In the current paper, we have studied the effect of dark energy on for-mation where dark energy exists in the background. For this purpose, we used both WMAP9 and Planck data to study how the radius changes with redshift in these mod-els. We used different data sets to fix the cosmological parameters to obtain a solution for a spherical region under collapse. The mechanism of structure formation f...

Gravitational interaction is considered with use of the universal charge. Gravitational wave is defined as a tenzor electromagnetic like wave of the Planck mass. Within the Planck time it decays into four hypothetical Planck neutrinos. The quadrupole gravitational emission in the theory with the universal charge is the same as in general relativity. Gravitational radiation as Planck neutrinos d...

It is possible that the scale of gravity, parametrized by the apparent Planck mass, may obtain different values within different universes in an encompassing multiverse. We investigate the range over which the Planck mass may scan while still satisfying anthropic constraints. The window for anthropically allowed values of the Planck mass may have important consequences for landscape predictions...

In 1984, H. Risken authored a book (H. Risken, The Fokker-Planck Equation: Methods of Solution, Applications, Springer-Verlag, Berlin, New York) discussing the Fokker-Planck equation for one variable, several variables, methods of solution and its applications, especially dealing with laser statistics. There has been a considerable progress on the topic as well as the topic has received greater...

A quantum gravitational instability is identified at Planck scales between nonspinning extreme Schwarzschild black holes and spinning extreme Kerr black holes, which produces a turbulent Planck particle gas. Planck inertial vortex forces balance gravitational forces as the Planck turbulence cascades to larger scales and the universe expands and cools. Turbulent mixing of temperature fluctuation...

Stochastic differential equations (SDE) are used to model many situations including population dynamics, protein kinetics, turbulence, finance, and engineering [5, 6, 1]. Knowing the solution of the SDE in question leads to interesting analysis of the trajectories. Most SDE are unsolvable analytically and other methods must be used to analyze properties of the stochastic process. From the SDE, ...