Financial development and the energy transition in China: Does green capital accelerate decarbonization?

China's dual carbon targets peak CO2 by 2030 and carbon neutrality by 2060 place financial markets at the centre of the country's clean energy transition. This paper investigates whether financial development, and green finance in particular, accelerates decarbonization across China's 30 provinces over the period 2003 to 2022. A composite Financial Development Index (FDI) is constructed using principal component analysis from four dimensions: banking sector depth, stock market development, insurance market penetration, and green finance intensity (green credit ratio and green bond issuance). The analysis employs a two-way fixed-effects spatial Durbin model (SDM) with a queen-contiguity weight matrix to capture spatial spillovers, a double-threshold panel regression to identify nonlinear green finance effects, and a bootstrap mediation analysis to decompose transmission channels. Results demonstrate that a one-standard-deviation increase in the composite FDI reduces provincial CO2 emissions by 21.8% (direct effect) and generates a cross-provincial spillover reduction of 9.6%, for a total effect of 31.4%. Green finance exhibits the strongest individual sub-component effect, reducing emissions by 28.4% and displaying threshold behaviour: the decarbonization impact is insignificant below a green finance intensity ratio of 0.32, rises sharply in the intermediate regime (0.32 to 0.62), and intensifies further above 0.62 as capital allocation shifts systematically toward renewable energy and low-carbon technology. Mediation analysis identifies four significant channels technology innovation, renewable energy investment, industrial ecology upgrading, and energy efficiency improvement which together account for 21.3% of the total effect. Regional heterogeneity analysis reveals that the green finance channel is strongest in Eastern provinces, where capital markets are deepest, and weakest in Western provinces, suggesting a financial geography constraint on clean transition. The findings imply that accelerating green bond market development, expanding the green credit incentive framework, and closing cross-provincial financial integration gaps are essential policy levers for meeting the 2030 peak-emissions deadline.