Lyttleton-Bondi Model for the Expansion of the Universe

In 1959, Lyttleton and Bondi suggested that the expansion of the Universe could be explained on the basis of Newtonian mechanics if matter carried a net electric charge. Imagine a spherical volume of astronomical size and radius R containing un-ionized atomic hydrogen gas of uniform density η, and assume that the proton charge e(p) = (1 + y).e, where is the modulus of the electron charge.

a) Obtain the value(expression) of y for which the electrostatic repulsion becomes larger than the gravitational attraction and the gas cloud expands.

b) Obtain an expression for the force of repulsion on an atom which is at a distance R from the centre of the spherical volume. Hence show that the radial velocity is proportional to R. Let us label the proportionality constant as H. Assume that the density is maintained constant somehow by the continuous creation of matter in space. Assume also that the value of y is quite larger than the equilibrium value calculated in (a) above and hence ignore gravity.

c) Given that at time t = 0, the volume of the Universe was Vo, obtain an expression for the volume expansion of the Universe.

Note: Experiments do not indicate a difference in the magnitudes of the electron and proton charge. Some theories regarding the nature of the fundamental forces and elementary particles also do not point to a difference. Hence the Lyttleton-Bondi model has been largely discarded by the scientific community.