Frequently asked questions about dark energy

[ Sean Michael Carroll - cosmologist, professor of physics, specializes in dark energy and general relativity, is engaged in research at the Department of Physics at the California Institute of Technology - approx. trans. ]

What is “dark energy”?

This is what causes the universe to accelerate, if in fact there is some entity with such a property.
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Apparently, I have to ask - what does the "acceleration" of the universe mean?

First, the Universe is expanding: Hubble showed that distant galaxies run away from us at speeds roughly proportional to the distance to them. "Acceleration" means that if you measure the speed of one of these galaxies, and then return to it after a billion years, and measure the speed again, you will see that it has increased. Galaxies are moving away from us at an increasing rate.

But this is some kind of explanation in simple words. Can this be explained more abstractly and scientifically?

The relative distance between distant galaxies can be summed up into a single indicator, the “scale factor”, often written as a (t) or R (t). This is, in fact, the “size” of the Universe - although not quite, since the Universe can be infinitely large. More precisely, it is the relative size of the space from one moment of time to another. The expansion of the universe means an increase in scale factor over time. Acceleration of the Universe means its increase with acceleration - that is, with a positive second derivative.

Does this mean that the Hubble constant, which measures the rate of expansion, is growing?

Not. Hubble's "constant" (or Hubble's "parameter", since it changes over time), describes the rate of expansion, but it is not just a derivative of the scale factor: it is a derivative divided by the coefficient itself. Why? Because so it becomes dimensionless and does not change with the change of agreements. The Hubble constant is a multiplier showing the rate of change of the scale factor of the Universe.

If the universe slows down, the Hubble constant decreases. If the Hubble constant increases, the Universe is accelerating. But there is an intermediate mode in which the Universe expands, but the Hubble constant decreases - and we think that our Universe lives in that mode. The speeds of individual galaxies are increasing, but doubling the size of the Universe takes more and more time.

In other words: the Hubble law relates the speed of a galaxy v with its distance d in the equation v = H * d. This speed may increase even if the Hubble parameter decreases; if it decreases more slowly than the distance grows.

And what, the astronomers really waited a billion years to re-measure the speeds of galaxies?

Not. We measure the speeds of very distant galaxies. As the light travels at a fixed speed, one light year per year, we look into the past. The reconstruction of the history of speeds and their differences in the past reveals to us the fact of acceleration of the Universe.

How to measure the distance to a distant galaxy?

It is not simple. The most reliable method is through a “standard candle” - a rather bright object that can be seen from afar, and whose own brightness is known in advance. Then you can calculate the distance to it, simply by measuring its brightness. The dimmer it is, the further.

Unfortunately, standard candles do not exist.

So how did they do it?

Fortunately, we have a method slightly inferior to the best: standardized candles. Supernovae of a special type, type Ia , are very bright, and have not quite, but approximately the same brightness. Fortunately, in the 1990s, Mark Philips discovered an amazing relationship between his own brightness and the time it takes for a supernova to fade after reaching maximum brightness. As a result, if we measure the brightness, and it decreases with time, we can make a correction for this difference, and build a universal brightness scale, which can be used to measure distances.

And why type Ia supernovae turned out to be standardized candles?

We are not exactly sure - basically, everything is calculated empirically. But there is an idea - we think that these supernovae are obtained when white dwarfs attract matter outside, until they reach the limit of Chandrasekhar and explode. And since this restriction is the same throughout the Universe, it is not surprising that supernovae have similar brightness. Deviations probably occur due to different star compositions.

And how do you know when supernova comes about?

No They appear rarely, about once in a hundred years for an average galaxy. Therefore, you need to look directly at a bunch of galaxies with wide-angle cameras. Specifically, images of the sky made at different points in time, spaced a few weeks apart (usually images are made at the new moon, when the sky is darkest) are compared - just such a time is required by supernovae to add sharply to the brightness. With the help of computers images are compared in search of new bright points. These points are then studied to find out if these are really type Ia supernovae. This, of course, is very difficult, and it would be impossible if it were not for some of the latest technological innovations - cameras with CCD matrices and giant telescopes. Today we can be sure that as a result of observations, supernovae can be collected in dozens - but when Perlmutter began work with his group, it was not at all obvious.

And what did they find out by doing this kind of work?

Most astronomers (almost all) expected the Universe to slow down - galaxies would attract each other through gravity, which will slow down their movement. But it turned out that remote supernovae are dimmer than expected - a sign that they are located further than was predicted, that is, the Universe is accelerating.

Why did cosmologists so quickly accept this result?

