The End of the Universe

In this post I’ll talk about the far future of the Universe and also how there is a certain similarity with the very early Universe – one of the reasons which led  Roger Penrose to propose his Cyclical model of the Universe. Before we do this, it is worth having a very brief summary about what we know about our Universe.

The Universe

According to the standard big bang theory ,the Universe is 13.77 billion years old and began in a phase of extremely high (possibly infinite) density and temperature and has been expanding and cooling ever since.

Currently if we take the Universe as a whole its average composition is as follows.

Ordinary matter consists of the familiar protons, neutrons and electrons which make up atoms. Neutron stars (which I’ll talk about later) are also considered to be ordinary matter. Black holes which were formed from the collapse of massive objects, which consisted of ordinary matter, are included in the 5% of the mass of the Universe in the form of ordinary matter.

Dark matter is an invisible form of matter which doesn’t absorb or emit light. Even though there is believed  to be more dark matter than ordinary matter in the Universe, the nature of dark matter remains unknown . It is likely to consist of particles outside the standard model of particle physics. Despite physicists searching for dark matter particles for over forty years none have ever been found – but as they will barely interact with ordinary matter, they will be very difficult to detect.

Dark energy is a form of energy needed to explain why the expansion of the Universe is speeding up. Without dark energy, gravity due to all the matter in the Universe would slow down its expansion

The composition of the Universe isn’t fixed but changes over time. For example, when the Universe was only 10^-12 seconds old, it was at a temperature of 2000 trillion degrees and consisted almost entirely of radiation. The contribution of matter and dark energy being negligible.

Having had a (very brief!) summary of the Universe we can now talk about its end.

Stage 1 The End of Star formation

Stars are being formed all the time in our Milky Way galaxy and in other galaxies across the Universe. However, the rate of new star formation is slowing down. In 10 trillion (10¹³) years, which is roughly 1000 times the current age of the Universe, formation of new stars will cease. Most of the hydrogen in galaxies will have been used up and there won’t be enough free hydrogen to form new stars.

When all their fuel has been used up, stars cannot generate energy by nuclear reactions and so come to the end of their lifetimes. The ultimate fate of a star depends upon its mass.

White dwarfs, neutron stars and black holes

As they run out of hydrogen, stars burn other elements, such as helium, carbon and oxygen. However, the supply of nuclear fuel is finite and when it is exhausted for the vast majority of stars the remnant becomes an object known as a white dwarf.

White dwarfs are composed of a special form of matter where atoms are tightly squeezed together called electron-degenerate matter. White dwarfs are very dense:  a typical white dwarf has a mass comparable to the Sun, but its volume is comparable to the Earth’s. Even though no nuclear fusion reactions take place in a white dwarf, they still glow from the emission of residual thermal energy from what was the core of the original star.

For theoretical reasons, which I won’t go into detail here, the maximum mass of a white dwarf is approximately 1.4 times the mass of the Sun  ( If you want to find out more  see https://astronomy.swin.edu.au/cosmos/W/White+Dwarf ). This isn’t a hard limit; higher mass white dwarfs can exist if they are rapidly rotating. Because stars shed a lot of material at the end of their lives, as the outer layers of the star are blown away into space, stars which start their lives with a mass of up to ten solar masses will become white dwarfs. More than 98% of stars in our Milky Way galaxy fall into this category.

If the mass of what’s left of a dying star, after it’s shed all its outer layers, is too large to become a white dwarf but is smaller than an upper limit of around 2.2 solar masses then a neutron star is formed. Neutron stars largely consist of neutrons squeezed together. This makes them incredibly dense. A typical neutron star has a diameter of only 10 km giving it a density of 10¹⁷ kg/m^3.  One cubic centimetre of the material in a neutron star would weigh 100 million tonnes.

If the remnant of the star is heavier still, then the end result is a black hole. This has a surface called the event horizon. Anything which crosses the event horizon cannot escape from the black hole. So, the event horizon cuts the black hole off from the rest of the Universe.   If our current theories of physics are correct, at the centre of the black hole lies a singularity of zero volume and infinite density. However, it is possible that some as yet undiscovered theory of quantum gravity takes over at these extreme conditions

Stage 2 Over longer timescales the cooling of stellar remnants

As white dwarfs don’t generate energy by nuclear reactions, they gradually cool down becoming fainter. Eventually every white dwarf will have cooled down and will radiate so little energy it will be almost invisible. It is then a black dwarf. The rate at which an object such as a star radiates heat is proportional to its surface area.

(For the more mathematically inclined, the relationship is P = σAT⁴

Where P is the power radiated, A is the surface area, T is the temperature measured in degrees Kelvin and σ is a number known as the Stefan–Boltzmann constant)

Because white dwarfs are very dense, in relation to their mass, they have a relatively small surface area from which radiation can escape. This means, the cooling of a white dwarf into a black dwarf takes a great deal of time.  It will take 10¹⁵ years (100 000 times the age of the Universe) for a typical white dwarf to cool down to a black dwarf at a temperature of five degrees above absolute zero. Therefore, there are no black dwarfs in our Universe. It just isn’t old enough for any to have formed.

