I would say that the Big Freeze scenario is the most likely, as the Universe keeps expanding on forever, and ever, and ever, and ever, until nothing but sub-atomic particles remain. I’m no real expert in this field and there are plenty of answers here which explain Universe Death much better than I do, so I will just take a different route of answer and give you a hypothetical way the Earth and the Universe will end. I already wrote down this answer in the question: Hypothetical Scenarios: What will be the fate of our World and Universe in the future and how would it occur?, so I’ll just copy-paste the answer here.
Sources: Google, Timeline of the far future, Timeline of the far future(diff one), The Universe Death Clock (video)
There are quite a couple of scenarios of the ultimate fate of the Universe, with most stating it will end, although there is a theory that the Universe will just keep going on forever and ever. I will not talk about how humanity would advance, just the effects on Earth and the Universe. For this case, I will take the Big Freeze scenario, as it is the most likely. I’ll be going through the important events that may occur on Earth and in the Universe. Ready? Let’s go!!
One Thousand(1000) Years Later
By the time a thousand years pass, most of our languages would be gone, forgotten and never spoken ever again. Any language that does survive will have been changed so much it would never sound the same to us, and the grammar and words we use now will be gone in this time, like how we view Shakespeare’s English.
Two Thousand(2000) Years Later
Global Warming would still be going on and the Earth’s temperature would have risen by 8°C. The ice sheets and glaciers in Greenland mostly melt away, rising sea levels by 6 metres, potentially disastrous for low-lying poor countries.
Thirteen Thousand(13,000) Years Later
Earth’s axial tilt will reverse, and along with it, seasons. Northern hemispheric winter starts in June. The Northern hemisphere will suffer from extreme weather since there is more land above the equator. Either we live with it, or migration to the Southern hemisphere begins. Carbon dioxide levels are dropping slowly. According to Carter’s Doomsday argument, humanity has a 95% chance of being extinct, although in this case, I will take this as perhaps false.
Twenty Thousand(20,000) Years Later
Chernobyl becomes habitable once more. Yayyyyy! I just wanted to leave this here.
Twenty-Five Thousand(25,000) Years Later
The Arecibo Message, a collection of radio data transmitted on 16 November 1974, reaches the distance of its destination, the globular cluster Messier 13, at the far side of the galaxy. Any alien race that manages to receive the message will know that they are not alone. The reply message will only be received by us 25000 years later. The northern polar ice cap on Mars will recede due to a warming period. Human colonists on Mars could expand north if they still exist.
Thirty Thousand(30,000) Years Later
All fission-based breeder reactor reserves run out, forcing humans to swap to another energy source.
Fifty Thousand(50,000) Years Later
The Niagara Falls would have eroded the remaining 32 km to Lake Erie and have vanished. The global temperature would have increased by another 2°C, completely melting away all the ice in Greenland. According to Berger and Loutre, Earth plunges into another ice age despite global warming. This ice age could possibly be delayed by constant burning of fossil fuels. If any aliens have replied, we would receive the Arecibo Reply by this time.
Eighty-Five Thousand(85,000) Years Later
By this time, it is safe to assume that the World will have completely changed by this time. If humanity hasn’t been wiped out, no nation, religion or way of life will be the same. There would be new factions or hopefully a World Coalition Government, with no countries left. Religions like Judaism and Christianity that have persisted for so long would have been forgotten and given way to new religions, or religion may no longer be existent.
One Hundred Thousand(100,000) Years Later
VY Canis Majoris will explode into the largest hypernova seen in the Universe, probably even visible from Earth. Earth would most likely suffer a Supervolcanic eruption, likely the Yellowstone Caldera, that will hurl ash into the sky, blocking out sunlight and lowering temperatures, causing a global disaster. Titanium begins to corrode away. By this time, should humanity have the technology and the survival, terraforming of Mars will near its ending phases, with a now oxygen-rich atmosphere. I predict that most of humanity will live on Mars by now.