Even before the results were announced in 1998, it was clear that there was something wrong with the Universe. It seemed that the age of the universe was less than the age of its oldest stars. Matter was less than predicted by the theorists. On a large scale, the structures were not as pronounced. The discovery of dark energy solved all these problems in one fell swoop. Everything fell into place. Therefore, although people were fairly cautious, after this observation, the Universe became much clearer.

And how do we know that supernovae look dimmer not because of something that obscures them, or because in the past everything was different?

The question is legitimate, and two teams studying supernovae, very actively worked on his analysis. You can never be 100% sure, but you can always get new confirmations. For example, astronomers have long known that obscuring matter scatters blue light more easily than red, with the result that stars behind clouds of gas and dust "turn red." You can look for such redness, and in the case of supernovae it turns out to be insignificant. Moreover, we now have an abundance of independent evidence leading to the same conclusion - so it seems that the original measurements with the help of supernovae did not lie to us.

Is it true that there is independent evidence of the existence of dark energy?

Oh yeah. The simplest argument is subtraction. Relic radiation tells us the full amount of energy, including matter, in the Universe. Local measurements of galaxies and clusters give the total amount of matter. It turns out that matter exists only 27% of the total energy, which leaves us 73% in the form of some invisible substance to us, but not matter: "dark energy." This amount is enough to explain the acceleration of the universe. Other proofs are acoustic baryon oscillations (waves on large-scale structures, whose size helps to study the history of the expansion of the Universe) and the evolution of structures as they expand.

Well, okay, and what is dark energy?

Glad you asked! Dark energy has three main properties. First, it is dark. We do not see it, and as far as measurements tell us, it does not interact with matter at all (if it interacts, then it exceeds the capabilities of our observations). Secondly, it is evenly distributed. It does not accumulate in galaxies and clusters, or we would discover it by studying their dynamics. Thirdly, it is constant. The density of dark energy (the amount of energy per cubic light year) remains constant as the Universe expands. It does not dissipate, like matter.

The last two properties allow us to call it "energy", and not "matter." Dark energy does not behave like particles that have local dynamics and dissipate as the universe expands. Dark energy is something else.

Interesting story. And what exactly can be dark energy?

The leading candidate for this place is the simplest: “vacuum energy” or “cosmological constant”. Since we know that dark energy is evenly distributed and constant, the first thing that comes to mind is that it is ideally distributed and ideally constant. This will be vacuum energy: a fixed amount of energy that each piece of space possesses, and which does not change either from one place to another or over time. One hundred millionth erg per cubic centimeter, if you are interested.

And what, vacuum energy differs in nothing from a cosmological constant?

Yes. Do not believe the one who denies it. When Einstein first came up with this idea, he did not think about it as “energy”, he thought about it, as a modification of the way in which the curvature of space-time interacts with energy. But it turns out that this is the same thing. If someone does not believe it, ask what observations he is going to distinguish them from each other.

Doesn't vacuum energy come from quantum fluctuations?

Not really. A whole mountain of all phenomena can create the energy of empty space, and some of them are completely classical, having nothing with quantum fluctuations. But to the classical phenomena leading to the emergence of this energy, quantum fluctuations are also added. They are pretty strong, and this brings us to the problem of the cosmological constant.

What is the problem of the cosmological constant?

If only classical mechanics were known to us, then the cosmological constant would be just a number — there would be no reason for it to be particularly large or small, positive or negative. We would just measure it and calm down.

But our world is not classical, but quantum. And in quantum field theory, classical quantities must be subject to quantum corrections. In the case of vacuum energy, these corrections have the form of the energy of virtual particles, the fluctuations of which occur in the vacuum of empty space.

We can add up the amount of energy resulting in these fluctuations, and we get infinity. This, apparently, is not true, and we suspect that we are exaggerating the calculation. For example, this rough calculation includes fluctuations of all sizes, including wavelengths shorter than the Planck length, at which space-time may lose its conceptual certainty. If we sum only the wavelengths longer than the Planck length, we get the estimate of the cosmological constant.

And as a result, it goes out to 10 ¹²⁰ more than the observed value. This difference is the problem of the cosmological constant.

Why is the cosmological constant so small?

Nobody knows. While we were not able to work with supernovae, many physicists believed in the existence of hidden symmetry or a dynamic mechanism that nullifies the cosmological constant, since we were sure that it was less than our estimates. Now we need to explain both why it is small, and why it is non-zero. And besides, there is the problem of coincidence - why the orders of magnitudes of the density of dark energy and matter coincide.

