PROBLEM 3: THE DARK ENERGY PROBLEM

What is dark energy?

Also called the Cosmological Constant Problem

Something is causing the universe to accelerate it’s rate of expansion and we don’t know what it is. This is the Dark Energy Problem. We don’t know much about dark energy. We know it pushes space, creating a negative pressure so it expands. Gravity is only attractive and pulls matter together; mass attracts mass, it never repels. Dark energy is only repulsive, it repels space, and in that sense, dark energy can be considered as anti-gravity.

There exists a mathematical way of thinking about dark energy. The equations of general relat ivity (GR) include a term called the cosmological constant (Л). This was added into GR by Einstein to make the universe not expand or contract. When Hubble found that the universe was expanding then the cosmological constant was taken out of the GR equations. When dark energy was discovered then the cosmological constant was put back in again to include an acceleration of expansion.

If dark energy is the cosmological constant then it has a property that can explain the acceleration. For dark energy to be constant, then as the universe expands the dark energy has to get stronger, otherwise as space got bigger then the dark energy density would get smaller and there would be no acceleration. What happens is that the more space there is, then the more dark energy there is, so the density of dark energy stays constant. The strength of dark energy is small and in the early universe space was small so there was not much dark energy. As the universe expanded and space got bigger the amount of dark energy has got bigger and now there is a lot of it and we can see the effects in the acceleration. It is only in the last two billion years that the accelerating effect of dark energy has dominated the expansion of the universe.

The weird thing about a constant dark energy density is that energy is being created as space expands. This seems to contradict the law of conservation of energy, a law that physicists do not break. It is allowable though. This law only applies to a static, non-expanding space where Newton’s laws apply. In an expanding space, where space is changing with time, the laws of conservation of energy do not apply and energy can be lost and gained. What is conserved though is the energy density.

What is the Cosmological Constant? The answer to this is dark energy but what is dark energy is answered by ‘it’s the cosmological constant’. So mathematically the cosmological constant is helpful but it doesn’t answer what is dark energy. What we want is a physical explanation of what dark energy is.

A possible physical explanation could come from the vacuum energy of space. Space has energy and the lowest energy it can have is called the vacuum state. This is not zero; from quantum theory we know that there are quantum fluctuations in the vacuum state from which particle pairs can form and annihilate, called virtual particles. They live for a very short time between the events of real particles. The vacuum energy is an energy that we know exists within space so maybe it is dark energy. If dark energy is the vacuum state then we can calculate how much energy there is. Knowing how fast the universe is accelerating we can calculate that the vacuum energy density would be 10^-8 erg/cm³. We can also calculate the energy density of the vacuum state from quantum theory. From this we get a value of 10¹¹² erg/cm³. That is not just a big difference, that is an unbelievably enormous difference; a difference of 10¹²° times. Either dark energy is not the vacuum state or our understanding of quantum theory is wrong. This is called the ‘vacuum catastrophe’.

The quantum energy in the vacuum state is so big that there would not be a gently expanding universe, there would have been so much energy that expansion would have been rapid and no stars or galaxies would have formed. There is a solution to this. The theory of supersymmetry can produce an opposite energy that cancels out the quantum vacuum energy. This sounds great, but it introduces another problem. SUSY cancels out the vacuum energy so that it is zero. To get the tiny value of dark energy from the vacuum energy there would need to be some fine tuning of the value of SUSY to exactly match the dark energy value. This then becomes a ‘fine tuning problem’ that astronomers do not like. It seems too coincidental and we like to have a reason why a value is what it is. The problem of fine tuning led to ideas of the ‘anthropic principle’; that the universe is as it is today because otherwise we would not be here. They then led on to ideas for multiverses based on the premise that all possible values of Л can exist in other universes but only our value of Л produced stars, galaxies and life. Many scientists do not like the anthropic principle because it is not falsifiable so do not consider it scientific.

A more scientific explanation could be that the cosmological constant is changing and becoming smaller over time. It has been evolving for so long that it is almost zero and has reached the value that we see for dark energy. This idea is called ‘quintessence’. The name comes from the latin term Quinta Essentia meaning Fifth Essence and quintessence is sometimes called the fifth force. This was another scientific problem that Nobel prize winner James Peebles worked on [91].

If dark energy is not the vacuum energy, are there any other alternatives? There are a few ideas such as holographic dark energy, ghost condensates, dark fluid flow and let’s not forget matter creation from the Steady State Theory which could create a push on space. These are speculative and require some evidence, hut they are interesting ideas.

There has been recent work that suggests that maybe dark energy does not exist. Jacques Cohn and team [92], in 2019, looked at 740 supernova and suggested that the dark energy previously observed may be an artefact due to the movement of Earth, although most scientists accept that dark energy exists.

Another theory that avoids the need for dark energy comes from the voids in the cosmic web. If the Milky Way lives within the Local Hole, a very large void in the cosmic web, rather than outside it then the space we live in would have less density than outside the void and there will be negative pressure around us. This could look like dark energy. As more observations are being made about the Local Hole then the evidence in support of this theory is getting less.

