A group of start-ups is promising a new and virtually unlimited source of power, one that produces none of the gases scientists say contribute to global warming. The only problem? A way to harness the energy source, nuclear fusion — the reaction that gives birth to sunlight — still needs to be invented. Such an achievement has long evaded government scientists and university researchers, despite decades of work and billions of dollars in research. But backed by hundreds of millions in venture capital and some of the wealthiest people in the technology industry, a handful of young companies say they can succeed where government has fallen short. Nuclear fusion is one of many areas of science and energy now getting the backing of venture capitalists. The investor dollars coming into fusion start-ups, like those in many areas of science, still pale in comparison with the money spent by governments. But signs of progress, including some results that have eclipsed government projects, have generated hope among some scientists that the companies could help develop a fusion reactor within their lifetimes. At the very least, they talk a confident game — even though the history of fusion science is littered with frustration and false starts. Some fusion scientists, unable to evaluate the start-ups’ unpublished scientific results, doubt the companies’ chances. “The fusion era is here and coming,” said William D. Lese, a managing partner at Braemar Energy Ventures, a venture capital firm with a stake in General Fusion, one of the leading start-ups in the field. “The increase in activity in this space is perhaps a sign of that.” Nuclear fusion occurs when two atoms are squeezed together so tightly that they merge. That single, larger atom releases a tremendous amount of energy. This happens naturally at the center of the sun, where gravity easily crushes hydrogen into helium, spewing forth the sunlight that reaches Earth. But on Earth, making hydrogen hot and dense enough to sustain a controlled fusion reaction — one that does not detonate like a thermonuclear bomb — has been a challenge. The potential upsides of the power, though, provide a huge incentive. Fusion reactions release no carbon dioxide. Their fuel, derived from water, is abundant. Compared with contemporary nuclear reactors, which produce energy by splitting atoms apart, a fusion plant would produce little radioactive waste. The possibilities have attracted Jeffrey P. Bezos, founder of Amazon.com. He has invested in General Fusion, a start-up in British Columbia, through Bezos Expeditions, the firm that manages his venture capital investments. Paul Allen, a co-founder of Microsoft, is betting on another fusion company, Tri Alpha Energy, based in Foothill Ranch, Calif., an hour south of Los Angeles, through his venture arm, Vulcan Capital. Peter Thiel — the co-founder of PayPal, who once lamented the superficiality of the technology sector by saying, “We were promised flying cars and we got 140 characters” — has invested in a third fusion start-up, Helion Energy, based near Seattle, through Mithril Capital Management. Government money fueled a surge in fusion research in the 1970s, but the fusion budget was cut nearly in half over the next decade. Federal research narrowed on what scientists saw as the most promising prototype — a machine called a tokamak, which uses magnets to contain and fuse a spinning, doughnut-shape cloud of hydrogen.