# RUDN Physicists Gave a Mathematical Description of Accelerated Expansion of the Universe According to the Multidimension

*RUDN physicists have a mathematical description of the observed expansion of the Universe using cosmological solutions in the (n+1)-dimensional Einstein-Gauss-Bonnet model. The researchers also proved the existence of stable solutions with relatively small variability of the effective gravity constant G. The work was published in the*General Relativity and Gravitation

*journal.*

In 19998-1999 Saul Perlmutter, Brian P. Schmidt, and Adam Riess together with their colleagues discovered accelerated expansion of the Universe and in 2011 were awarded the Nobel Prize in Physics for it. To explain this and a number of other discoveries, the scientists created a theoretical Lambda-CDM model using the terms "dark energy" and "dark matter". Currently it is the simplest and most realistic explanation of accelerated expansion of the Universe. Based on this model (less the dark matter) with the added Gauss-Bonnet component, RUDN physicists managed to find and study sample solutions of mathematical equations that correspond to the experimental data.

RUDN researchers found numerous solutions of equations that describe exponential expansion of our universe and anisotropic (i.e. independent of direction) dynamics of its inner subspace. To do so, the authors used (n+1)-dimensional space-time with n spatial and 1 time dimension. They also introduced mathematical parameters: two size constants and a lambda-term of the multidimensional theory. These are constant values that set up physical parameters of the 4-dimensional theory and describe the accelerated expansion of the Universe.

As a result, RUDN scientists managed to reduce the task to an algebraic quadratic equation. By changing the global parameters of the system, they found all cases in which the real roots of this equation exist. In particular, they found lambda value limitations that guarantee the existence of the solutions.

The work of the researchers was divided into several stages. First, RUDN scientists developed a system of three quadratic equations in the given mathematical model. Then they reduced it to a quadratic equation to find out a non-dimensional parameter. On the second stage the physicists studied the existence of solutions of such an equation for various values of the initial lambda-term. On the third stage the scientists considered the stability of the obtained solutions using the results of their previous works. After that the physicists studied a subclass of solutions with relatively small variations of the effective gravity constant G—the one that determines the force of gravitational interaction in our world—and demonstrated the stability of such solutions.

"From the physical perspective, we've found multidimensional cosmological models describing the accelerated expansion of a 3-dimensional subspace and a relatively small variation of the effective gravity constant that meets current observational limitations, including the strictest ones obtained by our colleagues from the Pulkovo observatory based on the total of ephemerides, e.g. planets and their satellites," says Vladimir Ivashchuk, a co-author of the work, Ph.D. in Physics and Mathematics, and Professor of the Science and Educational Institute of Gravitation and Cosmology at RUDN.

**More information:**

V. D. Ivashchuk et al. Stable exponential cosmological solutions with two factor spaces in the Einstein–Gauss–Bonnet model with a $$Lambda $$Λ-term,

*General Relativity and Gravitation*(2018). DOI: 10.1007/s10714-018-2447-4

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