Two Hundred and Ninety-Six Thousand(296,000) Years Later
Voyager 2 passes within 4.3 light years of Sirius. Any intelligent aliens will probably recover it and find the Golden Record and realise that they…are not alone.
Five Hundred Thousand(500,000) Years Later
Earth is struck by a 1 km asteroid, that has an impact of 6 × 10^4 megatons, equivalent to an earthquake of magnitude 9.4 on the Richter scale. This isn’t an extinction event, not even close, but causes significant damage to Earth’s environment and could wipe out any humans still living on Earth. If we have just kept burning fossil fuels, the ice age can be delayed till this time. Spent nuclear fuel in reactors would also be safe by this time.
One Million(1,000,000) Years Later
Glass left on Earth would have fully decomposed by this time, and so will every structure that we have today, except for stone structures like Mount Rushmore or the Pyramids of Giza, although the Pyramids would probably be unrecognisable. Nearly everything we left on the Moon will also be gone. Humanity, if still alive, would have spread throughout the galaxy. This is the shortest time it will take for humans to colonise the Milky Way.
Two Million(2,000,000) Years Later
Coral Reefs will finally physically rebuild and biologically recover from current human-caused ocean acidification. The Grand Canyon will further erode into a wide valley.
Seven point Two Million(7,200,000) Years Later
Mount Rushmore erodes away. Basically nothing left of human civilisation will be left, except for our trash. There will be little trace of any intelligent species that lived here. If aliens finally visit after receiving a message or info, they may find nothing.
Ten Million(10,000,000) Years Later (Mass Extinction)
Earth is hit by a Gamma Ray Burst from the supernova of nearby star T Pyxidis that irradiates the planet, destroys the ozone layer and triggers a mass extinction. Funny, seeing how ten million years is the time it takes for the Earth to recover from the Holocene extinction that humans cause. So Earth went from one mass extinction to another. The East African Rift Valley is flooded, causing a new ocean basin to divide Africa.
Twenty-Seven Million(27,000,000) Years Later
By this time, Homo Sapiens will go extinct and what remains of humans will be another step in evolution. Humans, having spread into space, may split into different species due to going separate ways through the cosmos, possibly leading to wars between different species of future humans. By this time, humanity will have advanced so far that things like nuclear fusion and basic space flight will be practically primitive to them and they may scoff at us working so hard to land a rocket.
Fifty Million(50,000,000) Years Later
By this time, if humanity did indeed set out to colonise the Milky Way, this is the time when we would have finally conquered the galaxy, presumably exterminating life and waging wars against aliens inside the Milky Way. Europe and Africa collide and merge to form one continent, allowing animals to cross and spread. Indonesia and Australia also merge together at roughly the same time. Many mountain peaks start to erode, and Earth starts to draw to a close. It would still take hundreds of millions of years, but Earth starts to slowly die. The Universe however, is nowhere close to ending yet. Antarctica, moving North, finally melts all of its ice, raising seas worldwide by 75 metres, causing massive floods in practically every region. Mars, will have its moon, Phobos, smash into it, potentially causing a mass extinction of any Martian life that exists after terraforming and if still colonised, perhaps human colonies too. However, there is the possibility that this is averted. I’m not here to say what the tech prowess is for future us.
NEXT!
One Hundred Million(100,000,000) Years Later
Earth will likely be hit by a huge asteroid, similar in size to the one that caused the KT Extinction that killed the dinosaurs. With likely no humans left on Earth, this asteroid will not be deflected and can potentially cause a mass extinction…again. Earth’s orbit will no longer be nearly uniform, but rather completely random, having devastating impacts on Earth’s climate and ecosystem. Saturn’s rings will have disappeared and according to Drake’s Equation, this will be the furthest humans will ever get with an advanced civilisation.
