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# Dark Energy

In 1997 the California Institute of Technology and the University of Rome collaborated on an experiment known as BOOMERanG (Balloon Observations Of Millimetric Extragalactic Radiation and Geophysics). This experiment took highly detailed images of the Cosmic Microwave Background (CMB) from telescopes lifted above the atmosphere by high-altitude balloons. It measured differences in the density of the early universe by observing differences in the apparent temperature of the cosmic microwave background in different regions of the night sky.

We closed the last quiz with a demonstration of how we might deduce the shape of the universe by leveraging triangle geometry on curved surfaces. As they are the farthest detectable sources, anisotropies in the CMB are ideal candidates for this approach; in fact BOOMERanG data originally gave cosmologists precise measurements of angular size. But how do we work out their size?

The BOOMERanG project correlated the temperature differences in the CMB to differences in density of the early universe. Cosmologists speculate that small differences in density arose in the pre-recombination universe because of gravity and small fluctuations that are required by quantum mechanics.

Imagine for a moment that instead of light, regions of the early universe were all emitting streams of matter particles. Would a matter particle lose more energy escaping from a high-density region or a low-density region of the same size?

Now replace the matter particles in the previous question with photons. Assuming the photons lose energy as they escape their source the same way matter particles would, what would happen to the wavelength of particles from higher density regions?

Observations of the CMB tell us that the early universe was very nearly homogeneous—cosmic microwave background radiation is of almost constant wavelength. However, there are some regions of very slightly differing wavelength, corresponding to different densities of matter in the early universe.

These slight variations in the cosmic microwave background are limited in size by the influence of gravity in the early universe. Given that CMB radiation was emitted $$\SI{380000}{years}$$ after the big bang, what is an approximate upper limit on the size of these structures?

By the time the BOOMERanG project was getting underway, cosmologists had calculated that the largest structures in the cosmic microwave background should have an angular size of about $$1^\circ$$ for a flat universe.

Based on our results in the dark matter quiz—the amount of matter in the universe (including dark matter) is only $$30\%$$ of the critical density—we anticipate the universe is actually open. If this is the case, what angle would we expect the largest structures in the cosmic microwave background to subtend?

When the results came in for the BOOMERanG experiment their results were startling to many. The universe was exactly flat (to within experimental error). Given that we know that mass can distort the shape of the universe freely, for it to average out at being exactly flat seemed to some like a weird coincidence. But BOOMERanG's results were backed up by other teams working on the same puzzle.

The amount of mass we can account for in the universe should not be enough to make it flat. We have found only $$30\%$$ of the necessary mass. We might not really know what dark matter is, but at least we can find it, and see where it is in the universe by gravitational lensing.

Now we see that $$70\%$$ of what is shaping the fabric of the universe is something else entirely that we know nothing about. Physicists dubbed this dark energy and speculated that it formed part of the fabric of space itself.

At almost the same time as the BOOMERanG result, other teams were approaching the questions we have been asking from a different angle. In the distances chapter we used distances and recession velocities of distant supernovae to measure how quickly the universe was expanding, and measure its age. But this assumed that the universe was expanding at a constant rate.

Given the effects of gravity, how should we expect the speed of expansion to change over time?

The graph below shows the observed motion of supernovae, compared to their distance to us. Remember that when we look at more distant supernovae, we are actually seeing them as they were long ago, whereas the closer supernovae are telling us how fast objects at this closer distance are moving away from us now.

The purple line shows the relationship we would expect if expansion had always happened at a constant rate. Where should we expect more distant supernovae to appear if we factor in the effect of gravity?

This is where we actually observe them. What does this tell us about the expansion of the universe?

For all of this chapter, we have assumed that the universe is expanding, but at an ever slowing rate as gravity takes effect. Now we know that there is something dramatically different going on, and no known physics can explain it. A huge amount of energy is going into making the universe expand, and we have no idea where it is coming from. Cosmologists call this dark energy and they estimate it constitutes $$70\%$$ of the critical density of the universe (relating mass to energy by $$E=mc^2$$), i.e. exactly the missing mass required to make our universe flat.

That sounds pretty useful, if only we could harness it. Given that we found the critical density of our universe is $$\SI[per-mode=symbol]{8.3e-27}{\kilo\gram\per\meter\cubed}$$, and it takes about $$\SI{100000}{\joule}$$ of energy to boil a cup's worth of water, calculate the side length $$d$$ of a cube containing enough dark energy to boil a cup of tea (in $$\si{\kilo\meter}$$).

Details

• At the critical density, use Einstein's mass-energy relation, $$E=mc^2$$ where $$c=\SI[per-mode=symbol]{3e8}{\meter\per\second},$$ to find the energy per volume.

Despite its name, dark energy is not going to become a power source. We do however hope to understand it better in the future. In the meantime it exists in our equations of the universe as a "cosmological constant", pushing the universe apart and dominating the effects of gravity. The cosmological constant had been used previously in cosmology back in the days when the universe was thought to be static rather than expanding. It was invented by none other than Albert Einstein, before he removed it after the discovery of an expanding universe, calling it his "biggest blunder". He didn't have any idea what would be causing it either.

The field of cosmology has taught us more about the universe than we have ever known, but it is still full of unanswered questions. Some of the world's brightest minds and most expensive experiments are working on these mysteries right now. If you have time to spend a few years studying physics you might be able to join them.

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