Neutron stars, because of their tiny surface area, take many orders of magnitude longer to cool down to low temperatures. For example, a neutron star 10 km in diameter will have a surface area one million times smaller than a white dwarf 10 000 km in diameter. So, it would radiate away one million times less heat than the white dwarf (assuming they were at the same temperature).

Stage 3 Over exceedingly long timescales – proton decay

Once all the stellar remnants have cooled to a temperature of near absolute zero the Universe is a cold dark place, but further changes occur.

Although radioactive atomic nuclei are unstable, protons and neutrons (in an atomic nucleus) are generally treated as though they were completely stable. (Interestingly, as an aside, neutrons outside an atomic nucleus are not stable. They decay with a half-life of about 10 minutes). Grand unified theories in particle physics predict that  protons aren’t completely stable. Instead, the proton is predicted to have an incredibly long half-life which is as yet unknown but must be greater than 10³⁴ years – perhaps it could be as high as 10³⁹ years. This rate of decay of proton is so slow it has never been detected so it cannot be confirmed if these predictions are correct.  

To illustrate the difficulty of detecting proton decay, even if the half-life of the proton were at the lower end of the range (10³⁴ years) and we observed 1000 tonnes of hydrogen looking for protons to decay it would take on average 24 years to see a single one. If the half-life were at the upper end (10³⁹ years) it would take on average 2.4 million years for a single decay to happen!

Assuming proton decay occurs, the end product is an anti-matter particle called an anti-electron also known as a positron. Positrons carry a positive charge which has an equal and opposite value to the negative charge on an electron. Anti-matter particles are rarely found in nature. Electrons are far more plentiful than positrons, as soon as a positron encounters an electron, they both annihilate – producing two gamma ray photons.

Neutrons inside an atomic nucleus are also thought to decay by a similar mechanism. In this case the final end product is a low mass anti-matter particle called an anti-electron neutrino, The anti-electron neutrino will in general eventually encounter an electron neutrino and the pair will annihilate.

If proton decay occurs, it gives rise to an interesting conclusion. Ordinary matter doesn’t last for ever. If we wait long enough, say 300 times the proton half-life, then all the ordinary matter in the Universe will have decayed to photons. This is true for ALL ordinary matter regardless of the form it is in. Stellar remnants such as neutron stars and black dwarfs (but not black holes) and other objects such as gas clouds, planets, asteroids will all decay to photons.

Note what are photons?

Electromagnetic radiation such as light can be considered both as waves of oscillating electric and magnetic fields and also zero mass particles called photons.

• Short wavelength electromagnetic radiation is emitted by very hot objects and has high energy photons.
• Long wavelength electromagnetic radiation is emitted by cooler objects and has lower energy photons.

The final stage black hole evaporation

Even black holes do not last forever. In 1974 Stephen Hawking predicted that black holes should emit radiation from the region of space around the event horizon. This is now known as Hawking radiation. Assuming Hawking’s prediction is correct and Hawking radiation actually exists, it means that black holes have a temperature. I won’t discuss Hawking radiation in any great detail, because there is a good summary at https://bigthink.com/starts-with-a-bang/hawking-radiation-black-hole-evaporation/

However the key fact is that , for all known black holes their temperature is exceedingly low – only a tiny fraction above absolute zero. In fact, because all known black holes have a temperature much lower than surrounding space, which is roughly 2.7 degrees above absolute zero, they will absorb radiation from the surrounding space and grow even if there are no massive objects to gobble up.

But as our Universe continues to expand and cool, for every black hole there will eventually be a time, in the far future, when the black hole temperature is above the temperature of the surrounding space. The black hole will then be a net emitter of radiation and as it emits radiation – it will start to lose mass and shrink eventually disappearing all together.

Here are some sample lifetimes of black holes. As you can see, particularly for the larger mass black holes, the lifetimes are incredibly long.

The end or is it a new beginning??

So, if we fast forward in time to around one googol (that’s 10¹⁰⁰) years in the future, all the ordinary matter and matter in black holes will have been converted into low energy photons. However, most of the matter in the Universe is dark matter the nature of which is unknown.

 Although there is no firm evidence for this, Roger Penrose in his book Cycles of Time speculates that the, as yet undiscovered, dark matter particles will have a finite lifetime too. Their mass(es) will gradually fade away to zero over extremely long timescales.

Therefore, after around one googol years, the expanding Universe will contain dark energy but will have no particles which have a mass which isn’t zero. Its only other constituent will be extremely low energy photons plus possibly gravitons, which are hypothetical massless particles carrying the force of gravity. The Universe enters a very boring era in which nothing happens but further expansion and cooling.

However, because the Universe consists only of massless particles and dark energy there is nothing around to observe this tedium. Photons (and also gravitons assuming they exist) have zero rest mass, travel at the speed of light and from Einstein’s theory of special relativity anything travelling at the speed of light does not register the passage of time. So, in a sense the Universe “loses track of time”.

As Roger Penrose points out, this gives rise to certain symmetry with the very early Universe. In which

• Universe is expanding rapidly.
• It contains no massive particles.
• Its main constituent is extremely high energy photons.

I will talk about this interesting symmetry in more detail in a subsequent post.

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