Oscillating universe

A problem that has always fascinated philosophers and scientists is how the universe began. Current thinking assumes that universe began as a singularity in space and time. This singularity is called big bang at which time everything was condensed into a very small space where both density and temperature were exceptionally high. Since then the universe has been in continuous expansion. Rate of expansion of universe is given by Hubble's law which states that rate of separation of any two galaxies is increasing with respect to time is given by $V = HR$ , where $R$ is separation between galaxies, $V$ is relative velocity of separation and $H$ is Hubble's constant having value \(H = \SI{2.38 \times 10^{-18}} {s^{-2}}\).

However rate of expansion is decreasing continuously as kinetic energy transforms into gravitational potential energy. So a possibility exists that universe will either continue to expand forever or stop expanding and begin to contract under gravitational attraction. In such a case the gravitational potential energy will transform back into kinetic energy and all matter will eventually collapse into a Big crunch.

The universe could then re-emerge with a new Big Bang and start all over again. This possibility corresponds to the oscillating universe. We call an oscillating universe closed and expanding universe open. To estimate the necessary requirement for either case, consider a sphere of radius $R$ large enough to contain several galaxies. Let $\rho$ be the average density of this sphere. Now consider a single galaxy of mass m on the surface of the sphere. Total energy of such a system is

$E = \frac{1}{2}m{H^2}{R^2} - \frac{4}{3}\pi {R^3}\rho \frac{{Gm}}{R} = m{R^2}\left( {\frac{1}{2}{H^2} - \frac{4}{3}\pi G\rho } \right).$

So $m$ will continuously move away or eventually start falling back depending on whether $E > 0$ or $E < 0$ . The average density of universe for which E = 0, is called critical density $\rho_c$ .