Ask Ethan # 107: Is inflation linked to dark energy?

The exponential expansion of the universe is happening now, and another one happened a very long time ago. Are they related?

Nature cannot be bought or sold, borrowed, or copied. Incomparable, unforgettable, shameless, spontaneous, like earth and ice, water, fire and air, quintessence, pure spirit, not decomposable into components.
- Jay Griffiths

Every week, while we are writing about wonders, interesting and challenging tasks and new discoveries in the nature of the Universe, you have the opportunity to send me questions and suggestions for the weekly issue of “Ask Ethan.” And although there are more and more questions every week, there are still some interesting ones among them. This week, the honor goes to John Pashkov (the second time already), who asks:

Are the forces of expansion of inflation and dark energy connected in some way? It would be very strange if there were two different forces that caused the expansion of the Universe.

In the case of the universe, much of what is happening looks very strange, that's for sure.



Firstly, the Universe is absolutely uniquely expanding. But for this she does not need any strength. If you take such as ours, the universe, which:

• Powered by Einstein’s UTO
• Filled with substance, radiation, and other things
• Approximately homogeneous in all directions and in all places,
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you will come to a funny and inconvenient conclusion. For the first time, Einstein reached it in the first years of the existence of the theory of relativity: such a universe is essentially unstable with respect to gravitational collapse.



That is, without applying any magical correction, your Universe will either expand or decrease, and these possibilities are equal. What she cannot do is remain unchanged.

Of course, Edwin Hubble’s work has not yet been done. Not only did we not know that the Universe is expanding, we did not even know whether these spiral objects in the sky are objects located inside our Milky Way, or whether they are separate galaxies. Since Einstein, like most at that time, liked the static Universe more, he invented a special, ad hoc, correction for the stability of the Universe: a cosmological constant.



The idea of ​​Einstein's relativity is that the equation has two sides: one with matter and energy, and one with space and time. She argues that the presence of matter and energy determines the curvature and evolution of space-time, and how space-time bends and evolves, determines the fate of each quantum of matter and energy inside it.

The addition of the cosmological constant meant “there is a new type of energy inherent in the space itself, causing the fabric of the Universe to expand at a constant speed”. Therefore, in the presence of gravitational force, working due to the presence of matter and energy, on the collapse of the Universe, it was possible to take this cosmological constant, working on the expansion of the Universe, and get a static Universe. It was only necessary to equalize these two quantities, so that they mutually destroyed.



It turned out that the Universe is expanding, and it does not require any cosmological constant to counter gravity. In the initial position, the universe began to expand very quickly, which counteracted the force of gravity from all matter and energy. Instead of compression, the universe expanded, and the expansion rate slowed.

It will be natural to ask two questions that became logical after this discovery in the 1920s:

1. What was the reason for such a rapid expansion of the Universe in the early stages?
2. What will be the fate of the universe? Will it expand forever, can its extension be reversed, to the recollapse, will it be in the boundary state, or will something else happen?



The first question remained unanswered for more than 50 years, although, interestingly, Willem de Citter almost immediately suggested that the expansion is due to a cosmological constant.



Finally, in the early 1980s, a theory of cosmological inflation emerged, suggesting the presence of an early phase of exponential expansion, when something very similar to the cosmological constant dominated in the Universe.

But this could not be a real cosmological constant, also known as vacuum energy, since the Universe did not remain in this state forever. The universe could be in a state of false vacuum, when it had some inherent energy in space, which then faded to a low-energy state, which led to the emergence of matter and radiation: hot Big Bang!



Inflation has made other predictions, four of which have already been confirmed, as a result of which we accept the existence of such an early phase of the universe.

Turning to the second question, about the fate of the universe, we discover something strange. We expected to find some kind of race between the initial rapid expansion and the force of gravity affecting all matter and radiation, but instead we suddenly found a new form of energy called dark. And what would you think? This dark energy, in our current understanding, looks just like a cosmological constant.



But there were two types of exponential expansion, earlier and later, which are very different in details.

• The Universe’s early inflation period lasted indefinitely — perhaps ^10–33 s, perhaps almost indefinitely — and today's dark energy has been dominant for six billion years.
• The early inflation period of the universe was very fast, the cosmological expansion went 10 ⁵⁰ times faster today. Today, on the contrary, dark energy is responsible for 70% of the rate of expansion.
• The early state somehow interacted with matter and radiation. At sufficiently high energies, there must exist a certain “particle of inflation” if quantum field theory is not lying to us. The dark energy of the late time is not known interaction of any kind.

But there are similarities.



Both have the same equation of state, that is, the relationship between the scale of the universe and time.

Both have the same relationship between energy density and pressure in GR.

Both lead to an exponential expansion of the universe.



But are they related? It is very, very difficult to say. Because, of course, we do not understand them well enough! Personally, when I think about inflation, I like to imagine a two-liter bottle of soda filled by half. I imagine that a drop of oil is floating on the surface of the liquid inside the bottle. This state of high energy resembles the Universe during inflation.

Then something happens that forces the liquid to pour out of the bottle. Oil is sent to the bottom, in a state of low energy.





But if the drop does not reach the bottom - it will not remain at zero, but at some final point (like the Higgs field during the symmetry breaking) - it can cause the appearance of dark energy. The models connecting these fields, the field of inflation and the field of dark energy, are known as quintessence .

It's pretty easy to create a working quintessence model. The problem is that it is just as easy to create two separate working models - one for inflation, and one for dark energy. We have two new phenomena that require the introduction of at least two “free parameters” in order for the theory to work. They can be connected, it is possible not to connect, but these models cannot be distinguished from each other.



To date, we have only been able to exclude certain classes of models in which the rate of expansion in the early or late stages does not coincide with the observations. But observations are consistent with the fact that inflation is in itself, and dark energy arises from a completely different source. I really do not like to talk about the knowledge we have gained, that inflation occurs at energies of the order of 10 ¹⁵ GeV, and dark energy — at energies of about 10 ^-3 eV, and then explain that “we don’t know whether they are related” - but that’s what and things are.

Unfortunately, even with all the proposed experiments - James Webb, WFIRST, LISA and ILC - we do not expect to receive an answer to this question in the near future. It remains to hope for a theoretical breakthrough. I myself worked directly on this task, and I can say that I do not know when it can happen.