# Our research (Cosmology)

Introduction to the expanding universe

In the frame work of cosmological principle, Alexandre Friedmann derived a set of solution for the Einstein field equations. This was the frame work for the Big Bagng theory. On the other hand, solution for the Einsten field equations for the case of expanding universe already had been derived by George Lameiter without Friedmann's knowledge in 1927. His theory was proved from the observation of Edwin Hubble in 1927. Hubble discovered that the distance galaxies all appeared to be receding from us at speed proportional to their distances. This Hubble parameter express the expanding rate of the universe. This expanding rate is changing with the energy desnities of the universe.Then, it is necessary to investigate the energy content of the universe and their role to expand the universe.

The expansion rate of the universe is mathematically described by the equation Friedmann equation.

$H^2 = \frac{8\pi G}{3}\rho - \frac{k}{a^2}$

The left side of the equation is directly corresponding to the expansion rate of the universe and the right hand side describes the energy densities[1]. kThe < / ref > spacewhere is curvature means at which it has turned. Even if it is said that space has vurved, we may not realize right away by tic [ SF ]. In fact, we are living on the "curved two-dimensional space" the "earth." </ref>. As for densities, such as photons, neutrinos, and a dark matter, are contained. The expansion rate with the energy content of the right-hand side. It implies that if expansion speed can be measured, then the energy densities of the universe can be understood. Then we can obtain what kind of ingredients are occupied in the universe and can predict the ultimate fate of the universe from there.