Probing a cosmological model with a $Λ= Λ_0 + 3βH^2$ decaying-vacuum

In this work we study the evolution of matter-density perturbations for an arbitrary $Λ(t)$ model, and specialize our analysis to the particular phenomenological law $Λ= Λ_0 + 3βH^2$. We study the evolution of the cosmic star formation rate in this particular dark energy scenario and, by constraining the $β$ parameter using both the age of the universe and the cosmic star formation rate curve, we show that it leads to a reasonable physical model for $β\lesssim 0.1$.

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