How is Dark Energy Density Calculated in the Universe?

[Quarlep]

Physical cosmology and astronomy, dark energy is an unknown form of energy which permeates all of space and tends toaccelerate the expansion of the universe. Dark energy is the most accepted hypothesis to explain the observations since the 1990s indicating that the universe is expanding at an accelerating rate. According to the Planck mission team, and based on the standard model of cosmology, on a mass–energy equivalence basis, the observable universe contains 26.8% dark matter, 68.3% dark energy (for a total of 95.1%) and 4.9% ordinary matter.Again on a mass–energy equivalence basis, the density of dark energy (6.91 × 10−27 kg/m3) is very low, much less than the density of ordinary matter or dark matter within galaxies. However, it comes to dominate the mass–energy of the universe because it is uniform across space. Source Wikipedia

I am curious about how physicist calculate Dark Energy density in the universe and What mass-energy equivalance means ? Whats the theory behind it ?

Thanks

 

[Orodruin]

I am curious about how physicist calculate Dark Energy density in the universe

Essentially you look at the expansion history of the Universe (by looking on far away objects, i.e., back in time). From this you can infer the acceleration rate and therefore the energy density of dark energy.

What mass-energy equivalance means ? Whats the theory behind it ?

Relativity. See https://www.physicsforums.com/threads/what-is-the-massenergy-equivalence.763067/

 

[mfb]

I am curious about how physicist calculate Dark Energy density in the universe

They measure the rate of acceleration of the expansion and calculate which energy density is needed in general relativity to get this acceleration.

What mass-energy equivalance means ?

See the link in your text. Mass has energy and it is often possible to assign a mass to energy.

Whats the theory behind it ?

General relativity.

Edit: Parallel to Orodruin.

 

[Chalnoth]

Physical cosmology and astronomy, dark energy is an unknown form of energy which permeates all of space and tends toaccelerate the expansion of the universe. Dark energy is the most accepted hypothesis to explain the observations since the 1990s indicating that the universe is expanding at an accelerating rate. According to the Planck mission team, and based on the standard model of cosmology, on a mass–energy equivalence basis, the observable universe contains 26.8% dark matter, 68.3% dark energy (for a total of 95.1%) and 4.9% ordinary matter.Again on a mass–energy equivalence basis, the density of dark energy (6.91 × 10−27 kg/m3) is very low, much less than the density of ordinary matter or dark matter within galaxies. However, it comes to dominate the mass–energy of the universe because it is uniform across space. Source Wikipedia

I am curious about how physicist calculate Dark Energy density in the universe and What mass-energy equivalance means ? Whats the theory behind it ?

Thanks

When we talk about the energy of particles, we split their energy into two pieces: the energy of motion (kinetic energy), and the energy internal to the particle (mass).

For example, if you throw a rock, you give it kinetic energy. If you heat a rock up, you increase its mass (albeit not very much: you'll destroy the rock long before the increase in mass from the added thermal energy becomes measurable).

 

[mfb]

For example, if you throw a rock, you give it kinetic energy. If you heat a rock up, you increase its mass (albeit not very much: you'll destroy the rock long before the increase in mass from the added thermal energy becomes measurable).

For a looser definition of "rock", it is measurable: heating the whole Earth by ~100 K would increase its mass (and therefore the gravitational acceleration) by more than one part in a trillion, which is in the sensitivity range of (relative) accelerometers.

 

[Chalnoth]

For a looser definition of "rock", it is measurable: heating the whole Earth by ~100 K would increase its mass (and therefore the gravitational acceleration) by more than one part in a trillion, which is in the sensitivity range of (relative) accelerometers.

Unfortunately (or perhaps fortunately...) heating the Earth that much is just as impossible.

 

[mfb]

Well, at least it would not destroy Earth - just life on the surface ;).
It is the energy the sun radiates away in about 30 minutes.

 

[wabbit]

This makes me wonder, are there experiments where we can actually weigh the energy ? I mean, a tabletop-like E=mc^2 demonstration. Google tells me 1 microgram = 25 kWh so both seem within range but is it feasible to combine them in a single apparatus and weigh the heat or another form of energy ? This would be cool... (or hot rather I guess : ))

 

[mfb]

The hard part is to find a system light enough to allow scales to see this microgram difference.
The measurements seem to get close. Splitting water into hydrogen and oxygen needs about 3 eV per molecule, that is 0.18 parts in a billion.
As far as I can see, measurements of a few parts in a billion are feasible, and used to "copy" the kilogram prototype.

For nuclear energy, it is easy - the mass differences are in the range of .1%, many scales can see the difference.

 

[Chalnoth]

This makes me wonder, are there experiments where we can actually weigh the energy ? I mean, a tabletop-like E=mc^2 demonstration. Google tells me 1 microgram = 25 kWh so both seem within range but is it feasible to combine them in a single apparatus and weigh the heat or another form of energy ? This would be cool... (or hot rather I guess : ))

There are two known effects of dark energy:

1. It changes the rate of expansion of the universe.
2. It adjusts how large cosmic structures change over time.

The first effect comes from multiple independent measurements of the rate of expansion and matter content of our universe: galaxy cluster counts, the cosmic microwave background, the typical separation between galaxies, and supernova observations are some (there are probably others I can't think of off the top of my head).

