### Exact Vacuum Solutions of Five-Dimensional Bianchi Type-I Space-Time in f (R) Theory of Gravity

#### Abstract

In the present paper, we have discussed the well-known phenomenon of the universe expansion in the context of *f(R)* theory of gravity in five dimensional Bianchi type-I space time using the vacuum field equations on the lines of M. Sharif and M. Farasat Shamir (2009). In particular, we have obtained two exact solutions by using the variation law of Hubble parameter. These solutions correspond to two models of the universe in *V _{5}*. The first solution (

*n*

*≠*

*0)*gives a singular model while the second (

*n=0*) provides a non-singular model. The physical behaviour of these five dimensional Bianchi type-I space time models has also been discussed. Moreover, the function

*f(R)*of the Ricci scalar has been evaluated for both the models. The work of M. Sharif and M. Farasat Shamir (2009) regarding exact solutions of the four dimensional Bianchi type-I space-time in

*f(R)*theory of gravity emerge as special case of the work carried out in the present paper.