Dark energy is a puzzle. We have evidence for it, although there are still some doubters, and it does fit with many aspects of the ACDM model but it is hard to explain where it comes from. We are still trying to understand what dark energy is; it could be the cosmological constant or it could turn out to be more complex. We need more data and more Cosmological Clues.

PROBLEM 4: THE COSMIC WEB PROBLEM

What are the primordial fluctuations that seeded the cosmic web?

Also called the Density Fluctuation Problem

An important strand of the ACDM model is how the structure of matter forms: the stars, galaxies and the cosmic web. This is a complex process involving dark matter, oscillations in the early universe, the birth and death of stars, and galaxy mergers, all within an expanding and cooling universe. The model works well. It can explain much of what we see in the sky and we have developed computer simulations that can recreate the cosmic web as we see it today.

There is a missing piece though and that is why did structure formation happen at all? For matter to form into clumps there had to be denser regions for the clumps to start from. If all matter were evenly spread throughout the universe there would be no differences in gravity between different regions so there would be nothing to pull the matter together. So where did these initial denser regions come from? What were the seeds of structure formation?

The seeds of structure must have formed in the very early universe because there is no mechanism within physics that could have caused them after the universe was one second old. The denser regions had to be there before the ACDM model starts and they had to be large enough by then to provide enough gravity to pull matter into oscillating clumps. ACDM does not explain where they came from; they are assumed to have been there. This is the Cosmic Web Problem.

A possibility is that the denser regions could have been created by quantum fluctuations in the hot early universe. This is an attractive idea, and is within the laws of physics, but ACDM does not have enough expansion to turn quantum fluctuations into the size of galaxies today nor into the size of the temperature fluctuations of the CMB by the time the universe was 380,000 years old.

A solution to this is to expand the universe by a very large amount, very rapidly, so that the quantum fluctuations become large enough. This is what inflation does. The quantum fluctuations can happen in the very early universe and are expanded exponentially and rapidly to become big enough to be the seeds of structure in ACDM. In a normal, Hubble expanding universe, any quantum fluctuations will be short lived and can disappear (annihilate). In an inflating universe quantum fluctuations form as space is exponentially expanding and a fluctuation will get stretched beyond the point where they annihilate so stay in existence. New fluctuations are created and they are stretched and this continues until inflation stops. Now the universe is full of small density fluctuations of all sizes, from the quantum size of the fluctuations that formed at the end of inflation, to the size of the universe of the fluctuations that formed at the beginning of inflation. It is what we call ‘scale invariant’ - there are equal numbers of each size. If we took a picture of the early universe on a large scale it will have looked exactly the same as when we zoomed in a thousand times, or a thousand times more; we would not have been able to tell the difference between the pictures. A graph showing the number of fluctuations at each size would be just a flat horizontal line - this graph is called the power spectrum of the density fluctuations.

We can look for this property of the fluctuations using the Cosmic Microwave Background (CMB). The density fluctuations were imprinted on the CMB when the universe was 380,000 years old, these are the ‘blobs’ that we see in Figure 4.2. We can use the CMB to measure the properties that the density fluctuations have by using the power spectrum of the CMB temperature anisotropies. The measurements show that the fluctuations are almost scale invariant as predicted by inflation. The flatness of the power spectrum graph is measured using the cosmological parameter n_s. An n_s value of one means that the fluctuations are exactly scale-invariant (the graph of number of fluctuations plotted for each size is flat). The Planck CMB measurements give a value of 0.958 which is almost one. The small deviation from one is called the ‘tilt’ of the initial density fluctuation spectrum.

Different models of inflation theory predict different values of n_s. By comparing the predictions from the different inflation theories to the measurements of n_s using the CMB it is possible to determine if one model is better than the others. It may also give us evidence for inflation theory and it is hoped that the next generation CMB telescopes may be able to do this.

There is other evidence from the CMB that can be explained by inflation. There are fluctuations in the CMB that are bigger than 1 degree, the size of the horizon (see the Horizon Problem Section 5.7). In ACDM, the Horizon Problem means that there should be no fluctuations larger than 1 degree. Inflation solves the Horizon Problem and allows the fluctuations to be much bigger, as observed.

There are other, more speculative, ways that the universe could have seeded the structure of matter. Cosmic strings are possible large, onedimensional defects caused by phase transitions as the universe cooled (they are not the same as the microscopic strings in string theory). These were speculated to have formed structure due to their gravitational attraction but it is now thought that they would not give the scale invariant spectrum that is seen in the CMB. Maybe the universe is holographic and the seeds are formed from higher dimensions leaving their imprint on a lower dimensional universe. Maybe we don’t need any seeds of matter. If the universe did not have a beginning but is cyclic or bouncing then the structure of the old universe could leave imprints that form the structure of the new universe.

There are various ideas as to what caused the seeds of the structure of matter but inflation is the best and preferred theory to solve the Cosmic Web Problem. For inflation to be accepted as the solution then some evidence is required. Perhaps the power spectrum of the density fluctuations could provide this evidence. If inflation did happen, then we exist due to microscopic random fluctuations that were a consequence of the quantum behaviour of the universe. Without these quantum fluctuations then matter would not have gravitated together and we would not be here.