That's how bad everything is: at the moment the anthropic principle serves as the best explanation of the cosmological constant value. If we live in the multiverse, in which the values ​​of vacuum energy differ in different areas, we can say that life can exist (as well as make observations and win Nobel prizes) only in those areas in which the vacuum energy is much lower than estimated. If it were large and positive, galaxies and even atoms would break apart. If it were large and negative, the Universe would quickly recollapse. In such situations, a typical observer would get a value close to the observed. Stephen Weinberg made this prediction in 1988, long before the discovery of the acceleration of the universe. But he did not strongly defend him, he simply said that "if everything is exactly like this, we will see something like the following." There are many problems with these calculations, especially when we begin to involve “typical observers”, even if we believe in the existence of the multiverse. I’m happy to think about the multiverse, but I’m rather skeptical about our ability to make any predictions about observables related to this theoretical platform.

We need a simple formula that predicts the cosmological constant as a function of all other nature constants. We do not have it, but we are trying to withdraw it. The proposed options work with quantum gravity, additional dimensions, wormholes, supersymmetry, nonlocality, and other interesting but speculative ideas. Nothing has taken root yet.

Did any experiments influence the development of string theory?

Yes: the acceleration of the universe. Prior to that, theorists suggested the need to describe the universe with zero vacuum energy. When there was a chance to distinguish it from zero, the question arose whether this fact could be shoved into string theory. It turned out that it is not so difficult to do. The problem is that if you find one solution, you find an absurdly large number of others. Such a landscape of string theory kills the hope of one unique solution that can explain the real world. It would be nice, but science has to take what nature offers.

What is the problem of coincidence?

With the expansion of the universe matter is blurred, and the density of dark energy remains constant. Hence, the relative density of dark energy and matter varies greatly with time. In the past, there was more matter; in the future, dark energy will dominate. But today they are about equal. When numbers can differ by 10 ¹⁰⁰ times or more, a difference of three times is not considered. Why is it so fortunate for us to be born when dark energy is enough for it to be discovered, and not enough for such attempts to deserve the Nobel Prize? Either this is a coincidence (why not), or we live in some special time. Partly for this reason, people are so willing to accept the anthropic principle. The universe turns out some kind of incongruous.

If dark energy has a constant density, and space expands, does this mean that energy is not conserved?

Yes, and that's fine.

What is the difference between dark energy and vacuum energy?

Dark energy is the generally accepted term of a uniformly distributed and constant substance, forcing the Universe to accelerate. Vacuum energy is one of the candidates for the role of dark energy, which is ideally distributed and constant.

So are there other candidates for dark energy?

Yes. You just need something fairly evenly distributed and constant. It turns out that most of these things lose their density, so finding sources of constant energy is not easy. The simplest and best of ideas is quintessence, simply a scalar field, filling the Universe, and slowly changing with time.

Is the idea of ​​quintessence natural?

Not particularly. It was originally planned that by considering something dynamic and changing, and not just fixed, you can find some clever explanation for why dark energy is so weak, and can be explained by the problem of coincidence. But these hopes were not justified.

Added only new problems. According to quantum field theory, scalar fields like to be heavy. But in the case of quintessence, the scalar field should be unrealistically light, 10 ^-30 of the mass of the lightest neutrino (but not zero). And this is one problem, and the second - a light scalar field must interact with ordinary matter. Even if such an interaction is frail, it should be possible to detect it - but it was not found. Of course, this is not only a problem, but also an opportunity - maybe the best experiments will find "the power of quintessence", and we will finally deal with dark energy.

How else can we test the idea of ​​quintessence?

Directly - use supernovae, only smarter. In general: to build a map of the expansion of the Universe with such accuracy that it could be seen whether the density of dark energy varies with time. This is usually represented as an attempt to measure the parameter w of the dark energy state equation. If w is -1, then dark energy is constant - it is vacuum energy. If w is slightly greater than -1, the dark energy density decreases. If it is slightly less than -1 (for example, -1.1), then the density of dark energy increases. For many theoretical reasons, this is dangerous , but we still have to watch out for it.

What is w?

It is called the parameter of the equation of state, because it connects the pressure of dark energy p with its energy density ρ, through w = p / ρ. Of course, no one measures the pressure of dark energy, so the definition is rather stupid - but this is just a historical case. What matters is how dark energy changes over time, but in GR it is directly related to the parameter of the equation of state.

Does this mean that the pressure of dark energy is negative?

