I am writing a story that is meant to take place after the death of the sun. However, 7.5 billion years might be a little long for most people to stomach. Is there anything that could cause the sun to turn into a Red Giant sooner?
One possibility is that we're simply wrong on when the sun will go to the Red Giant phase.
Science has a good idea of how stars work, but it's not like we can actually look inside of it, or probe it to see what's going on. All of our information is secondary - it's like trying to create a 3D model of something based solely on seeing the silhouette. You can do a pretty good job, but there's also a lot of room for guesswork or mistaken assumptions.
So maybe, due to some mechanism we're not familiar with yet, we've misidentified where our sun is in its life-cycle, and it's actually a lot closer than we thought. That doesn't mean it's likely to go Red Giant tomorrow - we'll notice before that - but say, somewhere in the ten thousand to ~1 million years range is probably reasonable.
Red giants come into being when a star's core becomes depleted of hydrogen. AFAIK there is no "real science" method to speed up the process, as it's directly coupled to the rate at which the star is consuming fuel; the rate the star consumes fuel is coupled to the star's mass.
An in-universe method of sciency technobabble tech could do it, depending on what exactly you have planned for your story.
Issac Asimov's story "The Last Question" eventually uses the concept of "sunpower units." I'd always imagined these as some sort of power station drawing off the helium of the star and fusing it as fast as possible.
If it works in your story, it might be an interesting story hook if the Sun was used as a fueling depot by some alien species, who used hyperspace/subspace to extract hydrogen from the core. Maybe they need to draw it from the core so they can have the fuel at the right temperature, which would explain why they're not just "scooping it" off the surface. This goes on for a while until the solar system is finally flagged as "inhabited," but by that point the damage had been done, and in a few ten thousand years the sun baloons out into a red dwarf.
If you want to give humanity the technology you can do that as well. The thing to note is that you need to use some technology to pull the helium FROM THE CORE. Pulling it from the surface won't make a difference, as surface helium doesn't get burned until way late in the sequence. Sure, it reduces the lifetime of the star, but wouldn't affect the burning rate.
If you can artificially reduce the helium in the core, maybe even have whoever is doing it dumping trash hydrogen or carbon and iron in there, you could nudge the star along the main sequence.
The only other thing I'd point out is whatever you do to the Sun you have to have MASSIVE tech to pull it off. There are 5 billion years of fuel in the core, and the sun is burning ~600 million TONS of hydrogen to helium every SECOND. In order to burn out the sun, you'll need something that can eat up 2-10x that fuel.
Smashing another sun into the Sun won't make it burn off faster, it'll actually top it off. Having a binary style star show up wouldn't work, because it draws fuel off the surface (and would cause more harm elsewhere).
If you don't want some kind of alien tech, a "realistic" sounding idea to me is having a black hole migrate into the core. It would soak up fuel while also increasing the gravity within the core. This might work in causing the hydrogen to ignite, but I'm pretty sure any black hole big enough to do this would cause other gravitational problems to the solar system. Also, I'm not a nuclear physicist, so Stephen Hawking might have problems with this suggestion.
This is not a direct answer to your question, but could provide a different explanation for the same narrative. If your overall goal is to have an Earth without a sun, it would be easier to move the Earth than to put out the sun.
For example, a rogue black hole could pass through the solar system. It doesn't pass close enough to cause direct harm to the Earth through tidal forces, but it does pass close enough to give the Earth a gravitational boost. This increases Earth's velocity such that it is above the escape velocity of the sun. Over the next year or so, the Earth travels away from the sun, until it no longer provides an appreciable amount of light or heat.
The advantage is that this could happen at any point in the future, so you wouldn't need to extrapolate out to stellar lifetimes.
Accelerating the rate in which Hydrogen is burned off and the Sun migrates to burning helium and eventually heavier elements up the curve of binding energy is what causes the Sun or other stars to move into the Red Giant phase of their lives.
Some ideas have been discussed unthread, but perhaps the only other means of doing this would be to somehow speed up the rate at which time passes in the core of the star. There would be other noticeable effects, especially as the sudden surge in energy production and release reaches the surface (energy is generated in the core, but often it takes thousands of years to migrate to the surface. Neutrinos are the obvious exception to this), but if calibrated correctly, the hydrogen would be depleted in a few centuries or millennia, and then the "hotter" reactions involving helium would become dominant and the Sun would begin to expand.
OF course, the speeded up solar core would have pretty apocalyptic effects long before the time the Sun became a red giant, which might be what you need for your scenario.
