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The prime object of this article is to study the perfect fluid spacetimesobeying $f(\mathcal{R})$-gravity, when $\eta$-Ricci solitons, gradient$\eta$-Ricci solitons, gradient Einstein Solitons and gradient $m$-quasiEinstein solitons are its metrics. At first, the existence of the $\eta$-Riccisolitons is proved by a non-trivial example. We establish conditions for whichthe $\eta$-Ricci solitons are expanding, steady or shrinking. Besides, in theperfect fluid spacetimes obeying $f(\mathcal{R})$-gravity, when the potentialvector field of $\eta$-Ricci soliton is of gradient type, we acquire a Poissonequation. Moreover, we investigate gradient $\eta$-Ricci solitons, gradientEinstein Solitons and gradient $m$-quasi Einstein solitons in$f(\mathcal{R})$-gravity, respectively. As a result, we establish somesignificant theorems about dark matter era.

Characterizations of Perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity equipped with different gradient solitons