The idea of existence of extra dimensions first aroused in the beginning of the XX century. Nowadays this idea regains its popularity: thus the idea of extra dimensions underlies almost all modern theories. This field of research comprises a great variety of different branches: Kaluza-Klein theory, string theory, branes, supergravity and etc.

One of our groups develops the approach based on the existence of compact extra dimensions, and the Lagrangian contains as dynamical variables only the metric tensor and is nonlinear in Ricci scalar. Besides no additional assumptions are made concerning the existence of matter fields, strings and branes.

In past several years our group succeeded in solving such problems as:

• developing the method of reduction of multidimensional gravity with higher derivatives to 4 dimensions with observable properties;
• offering a unified description of inflationary and modern stages of Universe; one of the consequences this approach is the prediction of a future growth of the size of extra dimension;
• studying the problem of fundamental physical constants: a gravitational constant and a Planck constant. It is shown that numerical value of gravitational constant depends on the volume of extra space and its geometry and can be different in different regions of the Universe;
• explaining the origin of gauge invariance in low energy physics. It turns out that gauge invariance – the basis of the Standard Model of particle physics – is due to the growth of the entropy of the whole space and is caused by the decay of Kaluza-Klein particles. Thus the gauge invariance is not postulated from the very beginning but is establishing in the process of evolution of the Universe.

Currently, based on our approach, we:

1. develop the model of baryon asymmetry;
2. study the mechanism of formation of gauge and Higgs fields of the Standard Model
3. investigate the mechanism of formation and physical manifestations of spatial fluctuations of the size of the extra space.

We are ready to collaborate with those who are interested in:

1. Compact extra space dynamics;
2. Primordial black holes;
3. Early universe evolution;
4. Multidimensional fermions.