To achieve the goal of deep decarbonization of the electricity system, more and more variable renewable energy (VRE) is being adopted. However, there is no consensus among researchers on whether the goal can be accomplished without large cost escalation if nuclear power is excluded in the future electricity system. In Sweden, where nuclear power generated 41% of the annual electricity supply in 2014, the official goal is 100% renewable electricity production by 2040. Therefore, we investigate the cost of a future low-carbon electricity system without nuclear power for Sweden. We model the European electricity system with a focus on Sweden and run a techno-economic cost optimization model for capacity investment and dispatch of generation, transmission, storage and demand-response, under a CO2 emission constraint of 10 g/kWh. Our results show that there are no, or only minor, cost benefits to reinvest in nuclear power plants in Sweden once the old ones are decommissioned. This holds for a large range of assumptions on technology costs and possibilities for investment in additional transmission capacity. We contrast our results with the recent study that claims severe cost penalties for not allowing nuclear power in Sweden and discuss the implications of methodology choice.