Spatio-temporal impact of R&D innovation on carbon emission intensity: A comparative analysis of Beijing-Tianjin-Hebei and Pearl River Delta urban agglomerations

China places significant emphasis on reducing carbon emission intensity, with research and development (R&D) innovation serving as an effective approach, particularly among industrial businesses in the Pearl River Delta (PRD) and the Beijing-Tianjin-Hebei (BTH) urban agglomeration. Based on 2010- 2022 panel data, this study assesses the spatio-temporal effects of the R&D scale and innovation efficiency on carbon emission intensity in BTH and PRD. The findings reveal that (1) in terms of indicator calculation, there exist differences in R&D innovation between the BTH and the PRD. The R&D scale in the BTH followed an S-shaped growth pattern, while the PRD experienced steady growth; the innovation efficiency gap among areas in the PRD is generally smaller than in the BTH. (2) In a spatial perspective, both urban agglomerations exhibit spatial effects on carbon emission intensity through different transmission pathways. (3) In a temporal perspective, the BTH's R&D scale impact on carbon emission intensity evolves in two stages. In the PRD, the effect of innovation efficiency on carbon emission intensity reveals characteristics of extended accumulation. This study compares the spatio-temporal impacts of R&D innovation on carbon emission intensity in these two crucial urban agglomerations and highlights their differences.