Two Hundred and Fifty Million(250,000,000) Years Later
Due to tectonic plate movement, all continents on Earth will have joined in one of three configurations: Amasia, Novopangaea and Pangaea Ultima
Amasia
Novopangaea
Pangaea Ultima
The supercontinent most likely split 500 million years from now
Six Hundred Million(600,000,000) Years Later (Earth Starts to End)
The Sun has increasing luminosity (something with carbonate-silicate cycle or something, sorry bad chemist) and water starts to evaporate, rocks harden and plate tectonics screech to a stop. Without this, no more volcanoes exist, thus causing carbon dioxide levels drop. This eventually renders C3 photosynthesis impossible and kickstarts the greatest extinction in history, with around 99% of plant life dying. No plants=no herbivores=no carnivores.
Eight Hundred Million(800,000,000) Years Later (Extinction)
Carbon dioxide levels continue to plunge until C4 photosynthesis is no longer possible. Free oxygen and ozone disappear from the atmosphere. Every multicellular lifeform dies, leaving only unicellular organisms remaining on a now desolate and barren world. I would assume that most intelligent life in the Universe will begin dying off by 1 billion years into the future.
One Billion(1,000,000,000) Years Later
Ignore the clouds
The Sun’s luminosity would have increased by 10%, causing Earth’s surface temperature to be 47°C. The atmosphere will become a "moist greenhouse", resulting in a runaway evaporation of the oceans. This turns Earth into a dry, arid planet and many unicellular organisms that require water to live, die off. Pockets of water may still be present at the poles, allowing some simple unicellular organisms to live on. This is also the estimated time needed for an astroengineering project to finish to drag Earth away from the brighter Sun, but I find it unlikely that our descendants survived this long, and would most likely have abandoned Earth. The Golden Records of the two Voyager spacecraft lose all their information. Aliens will never find out about Earth again.
One point Three Billion(1,300,000,000) Years Later
Carbon dioxide runs out. Every cell with a nucleus perishes, leaving only cells without nuclei left on the barren ruined world once called Earth. Mars could potentially become habitable without the need of human terraforming a few million years after this.
Two point Three Billion(2,300,000,000) Years Later
The outer core of the Earth freezes as it loses heat out to space and the inner core keeps growing. The Earth stops spinning and the magnetic field shuts down and the now unprotected remnants of the atmosphere is depleted by the Sun.
Two point Eight Billion(2,800,000,000) Years Later (RIP LIFE ON EARTH)
Earth’s surface temperature hits a 149°C. This combined with a lack of atmosphere finally kills all life on Earth. Nothing survives this. The Earth will no longer sustain unicellular, non-nuclei-containing organisms. The ‘heartbeat’ of the Earth flatlines.
Four Billion(4,000,000,000) Years Later
The Milky Way Galaxy collides with the larger Andromeda Galaxy and will eventually, tens of millions of years later, merge to form ‘Milkomeda’, probably the dumbest name ever. The collision could potentially disrupt the orbits of hundreds of millions or billions of stars and their planets. The Solar System will also be sent flying from its original position, but is expected to be relatively unaffected.
Five point Four Billion(5,400,000,000) Years Later
The Sun’s hydrogen supply at its core is finally exhausted, the Sun starts to evolve into a Red Giant and expands outwards towards the Inner Planets. In a few billion years, the Earth and Mars will become tidally locked and have their surfaces superheated and scorched.
Seven point Nine Billion(7,900,000,000) Years Later
The Sun reaches its maximum radius, 256 times its normal, and consumes and destroys Mercury and Venus. Earth’s Moon breaks up into debris which fall down into the desolate Earth, which is then either consumed or fully scorched. Mars would probably not be consumed, but would not be habitable. It is theorised that Saturn’s moon Titan can support life now.
Eight Billion(8,000,000,000) Years Later
The Sun shrinks back to into a White Dwarf, with about 54.05 percent its present mass. If Earth has not been destroyed, the scorching temperatures will drop rapidly, as with the temperature of every other celestial body in the Solar System. All that’s left of the Solar System is a few cold, bleak planets and moons with no capability to support any form of life ever again.
