Abstract
The prime object of this paper is to study the perfect fluid spacetimes obeying [Formula: see text]-gravity, when [Formula: see text]-Ricci solitons, gradient [Formula: see text]-Ricci solitons, gradient Einstein solitons and gradient [Formula: see text]-quasi Einstein solitons are its metrics. At first, the existence of the [Formula: see text]-Ricci solitons is proved by a non-trivial example. We establish conditions for which the [Formula: see text]-Ricci solitons are expanding, steady or shrinking. Besides, in the perfect fluid spacetimes obeying [Formula: see text]-gravity, when the potential vector field of [Formula: see text]-Ricci soliton is of gradient type, we acquire a Poisson equation. Moreover, we investigate gradient [Formula: see text]-Ricci solitons, gradient Einstein solitons and gradient [Formula: see text]-quasi Einstein solitons in [Formula: see text]-gravity, respectively. As a result, we establish some significant theorems about dark matter era.
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