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 from Dark Energy Spectroscopic Instrument Data Release 2 (including $r_d$ constraint from cosmic microwave background), type Ia supernova observations from $\mathrm{Pantheon}+$ sample, logarithmic growth rate $f$ data, and $f{\sigma }_8$ data. While constraints on some parameters remain consistent, inclusion of cosmic curvature loosens constraints on ${\mathrm{\Omega }}_{\mathrm{m}0}$ and ${\sigma }_{8,0}$ in $\mathrm{\Lambda }$ cold dark matter (CDM) and $w_0\mathrm{CDM}$ models. The nonphantom behavior of dark energy proves more favorable in the $w_0\mathrm{CDM}$ model, whereas in the Chevallier-Polarski-Linder (CPL) model, there is certain evidence for nonphantom behavior at lower redshift and phantom behavior at higher redshift. Interestingly, we find certain evidence for nonzero cosmic curvature in the $\mathrm{\Lambda }\mathrm{CDM}$ model, but no evidence for it in both the $w_0\mathrm{CDM}$ and CPL models, which indirectly proves the nondegeneracy between dynamical dark energy and cosmic curvature.

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• Dark energy
• Large scale structure of the Universe