Fourteen point Four Billion(14,400,000,000) Years Later
After a few billion years as a White Dwarf, the Sun converts into a Black Dwarf, with low temperatures and practically zero luminosity, turning invisible to the eye. It is now nothing but a cold, dark carbon ball. The Sun thus ends its long lifespan. However, there are a large number of scientists who believe that it would take a quadrillion years for the White Dwarf to turn into a Black Dwarf.
One Hundred Billion(100,000,000,000) Years Later
With the Big Freeze scenario, the Universe keeps on expanding. This causes all galaxies beyond the Milky Way/Milkomeda’s Local Group to disappear beyond the observable Universe. It is very likely that any intelligent species that somehow manages to arise at this time will never see another major group of galaxies ever again, and may even conclude that their local galaxy group is the only thing in the Universe. By this point, the Big Bang is no longer detectable, perhaps causing any intelligent species left to believe that the Universe had no beginning and maybe no end. Local galaxies also start to merge together.
One Trillion(1,000,000,000,000) Years Later
No new stars will ever be produced as the gas clouds needed to form them no longer exist in the lonely giant galaxies floating around. Stars slowly, one-by-one die out and the sky turns black, leaving the planets still floating around the dark. The Local Group finishes merging together and it would be the only thing floating in space as everything else is too far away.
Thirty Trillion(30,000,000,000,000) Years Later
Stars in their stellar neighbourhoods start undergoing close encounters with other stars, disrupting the orbits of stars and their planets, sending both the planets and moons, and stars flying out of the galaxies entirely. These stars will go hurtling through the now empty cosmos, alone forever until they die.
One Hundred Trillion(100,000,000,000,000) Years Later
By this time, absolutely no free hydrogen existing to try to form new stars. The Universe enters what is known as the ‘Degenerate Era’.
One Hundred and Twenty Trillion(120,000,000,000,000) Years Later
Almost every existing star in the Universe finally burns out and they die off, with the Red Dwarfs the last to go. The only things left in the Universe would be Brown Dwarves, White Dwarves, Neutron Stars and Black Holes, which will then slowly, very slowly, die off in that order. The only real bright lights are supernovas when these stars collide.
A Neutron Star, that will be one of the last things in the Universe
One Hundred Quintillion Years Later
Well over 90% of all the aforementioned celestial bodies have already been ejected out of the slowly dispersing galaxies that are also being consumed by Black Holes. Most of everything is now solitary, never to see anything else again. The Solar System is finally destroyed when every planet collides with the Black Dwarf that was the Sun, which then decays away or is consumed by a black hole.
One Nonillion Years Later
Every star still not ejected is consumed by the Supermassive Black Holes, along with every galaxy still not dispersed yet. Only solitary objects manage to survive the Supermassive Black Holes. The Brown Dwarves still won’t die until many, many quintillion years later.
Most of the Universe is gone, but the Universe isn’t even halfway through its full lifespan yet.
3×10^43 Years Later
Every Brown Dwarf, White Dwarf and Neutron Star has already decayed away into nothingness by this point, leaving only Black Holes in the entire Universe. These dark celestial objects will remain for far longer than one thinks. The Universe still isn’t halfway through. In fact, Black Holes probably last longer than every other celestial object combined.
1.342×10^99 Years Later
Almost every Black Hole has already dissipated due to the emission of Hawking radiation, living just one gargantuan Supermassive Black Hole left, already dissipating away as well.
One Googol(1x10^100) Years Later
The last Black Hole has finally died. There is absolutely nothing left in the Universe other than sub-atomic particles. The Universe continues to expand further and further away, spreading these sub-atomic particles so thin, that they will never, ever, interact with another particle ever again. The Universe hits a tiny bit above absolute zero. Nothing left.
Just a cold, black void for an eternity…