The cosmological star formation history from the Local Cosmological Volume of galaxies and constraints on the matter homogeneity

The Lilly-Madau plot is commonly interpreted as the history of the cosmic star formation of the Universe by showing the co-moving star formation rate density (SFRD) over cosmic time. Therefore, the Lilly-Madau plot is sensitive not only to the star formation history (SFH) but also to the number density of galaxies. Assessing the Catalogue of Neighbouring Galaxies, we reconstruct the SFHs of galaxies located in the Local Cosmological Volume (LV) based on delayed-$\tau$ and power-law SFH models. Galaxies with stellar masses of $M_{*} \gtrsim 10^{10}\,\rm{M_{\odot}}$ typically evolve according to the delayed-$\tau$ model by having first increasing followed by exponentially declining SFRs, while the majority of less massive star-forming galaxies have an almost constant or increasing SFH. Deducing the cosmic SFRD evolution of the LV reveals that the SFHs of local galaxies are inconsistent with the Lilly-Madau plot. The SFRDs of the LV are significantly lower at redshifts of $z \lesssim 3$ underestimating the Lilly-Madau peak at $z = 1.86$ by a factor of $2.16\pm0.32$ (delayed-$\tau$ model) and $5.90\pm0.88$ (power-law model). Assuming the delayed-$\tau$ model for galaxies with $M_{*} \geq 10^{10}\,\rm{M_{\odot}}$ and a power-law model for less massive galaxies, the SFRD is $2.22\pm0.33$ lower than measured at $z = 1.86$. This inconsistency between the evolution of the local and global SFRD has cosmological implications. Since the Lilly-Madau plot also constrains the cosmological matter field, the near-constancy of SFHs of LV galaxies could imply that the peak of the Lilly-Madau plot at $z = 1.86$ is the imprint of an $\approx~5$ co-moving Gpc-scale inhomogeneity.