifts z≤1 (7.33 Gyr) accurately with only one free constant parameter. Conformal gravity (CG) has recently been fitted to anomalous rotation data for 138 galaxies. Conformal theory explains dark energy and does not require dark matter, providing a viable alternative to the standard ΛCDM paradigm. The theory precludes a massive Higgs particle but validates a composite gauge field W2 with mass 125 GeV.

The graviton Compton mass as Dark Energy

One of the greatest challenges of science is to understand the current accelerated expansion of the Universe. In this work we show that by considering the quantum nature of the gravitational field, its wavelength can be associated to an effective Compton mass. We propose that this mass can be interpreted as dark energy, with a Compton wavelength given by the size of the observable Universe, implying that the dark energy varies depending on this size. If we do so, we find that: 1.- Even without any free constant for dark energy, the evolution of the Hubble parameter is exactly the same as for the LCDM model, so this model has the same predictions as LCDM. 2.- The density rate of the dark energy is ΩΛ = 0.69 which is a very similar value as the one found by the Planck satellite ΩΛ = 0.684. 3.- The dark energy has this value because it corresponds to the actual size of the radius of the Universe, thus the coincidence problem has a very natural explanation. 4.- It is possible to find also a natural explanation to why observations inferred from the local distance ladder find the value H0 = 73 km/s/Mpc for the Hubble constant, we show that if we take the variability of the dark energy into account they should measure H0 = 67.3 km/s/Mpc as well. 5.- In this model the inflationary period contains a natural successful graceful exit.

The graviton Compton mass as dark energy

One of the greatest challenges of science is to understand the current accelerated expansion of the Universe. In this work we show that by considering the quantum nature of the gravitational field, its wavelength can be associated to an effective Compton mass. We propose that this mass can be interpreted as dark energy, with a Compton wavelength given by the size of the observable Universe, implying that the dark energy varies depending on this size. If we do so, we find that: 1.- Even without any free constant for dark energy, the evolution of the Hubble parameter is exactly the same as for the LCDM model, so this model has the same predictions as LCDM. 2.- The density rate of the dark energy is ΩΛ = 0.69 which is a very similar value as the one found by the Planck satellite ΩΛ = 0.684. 3.- The dark energy has this value because it corresponds to the actual size of the radius of the Universe, thus the coincidence problem has a very natural explanation. 4.- It is possible to find also a natural explanation to why observations inferred from the local distance ladder find the value H0 = 73 km/s/Mpc for the Hubble constant, we show that if we take the variability of the dark energy into account they should measure H0 = 67.3 km/s/Mpc as well. 5.- In this model the inflationary period contains a natural successful graceful exit.

Structure of the self-gravitating accretion discs in the presence of outflow

ABSTRACT Numerical simulations of self-gravitating accretion discs have shown that the evolution of such systems depends strongly on the rate at which it cools. In this work, we study the vertical structure of the self-gravitating accretion discs and also investigate the effect of the cooling rate on the latitudinal structure of such accretion discs. In the spherical coordinates, we write the hydrodynamics equations and simplify the basic equations based on the assumptions of axisymmetric and steady state. We use the self-similar method for solving the equations in the radial direction and we find proper boundary conditions. We find inflow–outflow solutions by considering the meridional component of the velocity field. In order to formulate the cooling term in energy equation, we introduce the new parameter β as a free constant that is the cooling time-scale in units of the dynamical time-scale. Our numerical solutions show that the thickness of the disc decreases with smaller β (or increasing the cooling term in energy equation) and it makes the disc colder and outflows form in the regions with lower latitude. So by increasing the cooling rate in the disc, the regions which belong to inflow decrease.

Some models with repulsion effect on superinfecting viruses by infected cells

In this paper, we study some models with repulsion effect on superinfecting viruses by infected cells [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are the density of uninfected cells, infected cells and viruses at time [Formula: see text] at location [Formula: see text], respectively. The functions [Formula: see text] and [Formula: see text] are assumed to be positive, continuous and bounded. [Formula: see text] denotes the production rate of uninfected cells. The infection rate is [Formula: see text] and the function [Formula: see text] is the production rate of free viruses. And [Formula: see text] is the rate of transfer from uninfected cells to infected cells. The positive constants [Formula: see text] and [Formula: see text] denote the death rate of uninfected cells, infected cells and viruses, respectively. The stability of the infection-free equilibrium solution and infection equilibrium solution is discussed. It is shown that if the basic reproduction number [Formula: see text] then the chemotaxis has no effect, that is, the infection-free constant solution is stable. For the system with chemotactic sensitivity [Formula: see text], if [Formula: see text], then the infection constant solution will be unstable under some conditions.