Exactly. Negative pressure means that the substance pulls, but does not push - like an elongated spring pulling inwards from both ends. Often this is called tension. Therefore, I proposed the term “smooth tension” instead of “dark energy”, but I was late.

Why does dark energy make the Universe accelerate?

Because it is constant. Einstein says that energy makes space-time warp. In the case of the Universe, this curvature manifests itself in the form of a curvature of space (and not space-time) and expansion of the Universe. We measured the curvature of space, and it is essentially zero. Therefore, constant energy leads to a constant rate of expansion. In particular, the Hubble parameter is close to a constant, and if we recall the Hubble law, v = H * d, you will understand that if H is almost constant, then v will increase due to the increase in distances. So much for the acceleration.

If negative pressure is like tension, why does it not tighten everything together, but push it apart?

Sometimes you can hear expressions like “dark energy accelerates the Universe due to negative pressure”. Strictly speaking, it is, but the opposite is the case: such an expression only gives the illusion of understanding. You are told that "the force of gravity depends on the density and tripled pressure, so if pressure is equal and opposite to density, gravity will repel." It sounds reasonable, but no one can tell you why gravity depends on density and triple pressure. And in general, not the force of gravity, but the local expansion of space depends on it.

The question “why doesn’t tension pull things together?” Is legitimate. The answer is that dark energy does not pressure anything and does not pull anything. It does not interact with ordinary matter, and is evenly distributed in space, so any tension that it would exert in one direction would be compensated for exactly the same in the opposite direction. The universe is accelerated by the indirect effect of dark energy, working through gravity.

In fact, dark energy causes the Universe to accelerate, because it is constant.

Does dark energy look like antigravity?

Not. Dark energy is not anti-gravity, but simply gravity. Imagine a world with zero dark energy, with the exception of two bubbles of dark energy. These two bubbles do not repel, they attract. But inside the bubbles, dark energy pushes space, and it expands. Such are the wonders of non-Euclidean geometry.

Is this a new repulsive force?

Not. This is just a new type of source of old force - gravity. No new forces.

What is the difference between dark energy and dark matter?

These are completely different things. Dark matter is a kind of particle that has not yet been discovered by us. We know about its existence, because we see how it affects with the help of gravity various objects (galaxies, a cluster, large-scale structures, relict radiation). It is 23% of the universe. But in essence, this is good old matter, just one that we cannot (for the time being) fix. It accumulates under the influence of gravity and dissipates as the universe expands. Dark energy, on the other hand, does not accumulate or dissipate. It is not made of particles, it is something completely different.

Or maybe there is no dark energy, just need a little tweak gravity on a cosmological scale?

This is possible. There are at least two popular approaches to this idea: gravity f®, which Mark Philips and I helped to develop, and DGP gravity - Dvali, Gabadadze and Porati. The first approach is phenomenological, it simply changes the Einstein field equation by correcting the action in four dimensions, and the second uses additional dimensions that can only be fixed at large distances. Both have problems — not necessarily insurmountable, but serious — with new degrees of freedom and the ensuing instability.

Modified gravity worthy of serious consideration. But, as in the case of quintessence, it creates more problems than it solves, at least for now. I prefer the following predictions of success chances: cosmological constant: 0.9, dynamic dark energy = 0.09, modified gravity = 0.01.

What does dark energy say about the future of the universe?

Depends on what dark energy is. If this is an eternal cosmological constant, then the Universe will continue to expand, cool and empty. As a result, there will be nothing left but empty space.

The cosmological constant may be permanently temporary; that is, in the future a phase transition may occur, after which the vacuum energy will decrease. Then the universe may be a recollapse.

If dark energy is dynamic, then everything is possible. If it is dynamic and increasing (w is always less than -1), we can even get a big gap .

What next?

We would like to deal with dark energy (or modified gravity) by improved cosmological observations. This means measuring the parameter of the equation of state, as well as improving observations of gravity in galaxies and clusters to compare different models. Fortunately, while in the United States they are abandoning ambitious research projects, the European Space Agency is developing a satellite to measure dark energy . Ground-based scientific projects are also being developed, and the Large Synoptic Survey Telescope should give us a lot after its launch.

But the answer may be boring - dark energy will be a simple cosmological constant. It's just one number, and what can you do with it? In this case, we obviously will need improved theories, as well as a contribution from adjacent empirical data sources — particle accelerators, fifth force searches, gravity checks — from wherever you can get information about how space-time and quantum field theory are combined on the basic level

What is great in science is that at the end of the book there are no right answers, you need to get to the bottom of everything yourself. And dark energy is one of the biggest challenges.