This paper explores the role of quantum complexity in detecting decoherence in the early universe, using the curved-space Caldeira-Leggett model in de Sitter space as a toy model. The study investigates how the complexity of purification (COP) can serve as an alternative diagnostic for decoherence, particularly in the context of inflation. The model includes two massive scalar fields, φ and χ, quadratically coupled to each other and minimally coupled to gravity in a de Sitter background. The analysis focuses on the time evolution of the complexity and linear entropy, and how these quantities can reveal signatures of decoherence. The paper demonstrates that in the curved-space Caldeira-Leggett model, the growth of complexity exhibits a distinctive feature, such as a bump, which correlates with the saturation of linear entropy. This feature is interpreted as a signal of decoherence. The study compares the time evolution of complexity with that of linear entropy and entanglement negativity, showing that the change in the growth rate of complexity is a faithful indicator of the timescale at which decoherence occurs. The results indicate that in the regime where the coupling strength λ² is less than 3MH/2, the complexity of purification exhibits a bump that aligns with the saturation timescale of linear entropy. This suggests that the bump in complexity is a sharper signature of mixedness than the linear entropy, which asymptotically approaches unity. In the regime where λ² is greater than 3MH/2, the complexity continues to grow linearly, and the bump is less pronounced, but the saturation timescale of linear entropy still coincides with the emergence of the bump. The study highlights the importance of quantum complexity as a tool for understanding the evolution of primordial cosmological perturbations in the early universe. It suggests that the growth of complexity can provide insights into the decoherence process, which is essential for the classicalization of quantum fluctuations during inflation. The findings open new avenues for exploring the quantum nature of the early universe and its connection to inflationary cosmology.This paper explores the role of quantum complexity in detecting decoherence in the early universe, using the curved-space Caldeira-Leggett model in de Sitter space as a toy model. The study investigates how the complexity of purification (COP) can serve as an alternative diagnostic for decoherence, particularly in the context of inflation. The model includes two massive scalar fields, φ and χ, quadratically coupled to each other and minimally coupled to gravity in a de Sitter background. The analysis focuses on the time evolution of the complexity and linear entropy, and how these quantities can reveal signatures of decoherence. The paper demonstrates that in the curved-space Caldeira-Leggett model, the growth of complexity exhibits a distinctive feature, such as a bump, which correlates with the saturation of linear entropy. This feature is interpreted as a signal of decoherence. The study compares the time evolution of complexity with that of linear entropy and entanglement negativity, showing that the change in the growth rate of complexity is a faithful indicator of the timescale at which decoherence occurs. The results indicate that in the regime where the coupling strength λ² is less than 3MH/2, the complexity of purification exhibits a bump that aligns with the saturation timescale of linear entropy. This suggests that the bump in complexity is a sharper signature of mixedness than the linear entropy, which asymptotically approaches unity. In the regime where λ² is greater than 3MH/2, the complexity continues to grow linearly, and the bump is less pronounced, but the saturation timescale of linear entropy still coincides with the emergence of the bump. The study highlights the importance of quantum complexity as a tool for understanding the evolution of primordial cosmological perturbations in the early universe. It suggests that the growth of complexity can provide insights into the decoherence process, which is essential for the classicalization of quantum fluctuations during inflation. The findings open new avenues for exploring the quantum nature of the early universe and its connection to inflationary cosmology.