Dark EnergyTopics

Context for dark energy’s discovery;Dark energy and the concordance cosmology;Attributes of dark energy;Conservation of energy?How dark energy drives the Universe’s acceleration;Vacuum Energy and quintessence;Coincidence Scandal.

MotivationIn one day, we talk about 3/4ths of the Universe!

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1970s-1980s – The existence of dark matter had become an accepted fact of life.– Recall the Friedmann solution to Einstein’s field equations:

Note, space is essentially flat (K≈0)…

Therefore, ρ = ρcrit

BUT…observations indicated that

ρmatter = ρvis + ρdark ≈ 0.05ρcrit + 0.25ρcrit ≈ 0.3ρcrit

1990s– Observational astronomers had accepted that ρmatter ≈ 0.3ρcrit.

(claiming, “Cosmologists are wrong!”)– Cosmologists were clinging to the hope that ρmatter = 1.0ρcrit.

(claiming, “Observational astronomers are wrong!”)

Before dark energy

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1. The age of the Universe

– Closed Universe: ~ 4.4×109 y.

– Critical Universe: ~ 8.8×109 y.

– Open Universe: ~ 13×109 y.

But the oldest objects in the universe, such as some globular clusters, are older than 13×109 y!

Upstart cosmologists did not have the authority to tell venerable stellar astronomers that their ages for stars were wrong!

Three annoying problems before dark energy

M15 age models 3

2. That irritating value of 0.3ρcrit. Why not 1ρcrit, or 10-6ρcrit?

As noted, observational astronomers no longer thought that more material was likely to be found. Too many measurement methods were sticking with the 0.25 ρcrit for dark matter, and were not budging much beyond that.

Certainly, estimates for dark matter were not going to reach the value of 0.95 ρcrit that cosmologists wanted!

3. The clumping of matter in the Universe

Big Bang and inflation models said that ρ = ρcrit.

But if all that ρ is ρmatter, computer models indicated that the Universe should have clumped much faster than it did.

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Three annoying problems before dark energy

Once Schmidt’s and Perlmutter’s teams detected the accelerating expansion of the Universe, cosmologists realized the acceleration is driven by large amounts of a mysterious energy

Thus, dark energy arrived!

Assuming this energy responds to general relativity as everything else does, it contributes to the density of the Universe…a lot!

Models indicate that the amount of dark energy we need, in order to explain the accelerating Universe, is…

ρdark energy ≈ 0.70ρcrit

Dark energy arrives

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Now, let us include dark energy in our calculations.

ρvisible matter ≈ 0.05 ρcrit

ρdark matter ≈ 0.25 ρcrit

ρdark energy ≈ 0.70 ρcrit

This gives us the standard framework for ourmodern understanding of the universe, what is nowcalled The Concordance Cosmology.

ρ = ρvisible matter + ρdark matter + ρdark energy

= 0.05ρcrit + 0.25ρcrit + 0.70ρcrit

That the math works out so easily—that ρ= ρcrit after all—gives us the feeling that we’re on the right track.

Dark energy’s Concordance Cosmology

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Recall that the CMB gives evidence that space is essentially (if not perfectly) flat: only in flat space would blobs in the cosmic microwave background maps should have a typical size of 1º, which they do.

Since the CMB proves that space is observably flat, the density of the Universe is essentially (if not perfectly) at the critical density, and not just 0.3ρcrit.

In other words, the variations in the CMB provides compelling evidence that dark energy must exist at a level of about 0.7ρcrit.

This argument, distinct from Type Ia supernovae observations, is an independent line of evidence for dark energy.

Dark energy agrees with the CMB

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Why was dark energy accepted so rapidly by astronomers, while dark matter had taken 40 years, from Zwicky’s first comments in the 1930s to the 1970s?

– Astronomers had become used to the “dark sector,” because of dark matter;

– It explained the acceleration that had been detected by TWO teams;

– Dark energy raised ρ from 0.3ρcrit to 1.0 ρcrit;

– It gets the age right for the Universe;

– It explains the formation rate for the large scale structure in the Universe;

– Perhaps dark matter had suffered from the Zwicky taint?