The second effect is much more subtle. If there is no dark energy, gravitational potentials are constant in time. But if there is dark energy, they tend to decay slowly.

When a photon enters a gravitational well, it picks up energy from traveling down the gravitational potential well. If dark energy has caused the potential to decay over time, then it doesn't have as much of a climb to get out of the well, so it ends up with a slight boost in energy (a blueshift). This is known as the Sachs-Wolfe Effect. The average result of this effect on the cosmic microwave background is to make it so that there is more variation of the CMB at large angular scales. It's a subtle effect, but visible by the WMAP and Planck satellites.

Add these together, and the evidence is very clear that General Relativity with no cosmological constant + matter cannot explain the behavior of our universe. To solve the discrepancy, you can either modify General Relativity (or just have a cosmological constant, which is a parameter of General Relativity), or you can modify the matter/energy content of the universe. A number of theorists have tried clever ways to modify gravity that might cause the effects that we see, but so far no compelling ideas have come forward. The simplest idea, by far, is the cosmological constant, but the value of the cosmological constant is very weird, so that many theorists have looked for other explanations. None of those ideas has proven to be particularly compelling either (mostly they go under the name "quintessence").

A few years ago, there were some other alternative explanations, but they've all been falsified. Modified gravity, a cosmological constant, and some form of dark energy are the only realistic possibilities that remain (people usually lump in the cosmological constant with dark energy, as it's possible to write the equations such that it looks like an energy density).

 

[wabbit]

@Chalnoth, you may have quoted my post by mistake, it seems to me you are replying to someone else.

 

[Chalnoth]

@Chalnoth, you may have quoted my post by mistake, it seems to me you are replying to someone else.

No, I was replying to you. These are the ways we can detect dark energy. Maybe if the dark energy is some kind of dynamic field there might be other, independent ways of measuring it. But as far as we know what I wrote are the only ways we can detect its effects.

 

[wabbit]

Ah OK - My post was only about the "mass energy equivalence" question in the op, not about dark energy but I understand that was ambiguous. In any case, perplexing as I found them as a reply, these were interesting comments, and I learned about gravitational potential decay and the Sachs-Wolfe effect - thanks.

 

[Quds Akbar]

What mass-energy equivalance means ? Whats the theory behind it ?

Thanks

The theory of relativity, this equation explains why nothing can go faster that the speed of light.

 

[stevebd1]

I am curious about how physicist calculate Dark Energy density in the universe and What mass-energy equivalance means ? Whats the theory behind it ?

From the WMAP data, we know the universe is (more or less) flat, this means we can remove the spatial curvature parameter from the Friedmann equation (k=0 for a flat universe). We can then derive what the critical density is in order to maintain a flat universe. This gives us a figure in kg/m³. From this, we establish how much of this density is due to visible matter (baryonic) (ρ_b) which can be observed and how much is dark matter (ρ_dm) which can be observed/calculated. What remains of the critical density is predicted to be dark energy (hence the precise figure for something we don't yet know very much about), the effects of which we can observe. You might also want to check out the Lambda-CDM model.

For the critical density see-
What is critical density

Another equation which might be of interest is the Friedmann acceleration equation which demonstrates a flat yet accelerating universe-
What is the Friedmann acceleration equation

 

[marcus]

...

I am curious about how physicist calculate Dark Energy density in the universe and What mass-energy equivalance means ? Whats the theory behind it ?

Thanks

That is a good question. There are several ways. I will show one approach, and do the calculation, and give the theory behind it.

To start, we can write the basic cosmic equation, the Friedmann equation for spatial flat case, in terms of observable quantities.
The observable quantiies are the current growth rate H
and the longterm growth rate H_∞ of 1/17.3 or about 0.06 per billion years, towards which the growth rate seems to be tending over time
and the matter and radiation energy density ρ which as I recall is about 0.26 nJ/m³ (nanojoules per cubic meter)

The Friedmann equation has a central constant that converts between square growth rate on the left, and energy density on the right.

$$H^2 - H_\infty^2 = \frac{8\pi G}{3c^2} \rho$$

H² - H_∞² = [Friedmann constant]ρ
these three things are in principle observable and have estimates based on observation.
the Friedmann constant is made up of known constants like Newton G and speed of light c.

People who like to think of H_∞ as caused by an "energy" will take the square growth rate H_∞ on the left, and DIVIDE by the Friedmann constant, so that it turns into an energy density, and put it over on the right side. This extra energy density is called "dark energy density."

It is very easy to calculate. We just take the known H_∞ which is about 0.06 per billion years or more exactly 1/17.3 per billion years,
and we square that to get (1/17.3)^2 per (billion years)^2
and we multiply by the reciprocal of the Friedmann constant, which google can tell us

If you put "3c^2/(8 pi G) in nJ/m^3 per (billion years)^-2" into google it says:
(3 * (c^2)) / ((8 * pi) * G) = 161.420106 (nJ / (m^3)) per ((billion years)^(-2))

So we just have to multiply (1/17.3)^2 by 161.42 and that will give us the "dark" energy density in nanojoules per cubic meter.
161.42 * ((1 / 17.3)^2) = 0.5393431120
So H_∞² converts to 0.54 nanojoule per cubic meter.

 

[Quarlep]

I got that.Thank you.Actually you are a good teacher.I understand it easily