Europe's contribution to global warming will be determined by the cumulative emissions until climate neutrality is achieved. Here, we investigate alternative transition paths under different carbon budgets. We use PyPSA-Eur-Sec, an open model of the sector-coupled European energy system with high spatial and temporal resolution. All the paths entail similar technological transformations, but the timing of the scale-up of important technologies like electrolysis, carbon capture, and hydrogen network differs. Solar PV and onshore and offshore wind become the cornerstone of a net-zero energy system, enabling the decarbonization of other sectors via direct electrification (heat pumps and electric vehicles) or indirect electrification (using synthetic fuels). For a social cost of carbon (SCC) of 120€/tCO2, transition paths under 1.5 and 1.6°C budgets are, respectively, 8% and 1% more expensive than the 2°C budget because building assets earlier costs more. The 1.5°C budget is cost optimal if a SCC of at least 300€/tCO2 is considered.