Dark energy is rapidly accepted

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What two observable characteristics do we know about dark energy?

1. Dark energy is smoothly distributed throughout space.

Since dark energy is uniformly distributed, it affects the Universe overall, but does not affect its components.

This is because its net gravitational pull on any element of the Universe is equal in all directions, i.e., it cancels out.

Key characteristics of dark energy

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2. Dark energy is persistent.

Since acceleration has been observed to be constant over the history of the Universe (via those Type 1a supernova studies), we know that the energy density due to dark energy is constant!

The density of matter drops as 1/R3, and the energy density of photons drops as 1/R4.

The behavior of dark energy is completely different from the behavior of either energy or matter—even dark matter!

Key characteristics of dark energy

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The (1) uniform and (2) persistent nature of dark energy means that as space in the Universe expands, dark energy forms to fill the new space.

Dark energy says that energy is not conserved!!! It increases as the Universe grows!!!

Conservation of energy is a long-cherished bedrock of physics—can you swallow the notion of abandoning such a thing?

The creation of “free energy” seems to be wrong. How do you feel about it?

Key characteristics of dark energy

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Why is energy conserved in the Universe?

Ultimately, if you examine the foundations of physics, the law of the conservation of energy comes from the fact that the laws of physics do not change with time.

More technically, this is described by saying the Universe obeys a “symmetry of time-translation invariance.”

(Noether’s Theorem says that, for every “symmetry” in nature, there is a conserved quantity.)

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Key characteristics of dark energy

Since the laws of physics do not change in time, Noether’s Theorem seems entirely justified in giving us the law of conservation of energy.

Or is it?

In Sir Newton’s day, there was no question that the laws of physics did not change in time—his conception was that the structure of the Universe was unchanging, with an immutable system of dimensions and time.

But Einstein’s General Relativity showed that space can change with time. And we have observed (the Big Bang) that the Universe HAS changed with time.

Since the structure of space changes with time, Newton’s cherished symmetry of physics with time has been broken.

Time-invariant symmetry does not exist.

As a result, energy does not have to be conserved, even though we (incorrectly) feel in our guts that it is.

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Key characteristics of dark energy

Actually, dark energy is the second of two violations of the conservation of energy that we have met—you just didn’t mind the first one.

(And I’m not talking about quantum mechanics trickery!)

Consider a cubical volume of expanding Universe. It contains both matter (visible and dark) and conventional energy.

The energy in the (slow-moving) matter is mostly locked in its rest energy, i.e., E = mc2. This stays constant as space expands.

But the energy in the photons decreases as space expands.

Energy is not conserved!

Strangely, people don’t mind the notion of a Universe losing energy, but they do object to a Universe gaining energy!

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Key characteristics of dark energy

Moving on…

How does dark energy accelerate the Universe? There are two equivalent ways to interpret this. Choose the one you like.

1) Isolating the effect of dark energy

Imagine a toy Universe with no matter or normal energy—only dark energy fills the void, at a forever constant density.

In the Friedmann equation, set the curvature (K) to zero (to fit observations).

This means that the Hubble parameter (H) will be constant for all time.

What does it mean to say that the Hubble parameter is constant for all time?

Dark energy and the Universe’s acceleration

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Let’s follow what happens to a galaxy some distance from our own.

Hubble’s law says that:

v=Hd

As the Universe expands over time, and the distance (d) between us and the galaxy increases, the galaxy moves away from us ever faster.

What we would see is an accelerating Universe.

Dark energy and the Universe’s acceleration

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This toy Universe tells us what dark energy does.

Dark energy tries to drive our Universe to accelerate, while the combined densities of matter and conventional energy slow down the expansion by gravity.

Long ago, when the space of our Universe was smaller, the combined density of matter and conventional energy was much greater; this combined density dominated the growth of the Universe. H was much larger in the past.

But now, as the Universe thins, dark energy calls the shots, H is leveling out to a constant value, and the Universe finds itself accelerating.

Dark energy and the Universe’s acceleration

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Here is a second way to understand how dark energy accelerates the Universe.

2) Consider a piston filled with conventional gas at a high temperature.

