Einstein's Cosmological Constant and the Expansion of the Universe

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Albert Einstein may be the greatest mind of the 20th century. He developed both the special and the general relativity and identified the photo-electric effect for which he earned a Nobel Prize on Physics. These concepts have had far-reaching implications in all fields of physics yet maybe one of his greatest contributions is also one which he gave the least importance to. In fact, he felt it was his “greatest blunder.” That mistake turns out to be the cosmological constant, or Λ, which explains the expansion of the universe.

Einstein
Einstein | Source

New Horizons

Einstein began his investigations into the universe while he was working at a patent office. He would try to visualize certain scenarios that tested the extremes of the universe, such as what a person would see if they went as fast as a beam of light. Would that light still be seen? Would it look like it was standing still? Can the speed of light even change? (Bartusiak 116)

He realized that the speed of light, or c, had to be constant so that no matter what type of scenario you were in the light would always look the same. Your frame of reference is the deciding factor in what you experience, but the physics are still the same. This implies that space and time are not “absolute” but can be in different states based on the frame you are in. With this revelation, Einstein developed special relativity in 1905. Ten years later, he takes gravity into account in the general relativity. In this theory, space-time can be thought of as a fabric on which all objects exist on and impress upon it, causing gravity (117).

Friedmann
Friedmann | Source

Now that Einstein showed how space-time can itself move, the question became if that space was expanding or contracting. The universe could no longer be unchanging because of his work, for gravity causes objects to collapse based on the impressions on space-time. He did not like the idea of a changing universe however, and he inserted into his field equations a constant that would act like anti-gravity so that nothing would change. He called it his cosmological constant, and it allowed for his universe to be static. Einstein published his results in a 1917 paper entitled "Cosmological Considerations in the General Theory of Relativity." Alexander Friedmann incorporated this idea of a constant and fleshed it out in his Friedmann equations, which would actually hint at a solution that implied an expanding Universe (Sawyer 17, Bartusiak 117, Krauss 55).

It was not until 1929 that observational evidence would support this. Edwin Hubble looked at the spectrum of 24 galaxies using a prism and noticed that they all displayed a redshift in their spectrums. This redshift is a result of the Doppler effect, where a moving source sounds higher when it comes towards you and lower when it moves away from you. Instead of sound, in this case it is the light. Certain wavelengths demonstrated that they were shifted from their expected locations. This could only happen if those galaxies were receding away from us. The Universe was expanding, Hubble found. Einstein immediately retracted his cosmological constant, stating that it was his “biggest blunder” because the Universe was clearly not static (Sawyer 17, 20, Bartusiak 117, Krauss 55).

The Age of the Universe

That seemed to be the end of the cosmological constant’s purpose until the 1990’s. Up to this point, the best estimate for the age of the Universe was between 10 and 20 billion years old. Not terribly precise. In 1994, Wendy Freedman and her team were able to use data from the Hubble telescope to refine that estimate to between 8 and 12 billion years. While this seems like a better range, it actually excluded some objects that were older than 12 billion years. Clearly a problem in the way we measured distance needed to be addressed (Sawyer 32).

A supernova in the lower left hand side.
A supernova in the lower left hand side. | Source

A team in the late 1990’s figured out that supernovas, specifically Type Ia, have bright spectra that were consistent in their outputs no matter their distance. This is because Ia result from white dwarfs surpassing their Chandrasekhar limit, which is 1.4 solar masses, thus causing the star to go supernova. for this reason white dwarfs are all typically the same size, so their output should be also. Other factors contribute to their usefulness in such a study. Type Ia supernovas happen frequently on a cosmic scale, with a galaxy having one every 300 years. Their brightness can also be measured to within 12% of its actual value. By comparing the redshifts of the spectra, it would be possible to measure distance based on that redshift. The results were published in 1998, and they were shocking (33).

When scientists got to the stars that were between 4 and 7 billion years old, they found they were fainter than anticipated. This could only have been caused by their position receding from us faster than if the Universe was just expanding at a linear rate. The implication was that the expansion that Hubble discovered was in fact accelerating and that the Universe may be older than anyone thought. This is because expansion was slower in the past then built up as time went along, so the redshift we are seeing has to be adjusted for this. This expansion seems to be caused by a “repulsive energy in empty space.” What this is remains a mystery. It could be vacuum energy, a result of virtual particles courtesy of quantum mechanics. It could be dark energy, the leading idea. Who knows? But Einstein’s cosmological constant is back and now in play again (Sawyer 33, Reiss 18).

The 1998 Report

The team who uncovered the accelerating expansion studied Type Ia supernova and gathered values of high redshift (far away) versus low redshift (close by) in order to get a good value for the cosmological constant, or Λ. This value can also be thought of as the ratio of the vacuum energy density to the critical density of the Universe (which is the overall density). Another important ratio to consider is between the matter density to the critical density of the Universe. We notate this as ΩM (Riess 2).

