Constraining Cosmological and Astrophysical Parameters with the Cosmic Star Formation History

Identifying new observational probes to constrain cosmological parameters has become an important goal in modern cosmology. In this work, we explore the potential of the cosmic star formation rate density (SFRD), compiled over the redshift range $z \in [0, 15]$, as a complementary probe of fundamental parameters, including $\Omega_{\rm m}$, $H_0$, and the dark energy equation-of-state parameter, $w$. Within the $\Lambda$CDM framework, SFRD combined with BBN data alone yields $H_0 = 65\pm11$ km\,s$^{-1}$\,Mpc$^{-1}$, reflecting significant degeneracies with astrophysical parameters. By jointly analyzing SFRD with recent BAO and Type Ia supernova (SNIa) data, these degeneracies are effectively broken, resulting in much tighter constraints, e.g., \texttt{SFRD + BBN} + \texttt{DESI-DR2} gives $H_0 = 68.28 \pm 0.18$ km\,s$^{-1}$\,Mpc$^{-1}$. We perform a statistical reconstruction of the SFRD as a function of redshift, finding a peak at $z_{\rm peak} = 2.600^{+0.114}_{-0.087}$ within $\Lambda$CDM. Our results demonstrate that combining SFRD with established cosmological probes not only improves constraints on cosmological parameters but also reduces uncertainties in astrophysical parameters governing star formation. We further extend the analysis to the $w$CDM model, highlighting the promise of SFRD as a robust complementary cosmological probe across different dark energy scenarios.