An analysis of historical cost trends of energy technologies shows that the decadeslong increase in the deployment of renewable energy technologies has consistently coincided with steep declines in their costs. For example, the cost of solar photovoltaics has declined by three orders of magnitude over the last 50 years. Similar trends are to be found with wind, energy storage, and electrolysers (hydrogen-based energy). Such declines are set to continue and will take several of these renewable technologies well below the cost base for current fossil fuel power generation. Most major climate mitigation models produced for the IPCC and the International Energy Agency have continually underestimated such trends despite these trends being quite consistent and predictable. By incorporating such trends into a simple, transparent energy system model we produce new climate mitigation scenarios that provide a contrasting perspective to those of the standard models. These new scenarios provide an opportunity to reassess the common narrative that a Paris-compliant emissions pathway will be expensive, will require reduced energy reliability or economic growth, and will need to rely on technologies that are currently expensive or unproven as scale. This research provides encouraging evidence for governments that are looking for greater ambition on decarbonising their economies while providing economic growth opportunities and affordable energy.