What is so important about those two values? They give us a way to talk about the behavior of the Universe over time. As objects get spread out in the Universe, ΩM decreases with time while Λ remains constant, pushing the acceleration forward. This is what causes the redshift values to change as our distance increases, so if you can find the function that describes that change in the “redshift-distance relation,” then you have a way to study Λ (12).

They did the number crunching and found that it was impossible to have an empty universe with no Λ. If it was 0, then ΩM would become negative, which is nonsensical. Therefore, Λ must be bigger than 0. It has to exist. While it concluded values for both ΩM and Λ, they change constantly based on new measurements (14).

Einstein's field equation with the constant highlighted.
Einstein's field equation with the constant highlighted. | Source

Potential Sources of Error

The report was thorough. It even made sure to list potential problems that would affect the results. While not all are serious problems when properly accounted for, scientists are making sure to address these and eliminate them in future studies.

  • The possibility of star evolution, or differences in stars of the past to stars of the present. Older stars had different compositions and formed under conditions that current stars did. This could affect the spectrums and therefore the redshifts. By comparing known old stars to the spectrums of questionable Ia supernovas, we can estimate the potential error.

  • The way the curve of the spectrum changes as it declines could affect the redshift. It may be possible for the rate of decline to vary, thus changing the redshifts.

  • Dust could impact the redshift values, interfering with the light from the supernovas.

  • Not having a wide enough population to study from could lead to a selection bias. It is important to get a good spread of supernovas from all over the Universe and not just one portion of the sky.

  • The type of technology used. It is still unclear if CCD (charged-coupled devices) versus photographic plates yield different results.

  • A local void, where mass density is less than the surrounding space. This would cause Λ values to be higher than anticipated, causing redshifts to be higher than they actually are. By gathering a large population to study, one can eliminate this for what it is.

  • Gravitational lensing, a consequence of relativity. Objects can gather light and bend it due to their gravity, causing misleading redshift values. Again, a large data set will ensure this is not a problem.

  • Potential known bias using just Type Ia supernova. They are ideal because they are “4 to 40 times” brighter than other types, but that does not mean other supernovas cannot be used. Also have to be careful that the Ia you have seen is not actually a Ic, which look different under low redshift conditions but look similar the higher the redshift is.

Just keep all of this in mind as future advances are made in the study of the cosmological constant (18-20, 22-5).

The Cosmological Constant as a Field

It is worth noting that in 2011, John D. Barrows and Douglas J. Shaw presented an alternate investigation into the nature of Λ. They noticed that its value from the 1998 study was 1.7 x 10-121 Planck units, which was about 10121 times larger than the “natural value for the vacuum energy of the Universe.” Also, the value is close to 10-120. If that had been the case, then it would have prevented galaxies from ever forming (for the repulsive energy would have been too great for gravity to overcome). Finally, Λ is almost equal to 1/tu2 where tu is the “present expansion age of the universe” at about 8 x 1060 Plank time units. What does this all lead to? (Barrows 1).

Barrows and Shaw decided to see what would happen if Λ was not a constant value but instead a field that changes depending on where (and when) you are at. That proportion to tu­ becomes a natural result of the field because it represents the light of the past and so would be a carry-through from the expansion all the way up to the present. It also allows for predictions about the curvature of space-time at any point in the history of the Universe (2-4).

This is of course hypothetical for now, but clearly we can see that the intrigue of Λ is just beginning. Einstein may have developed so many ideas but it is the one he felt was a mistake of his that is one of the leading fields of investigation today in the scientific community

Works Cited

Barrows, John D, Douglas J. Shaw. "The Value of the Cosmological Constant” arXiv:1105.3105: 1-4

Bartusiak, Marcia. “Beyond the Big Bang.” National Geographic May 2005: 116-7. Print.

Krauss, Lawrence M. "What Einstein Got Wrong." Scientific American Sept. 2015: 55. Print.

Riess, Adam G., Alexei V. Filippenko, Peter Challis, Alejandro Clocchiatti, Alan Diercks, Peter M. Garnavich, Ron L. Gilliland, Craig J. Hogan, Saurabh Jha, Robert P. Kirshner, B. Leibundgut, M. M. Phillips, David Reiss, Brian P. Schmidt, Robert A. Schommer, R. Chris Smith, J. Spyromilio, Christopher Stubbs, Nicholas B. Suntzeff, John Tonry. arXiv:astro-ph/9805201: 2,12, 14, 18-20, 22-5.

Sawyer, Kathy. “Unveiling The Universe.” National Geographic October 1999: 17, 20, 32-3. Print.

© 2014 Leonard Kelley

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Ruth Angel 11 months ago from New Mexico

I LOVE Alex Filippenko. I wish I could find more of his work!


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1701TheOriginal 11 months ago Author

Agreed!

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