An f(R) theory of gravity motivated by gravitational waves

Gravitational waves are an inevitable consequence of Einstein theory of gravitation. They are meaningfully comparable with electromagnetic waves except for their non-conformal invariance. So, to obtain them conformally invariant we modify Einstein field equations by choosing a. Lagrangian as a polynomial in of a finite number of terms without associating it with any other field except gravitation. In this modified field theory of gravity we have also studied the cosmological aspects and the spherically symmetric field along with equations of motion of a particle to bring out the features of this f (R) theory of gravitation.