On the acceleration of the Universe

 

Observation by Perlmutter and others have shown that the Universe expands with an acceleration. This phenomenon could be explained by considering a variable  term in the Einstein field equations. We write the field equations in the form, where  is a constant and  is a variable, and impose the condition that the entire right hand term is divergenceless, instead of the condition that  is divergenceless. Then it is not the energy momentum of matter and radiation that is conserved, but the energy momentum of matter, radiation and the energy of the  field.

 

Using the modified field equations, it can be shown that the density , the pressure  and  in the Robertson Walker metric satisfy the equations

 

 

and  where . denotes differentiation with respect to cosmic time t.

 

The above equations can be solved for different values of and.

 

For example if , they have the solutions

 

  and

 

where and  are constants, when.

 

Taking and  with  and could be schematically represented by

 

 

 

 

 

  

 

 

 

 

  

The graph shows that the universe expands initially, during phase AB then contracts in BC and expands again with an acceleration in CD, before deceleration sets in during the phase DE. The acceleration of the universe observed by Perlmutter and his colleagues could correspond to the phase CD.

 

The universe having reached a maximum ‘volume’ at E would contract to a minimum at H going through the intermediate minimum and maximum at F& G respectively, only to repeat the cycle.

 

M. D. P. Hemantha.
Department of Physics, University of Kelaniya, Kelaniya, Sri Lanka.

and

Nalin de Silva.
Department of Mathematics, University of Kelaniya, Kelaniya, Sri Lanka.