In this work we study the evolution of matter-density perturbations for an arbitrary $\Lambda (t)$ model and specialize our analysis to the particular phenomenological law $\Lambda ={\Lambda }_0+3\beta H^2$. We study the evolution of the cosmic star formation rate in this particular dark energy scenario and, by constraining the $\beta$ 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 $\beta \lesssim 0.1$.

• Received 13 August 2013

DOI:https://doi.org/10.1103/PhysRevD.88.083530