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L. S. LadkeAssociate Professor & Head, Department of Mathematics, Sarvodaya Mahavidyalaya, Sindewahi, Dist:Chandrapur (441222), India. |

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The vacuum solution of Bianchi types-I (Kasner form) cosmological model in f(R) theory of gravity has been obtained. The general solution of the field equations in respect of Bianchi type-I space-time in Kasner form have been obtained with the assumption of special form of deceleration parameter. The physical behavior of the model has been discussed by obtaining some physical quantities.

## Keywords |

f (R) theory of gravity, Bianchi type-I space-time in Kasner form, Special form of deceleration parameter. |

## INTRODUCTION |

The f (R) theory of gravity plays an important role in describing the evolution of the universe. The f (R) theory of gravity is the modification of the general theory of relativity proposed by Einstein. The f (R) actions were first studied by Weyl [1] and Eddington [2]. The f (R) gravity provides a very natural unification of the early-time inflation and late-time acceleration. Carroll et al.[3] explained the presence of a late time cosmic acceleration of the universe in f (R) gravity. As per Nojiri and Odintsov ( [4],[5] ) a unification of the early time inflation and late time acceleration is allowed in f (R) gravity. |

## RELATED WORK |

Multamaki & Vilja ( [6],[7] ) investigated static spherically symmetric vacuum solutions of the field equations and non-vacuum solutions by taking perfect fluid respectively. Sharif & Shamir [8] studied exact vacuum solutions of Bianchi type-I & type-V space times in f (R) theory of gravity. Non-vacuum solutions in Bianchi type-I & type-V using perfect fluid in f (R) gravity have been obtained by Sharif & Shamir [9]. Shamir [10] discussed the plane symmetric vacuum Bianchi type-III cosmology in f (R) gravity. Bianchi type-III space time with anisotropic fluid in f (R) gravity has been dealt with by Sharif & Kausar [11]. Aktas et al. [12] have studied anisotropic models in f (R) theory of gravity. Adhav [13] discussed the Kantowski–Sachs string cosmological model in f (R) theory of gravity. Singh et al. [14] studied functional form of f (R) with power-law expansion in anisotropic model. Recently, Reddy et al. [15] studied vacuum solution of Bianchi type-I and V models in f (R) gravity with a special form of deceleration parameter. |

Motivated by the above research, in this paper, the general solutions of the field equations of f (R) gravity for Bianchi type-I space-time in Kasner form have been obtained with the assumption of special form of deceleration parameter. The physical behavior of the model is also discussed. |

## f (R) THEORY OF GRAVITY AND DECELERATION PARAMETER |

The f (R) theory of gravity is nothing but modification of general theory of relativity. The action for f (R) theory of gravity is given by |

iv) It is observed that in Bianchi type-I model, the anisotropy increases as time increases and then it decreases to zero after some time and remains zero. Hence, the model reaches to isotropy after some finite time. |

v) It is seen that, the results obtained here are similar to the results obtained earlier by Reddy et al.[15].. |

## References |

[1] Weyl H.: Ann. Phys., 59, 101 (1919). [21]Cunha J.V. and Lima J.A.S.” Transition redshift: new kinematic constraints from supernovae” Mon. Not. R. Astron. Soc.: 390(1),pp.210-217 (2008). |