Researchers have developed a new cosmological framework that integrates decaying dark matter (DDM) with a semi-cosmographic reconstruction of dark energy. This model allows the study of nonlinear structure formation in the universe, where a non-relativistic dark matter component decays into relativistic dark radiation with a decay rate Γ. In parallel, dark energy is modeled directly from the cosmic expansion history, rather than assuming a fixed cosmological constant. This unified approach connects a reconstructed dark energy sector and DDM to the nonlinear formation of cosmic structures, offering a more flexible perspective on the universe's evolution.

To constrain this model, the team used data from the Baryon Acoustic Oscillation (BAO) measurements and compressed ShapeFit measurements from DESI DR1. These data were employed to determine the background cosmological evolution, propagating the resulting constraints into the nonlinear regime through spherical collapse and halo abundance calculations. The results indicate that the reconstructed dark energy equation of state can deviate from the standard ΛCDM value (w=-1), while the critical density threshold for structure collapse remains close to its standard prediction.

The most significant signatures of this model emerge in the abundance of massive halos, reflecting modifications to the growth of structures driven by both dark matter decay and dynamic dark energy. By combining DESI DR1 clustering constraints with halo mass function measurements from the DESI Legacy Imaging Surveys DR9, joint constraints on the DDM lifetime and dark energy parameters were obtained. This demonstrates that halo abundances provide a powerful complementary probe for investigating non-standard dark sector physics, opening new avenues for understanding the nature of these fundamental components of the universe.