Red giant might be impossible, but a collision with a white dwarf could kill a star. But I think the most likely result would be a supernova and a neutron star remnant. The mass limit is only 1.4 solar masses after all. I guess you could assume either a low mass white dwarf or a collision with high enough energy to blow off much of the mass of the sun. In any case the addition of the white dwarf would allow the composition of the sun to change relatively fast and it would add heavier elements and probably blow off significant amount of hydrogen, so it would drop the lifespan.
Downside of this solution is that the "special effects" would be spectacular, quite deadly, and entirely different from the red giant you asked for. The energy released on impact would be quite lethal and even a near miss by a stellar mass object would alter planetary orbits. But if that is okay...
Actually, maybe a near miss by a stellar mass object causing the Earth to be propelled out of the solar system would be close enough for your needs. Watching as the sun shrinks in the distance and atmosphere freezes would be very close in effect to sun dying.
The exponential dilemma might be a good bet.
lets say that there are 120 gallons per tank.
lets say that we can fill twice the gallons to the tank in the same time that we did before, a minute. So that in the first minute we fill one gallon.
1th minute 1 gallon **1** 2nd minute 2 gallons **2** 3rd minute 4 gallons **4** 4th minute 8 gallons + **8** 5th minute 16 gallons **16** 6th minute 32 gallons **32** 7th minute 64 gallons **64** = 127 total gallons, a little more 8th minute 128 gallons than than one tank. 9th minute 256 gallons
At this rate it took 7 minutes to fill a 120 gallon tank, the next minute will fill a whole new tank, and the next minute will fill 2 tanks
at the 7th minute we have a filled tank at the 8th minute we have a new filled tank at the 9th minute we have two more new tanks
Total of 4 tanks in 9 minutes, one in 7 minutes, one in 1 minute and two more in 1 minute.
this rate can be a a solution for your problem.
2^33 = 8589934592
you can say the sun death was predicted in linear growth but that it actually is in exponential growth. Using the example from above changing a minute for a year, it will take 33 years.
Another Asimov one: The Currents Of Space; no doubt the physics is dated, but the idea is useful.
The general concept here is that, rather than having a single collision with a massive body such as a white dwarf, there is a more continuous accretion of some kind of matter which accelerates the fusion processes.
First, note that due to the size of the sun normally a long time elapses between energy being released in the core and it being emitted from the star. This means that the changed process may have started a long time ago.
Perhaps rather than using normal hadronic matter, one might use some kind of exotic dark matter attracted to the Sun by gravitation and accreting in the core in such a way as to catalyze the fusion process.
I'll admit a problem with this line of thinking: to burn up the star faster it must lose a lot of energy. This means more of a Nova than a Red Giant.
A thousand years in the future, mankind has mastered physics to the point where we can mine the sun using force-fields and other "so advanced it looks like magic" tech. While great for allowing mankind to power their space-ships and spread throughout the solar-system (and possibly galaxy) it does rapidly advance the aging of the star. Keeping in mind that the sun is really really big, this would have to be a fairly huge mining operation, but if it's used to power, and provide matter for, a matter recombinator to terraform Mars, and other stellar bodies in the solar system it might just accelerate the "end of the sun" enough.
Perhaps something that the population do could cause the sun to die off a little quicker - use the fear that some people had of CERN destroying the world when it was turned on and adapt that.
Researchers in their quest for a more efficient energy source accidentally use their particle accelerator to create a stable black hole, but an unknown effect meant that the black hole was attracted to the greatest mass in the solar system - the Sun. The newly created singularity accelerated away from the Earth to reach a stable point near the Sun (or in it?) and accelerated the Suns loss of fuel.
Some of the other answers have possible rates of consumption that could be tweaked based on the size of the black hole.
Alternatively, perhaps scientists were looking for a way of opening wormholes between systems and accidentally latched our end of the wormhole into the Sun, causing the fuel in the Sun to be moved through it.
We make a lot of studies and assumption on elements that we can see or sense. Our experiments and results are a direct product of our analysis of known elements or bodies. What if there are celestial bodies that exist that we cannot sense? These objects could be moving at great speeds, invisible and could be causing sudden demises to stars by sucking in hydrogens.
This could possibly cause the early annihilation of our beloved sun and we wouldn't even know what hit us. Or probably we realise something approaching the sun, looking at the destruction caused by it on the way and we are unable to stop it.
Rather than trying to explain the sun misbehaving, you might invoke some handwavium time warp that propels the Earth 7.5 Billion years into the future. Or on an even smaller scale, that just transports your people, such as a slightly misconceived time machine.
I have read variants on this at least twice. In a short story (Niven?) where a hyperspace drive malfunction takes a space-liner even further into Earth's future, when the Sun has become a dwarf star. And in a Robert Charles Wilson series of novels Spin where an alien field wraps Earth and slows time down about 100-million fold for humanity compared to the universe outside. (The reason emerges later).