  This study explores the impact of cosmic curvature on structure formation
through general relativistic first-order perturbation theory. We analyze
continuity and Euler equations, incorporating cosmic curvature into Einstein
equations. Emphasizing late-time dynamics, we investigate matter density
contrast evolution in the presence of cosmic curvature, with a specific focus
on sub-hubble scales. Solving the evolution equation, we conduct data analysis
using cosmic chronometers, baryon acoustic oscillations, type Ia supernova
observations and $f\sigma_8$ data. While constraints on some parameters remain
consistent, excluding cosmic curvature tightens constraints on $\Omega_{\rm
m0}$ and $\sigma_{\rm 80}$ in $\Lambda$CDM and $w$CDM models. Intriguingly, the
non-phantom behavior of dark energy proves more favorable in both $w$CDM and
CPL models across diverse data combinations.
