“It’s a lucky charm,” says Rajesh, pointing to the solar-powered battery in his window that he has smeared with turmeric as a blessing. “It has changed our life.”

He lives in Rajghat, a village on the border of Rajasthan and Madhya Pradesh states, and until very recently was one of the 240 million Indians who live without electricity. In the poverty that results, Rajghat has become a village of bachelors, with just two weddings in 20 years.

“No one wants to give their daughter to me,” says Sudama, another young man. “People come, they visit, but they see the conditions here and they leave.”

For now, the technology is proving most useful to Rajesh as a way to charge his mobile phone, saving a lengthy journey to the nearest city, but he also hopes for future benefits: “I’ll use this to let my children study.”

According to an ambitious pledge by India’s prime minister, Narendra Modi, every Indian will have electricity, and the education, health and business benefits that follow, by the end of 2018. But how Modi achieves that, and the development of what will soon become the world’s most populous nation, matters to the entire world.

Of all the most polluting nations – US, China, Russia, Japan and the EU bloc – only India’s carbon emissions are rising: they rose almost 5% in 2016. No one questions India’s right to develop, or the fact that its current emissions per person are tiny. But when building the new India for its 1.3 billion people, whether it relies on coal and oil or clean, green energy will be a major factor in whether global warming can be tamed.

“India is the frontline state,” says Samir Saran, at the Observer Research Foundation in Delhi. “Two-thirds of India is yet to be built. So please understand, 16% of mankind is going to seek the American dream. If we can give it to them on a frugal climate budget, we will save the planet. If we don’t, we will either destroy India or destroy the planet.”

This view is shared internationally: Christiana Figueres, the UN’s former climate chief who delivered the landmark Paris climate change agreement says India is “very, very important” for everybody, and the nation will play a key role at the UN summit that starts in Bonn, Germany next week.

Lord Nicholas Stern, the climate economist who has worked in India for 40 years, says a polluting, high-carbon development would leave India alone accounting for a huge chunk of the world’s future emissions, making it “very difficult” to keep the global temperature rise below the internationally agreed danger limit of 2C.

What will happen remains in the balance. “Anyone who claims to be able to predict India’s emissions in 2030 doesn’t have a lot of humility,” says Navroz Dubash, a senior fellow at the Centre for Policy Research in Delhi.

But what is clear is the scale of the challenge. “India has a vast amount of energy-using infrastructure yet to be put in place,” says Ajay Mathur, the head of the Energy and Resources Institute, an influential Delhi-based thinktank. “No matter what numbers you look at, we will at least double or double-and-a-half our energy consumption in the decade to 2030.”

India is embarking on one of the fastest rural-to-urban transitions in human history, with 200 million more city dwellers expected by 2030, all using new buildings, roads and cars. In this context, keeping the rise in emissions to just a doubling would be truly remarkable, says Stern, and leave India’s emissions per person well below the current global average.

But India’s vast population means that even small increases in emissions per person add up to a huge amount of carbon dioxide and India is likely to become the world’s biggest polluter. “The sheer numbers of the population multiplied by anything makes it a big number – that is India’s reality,” says Saran.

There are signs of hope, however, driven by astonishing drops in the price of renewable energy in the last few years. Costs are falling faster than anyone predicted, with new record-low prices set this year for solar and wind. State governments can now pay less for clean energy than they pay for new coal power.

Mathur, who was the Indian delegation’s spokesman at the 2015 Paris climate summit, says that once batteries become powerful enough to store renewable energy for night time or when winds are weak, India’s energy emissions are likely to plateau and then fall. “I personally saw this happening around 2035, but in the past three years, that has shifted to 2025, driven by the news in the solar prices and the sharper than expected fall in the price of batteries.”

India’s government has now forecast that no new coal-fired power stations will need to be built for at least 10 years. By that time, Mathur argues, it will be cheaper to supply new demand using renewable power. “As [existing] coal plants retire they will be replaced by renewables, because that’s what makes economic sense.”

Another crucial driver is India’s appalling air pollution – half of the world’s most polluted cities are in the nation. “It is far, far worse than China,” says Stern. “That has really started to build into Indian consciousness and politics.”

That awareness is growing fast – India’s supreme court even banned Diwali festival fireworks in Delhi this year – and is putting heavy pressure on the government to act. In April, ministers announced that the sale of new petrol or diesel cars would be banned from 2030, a decade before the UK.

Cutting pollution also cuts carbon emissions, but filthy air is not the only incentive to act. Unchecked global warming will hit India hard, increasing extreme weather, like the floods that killed thousands in August, and affecting the monsoon upon which India’s farmers depend.

Heatwaves already cause thousands of deaths in India and rising temperatures that make outdoor work impossible have already seen the labour equivalent to about half a million people lost since 2000. But in coming decades, heatwaves could reach a level of humid heat classed as posing “extreme danger” for three-quarters of the population.

Despite the compelling reasons for India to follow a green path into the future, serious obstacles remain, not least the sorry state of the country’s coal-fired power industry, currently forced to slow its operations by a surplus of electricity in the market.

“These guys are hurting,” Mathur says, and that has knock-on effects for India’s slowing economy. “They have taken loans, and they can’t sell electricity, so they can’t repay the loans. And if they can’t repay the banks, the banks have no money to lend for more growth.” Recent months have seen a backlash against renewables, with intensified lobbying for coal.

Another problem is ensuring the buildings and transport systems shooting up in cities around India are energy efficient. “There is the risk of great, sprawling messes, and it is a very big risk,” says Stern, requiring the institutional ability of the government to shape the future to grow as fast as the cities themselves.

The political climate is – for now – behind the green growth story, says Saran: “Modi, unlike other populist leaders, has made climate into a strength and not an adversarial debate, like Donald Trump.” But he warns that could change: “The street capture of irrationality is not something India is immune from either.”

What happens in India also matters to the rest of the world for a practical reason, says Saran, by driving down the costs of, for example, rolling out solar plants and super-efficient LED bulbs. This would mean all developing countries can leapfrog a polluting fossil fuel phase as they grow.

“We will mass produce it, mass aggregate it, mass process it for the world,” he says. “America did it for the first billion people. India is now doing it for the rest of the six billion on the planet.”

The whole world would benefit from a clean, green India and can help make it happen, says Stern, by bringing down the interest rates on the loans used to fund the low carbon transition: “The best thing the world could do is help bring down the cost of capital.” That means long term finance and help to cut project risks.

The path India’s chooses will affect the whole world and, despite the uncertainties and risks, the mood is optimistic, for a variety of reasons. “India has all the institutions of democracy and a very smart entrepreneurial class which will respond, and that gives me optimism,” says Saran.

Dubash says: “We’ll do it because we don’t have that much high-quality coal. We are already hitting high pollution levels. We already have issues with imports, and so energy security is a big factor. All of those things will lead us to moderate.”

For those currently without any electricity, solar power is the perfect solution, both fast and affordable, says Stern. Back in Rajghat, a young mother called Ramhali agrees. Three days earlier, a group of students from a nearby city, Dholpur, installed a single, five-watt light in her home, powered by solar panels on the roof. It has replaced the old liquor bottle filled with kerosene, that flickered with toxic, black-tipped smoke and gave the children headaches.

So can India’s leaders bring light to its poorest people, build clean, green cities for its billion-strong population and end the plague of air pollution? Figueres says: “More important than my opinion is their opinion, and they think they can, and do so with many benefits.”