Question

In 1959 Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density N, which is maintained a constant. Let the charge on the proton be: e_p = – (1 + y)e where e is the electronic charge. 

(a) Find the critical value of y such that expansion may start. 

(b) Show that the velocity of expansion is proportional to the distance from the centre.

Answer 1

(a) Let the Universe have a radius R. Assume that the hydrogen atoms are uniformly distributed. The charge on each hydrogen atom is 

e_H = – (1 + y) e + e = – ye = |ye| 

The mass of each hydrogen atom is ~ mp (mass of a proton). Expansion starts if the Coulomb repulsion on a hydrogen atom, at R, is larger than the gravitational attraction. Let the Electric Field at R be E. Then

Thus the Coulombic force on a hydrogen atom at R is

(b) Because of the net force, the hydrogen atom experiences an acceleration such that

Thus, the velocity is proportional to the distance from the centre.