When the positive pressure in the gas moves the piston to the right, the gas cools (loses energy), because energy is taken from the system. The piston takes the energy, and performs work.

This is quite analogous to why the fast moving photons in the Universe cool as the Universe expands.

Dark energy and the Universe’s acceleration

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Dark energy acts differently. As the Universe expands, the dark energy does not lose energy density (i.e., cool). Instead, the dark energy keeps the same energy density.

Notice that the total energy in the chamber increases.

This weird effect could be described as a piston that puts energy into the chamber as it expands. This is opposite of the earlier case, where pressure expanded the chamber.

To describe this, cosmologists like to say that dark energy has negative pressure.

Dark energy and the Universe’s acceleration

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Dark energy and the Universe’s acceleration

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How can we understand this intuitively? You could imagine a different piston—this one filled with rubber bands.

As the piston is moved to the right, the energy density inside the piston increases because you have to work to pull the piston.

Notice that energy enters the system.

Because of this way to visualize the system, some cosmologists (such as Sean Carroll) like to repackage negative pressure as smooth tension.

Recall the two attributes of dark energy:

1. It is uniform;2. It is persistent.

Dark energy seems to be uniformly distributed in space.

In fact, it seems like dark energy is just space itself, almost as if there is an energy cost to having space.

This concept is called vacuum energy. It suggests that mere space has energy associated with it.

Vacuum energy

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Suppose you have a cubical volume of the Universe.

Remove all matter, dark matter, and energy from the volume. It is now a perfect vacuum. But the vacuum is not empty—it is filled with a sea of virtual particles and antiparticles.

According to quantum physics, each of these particles will have a tiny amount of “zero-point energy.” They cannot be absolutely motionless (ultimately, because of the uncertainly principle).

If you sum all the zero point energies of all those virtual particles, you will calculate the vacuum energy.

Vacuum energy

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This sea of particles, winking in and out of existence, is not merely the mad dream of addled physicists—it has been observed!

Metal plates in a vacuum, a few microns apart, have a net force due to the Casimir effect!

Casimir effect

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In a first attempt to make a quantum calculation for the value of vacuum energy, when the zero-point energies of all the possible virtual particle-antiparticle pairs were summed, quantum mechanics calculated that…

…the zero-point energy is infinite!

Not to worry… Quantum physics often comes up with weird results like infinities. Quantum physicists are used to these, and have methods for dealing with them. For example, they eliminate fluctuations that occur over timescales smaller than Planck timescales.

With this refinement, the most accurate prediction for the vacuum energy is 10112 ergs/cm3.

The energy density of dark energy is…

Not very close to 10112 ergs/cm3.

What is the value of the vacuum energy?

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10-8 ergs/cm3.

Interestingly, the disagreement by a factor or 10120 is the largest discrepency in the history of mainstream science.

This is called the Cosmological Constant Problem.

For comparison, if you (over) estimate the mass of our known universe (1011 galaxies, each 1012 M, 1M = 2×1030kg)…the ratio of this to the mass of a single electron (9×10-31 kg) is about 2×1083.

What is the value of the vacuum energy?

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Before dark energy was discovered, it was assumed that this prediction of an incredibly huge number would somehow disappear when scientists had figured out some as-yet-unknown cancellation effect.

Now that dark energy has been found to be tiny but nonzero, it is much harder to deal with—you can’t just multiply the vacuum energy by zero. Some tiny amount has to be left over.

Strangely, some cosmologists feel that it is a success that vacuum energy predicts any value at all for dark energy, accuracy be damned!

Ultimately, vacuum energy might not be the total or even partial explanation of dark energy. However, it might still be there.

What is the value of the vacuum energy?

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When Einstein was solving the equations of general relativityfor the Universe, astronomers told him that the Universe was static. This was 1916-1918, about 11 years before Hubble’s discovery of the expansion of the Universe.

To create a static Universe, he added the cosmological constant to his equations. It was a zero point for his equations, and thus permissible:

Rμν - ½Rgμν + Λgμν = (8πG)Tμν

His modification of the curvature of space kept the observable Universe static. The model therefore fit the observations of the day—including it was scientifically cautious and conservative.

“Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder of his life”.

 — George Gamow (1970)

Now, we see that his cosmological constant was a kind of antigravity effect that was not a blunder, but rather anticipated dark energy!

Einstein and the cosmological constant

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Vacuum energy has not been very successful.

Another possible explanation for dark energy is dynamical dark energy. Exploring dynamical dark energy is one of the biggest issues in modern cosmology.

Dynamical dark energy suggests that perhaps the source of dark energy evolves over time—possibly very slowly.

No dynamical dark energy model has yet been successful, but perhaps something will come out of future research.

Let us examine a few of the issues associated with dynamical dark energy.

Dynamical dark energy

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Quintessence: the leading version of dynamical dark energy.– A new force in nature, mediated by a boson;– Not directional (like electromagnetism), hence a “scalar field”;– Evolves very slowly by an unknown mechanism;– Might involve VAMPs (variable mass particles)– No models are yet very successful.

Phantom energy– Dark energy that increases with time!– Not only is the Universe accelerating, but the acceleration itself is

accelerating!– The Universe will eventually tear itself apart in a final event that some

cosmologists like to call the Big Rip.

Dynamical dark energy models

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Consider the ratio of energy density vs. matter density. It drops off with increasing Universe size, by the ratios 1/R3 (matter), and 1/R4 (energy). Meanwhile, the energy density of dark energy is constant.

At recombination, the ratio was 109:1. Today, it is 70:30 ( = 2.3:1).

Why is it that, right now, we happen to live at a time where the ratio is so close to 1:1?

This violation of the Copernican Principle is called the Coincidence Scandal.

There is no known resolution to the Coincidence Scandal, and it is a serious problem.

A dynamical dark energy model might be able to address this better than a static model. Dynamical dark energy might be able to adjust somehow, perhaps to make it easier for the ratio to stick to near 1:1 for long periods of time.

Coincidence scandal

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One side effect of a changing dark energy field is that we would expect some of the basics constants of the Universe to be changing with time.

However, the nucleosynthesis that occurred during the Big Bang (14 BYA) seems to be perfectly consistent with all the forces and constants being exactly as we see them today.

In Oklo (Gabon), the Uranium deposits are depleted in radioactive 235Ur, indicating that it was removed by a sustained, natural fission chain reaction about 2 BYA.

These reaction rates are well understood by current radioactivity models.

Apparently, basic physical properties in our Universe are not changing, at least as measured 2BYA and 14BYA.

Side effects of dynamical dark energy

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Despite a string of failures, cosmologists are continuing to model the Universe, looking for possibilities that dark energy is evolving.

Dynamical dark energy wrap-up

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The “equation of state” parameter (w) tracks the possibility that dark energy is dynamical.

w = -1; dark energy is static

w > -1; quintessence (i.e., w = -0.8, etc.)

w < -1; phantom energy (i.e., w = -1.2, etc.)

Perhaps in the future, this will seem more like science, and less like bored cosmologists scribbling on the wall of an insane asylum…

Appendix

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Philosophically, Einstein considered the quantity to be a modification of space, and so deserved to be on the left side of the equation:

Rμν - ½Rgμν + Λgμν = (8πG)Tμν

However, interpreting the cosmological constant term as a new form of energy density merits moving it to the right side of the equation:

Rμν - ½Rgμν = (8πG)Tμν - Λgμν

These two equations are, of course equivalent, but cosmologists like to argue.

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Einstein and the cosmological constant

How does the affect of negative pressure affect the structure of space?

Einstein’s field equations:

Rμν - ½Rgμν = (8πG)Tμν

(curvature) (E-momentum tensor)

The energy-momentum tensor sums all forms of energy, including dark energy. How does the negative pressure of dark energy fit in?

Dark energy contributions to Tμν = (energy density) + 3× (pressure)

Dark energy adds to the energy density, but its negative pressure also contributes negatively to the pressure, multiplied by three (because of three dimensions).

Overall, the negative pressure aspect of dark energy drives the Universe to expand, much like an anti-gravity affect.

Dark energy and the Universe’s acceleration

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