Cosmological Constant

The cosmological constant, symbol Λ (Greek capital lambda), was ‘invented’ by Einstein, not long after he published his theory of general relativity (GR). It appears on the left-hand side of the Einstein field equations.

Einstein added this term because he – along with all other astronomers and physicists of the time – thought the universe was static (the cosmological constant can make a universe filled with mass-energy static, neither expanding nor contracting). However, he very quickly realized that this wouldn’t work, because such a universe would be unstable … and quickly turn into one either expanding or contracting! Not long afterwards, Hubble (actually Vesto Slipher) discovered that the universe is, in fact, expanding, so the need for a cosmological constant went away.

Until 1998.

In that year, two teams of astronomers independently announced that distant Type Ia supernovae did not have the apparent luminosity they should, in a universe composed almost entirely of mass-energy in the form of baryons (ordinary matter) and cold dark matter.

Dark Energy had been discovered: dark energy is a form of mass-energy that has a constant density throughout the universe, and perhaps throughout time as well; counter-intuitively, it causes the expansion of the universe to accelerate (i.e. it acts kinda like anti-gravity). The most natural form of dark energy is the cosmological constant.

A great deal of research has gone into trying to discover if dark energy is, in fact, just the cosmological constant, or if it is quintessence, or something else. So far, results from observations of the CMB (by WMAP, mainly), of BAO (baryon acoustic oscillations, by extensive surveys of galaxies), and of high-redshift supernovae (by many teams) are consistent with dark energy being the cosmological constant.

So if the cosmological constant is (a) mass-energy (density), it can be expressed as kilograms (per cubic meter), can’t it? Yes, and the best estimate today is 7.3 x 10-27 kg m 3.

Ned Wright’s Cosmology Tutorial (UCLA) and Sean Carroll’s Cosmology Primer (California Institute of Technology) between them cover not only the cosmological constant, but also cosmology! NASA’s What Is A Cosmological Constant? is a great one-page intro.

Universe Today has many, many stories featuring the cosmological constant! Here are a few to whet your appetite: Universe to WMAP: LCDM Rules, OK?, Einstein’s Cosmological Constant Predicts Dark Energy, and No “Big Rip” in our Future: Chandra Provides Insights Into Dark Energy.

There are many Astronomy Cast episodes which include discussion of the cosmological constant … these are among the best: The Big Bang and Cosmic Microwave Background, The Important Numbers in the Universe, and the March 18th, 2009 Questions Show.


What is Einstein’s Theory of Relativity?

Albert Einstein's Inventions

There are two, theories of relativity, by Einstein, the special theory of relativity (or just special relativity, SR), and the general theory of relativity (or just general relativity, GR).

The special theory of relativity was published in 1905, in Annalen der Physik (“Zur Elektrodynamik bewegter Körper“, in the original German; “On the Electrodynamics of Moving Bodies” is its English translation), and the general theory of relativity published in 1915, in the Minutes of the Meetings of the Prussian Academy of Sciences (Berlin) (“Die Feldgleichungen der Gravitation” in the original German; “The Field Equations of Gravitation” is its English translation).

In its original form, special relativity is based on just two postulates (or assumptions); namely, that the speed of light (in a vacuum) is constant – no matter who measures it, or when, or where – and that the laws of physics are the same for in all inertial frames of reference (basically, for all observers who are not accelerating) … there are other, logically consistent, ways to construct SR, from different postulates, but they are equivalent to Einstein’s original.

The general principle of relativity at the heart of general relativity is easy to state (something like “the laws of nature are the same, everywhere, everywhen, and to everybody“), but the additional postulate (or postulates) is not. However, the consequence of this postulate is easy to say, in words – gravity is geometry … or in the words of John Wheeler “spacetime tells matter how to move; matter tells spacetime how to curve“.

Special relativity has been tested sixty ways to Sunday, and there are no experimental results which contradict it (or, rather, none which are reproducible). It is incorporated into all modern theories of physics, particularly quantum electrodynamics (which is the most precisely tested scientific theory, period), and general relativity. It is also (!) mathematically consistent (self-consistent, internally consistent), and reduces to Newtonian mechanics in the limit of small speeds.

General relativity has also been extensively tested, though not as thoroughly as special relativity (see The Confrontation between General Relativity and Experiment).

The internet has lots and lots of material on Einstein’s theories of relativity (but do be careful, some sites are overtly anti-science, and some are just crackpot nonsense); two examples of good summaries/intros: Albert Einstein and the Theory of Relativity (from the University of Tennessee), and Relativity Tutorial (Ned Wright, UCLA).

There are lots and lots (and lots and …) of Universe Today articles on Einstein’s theories of relativity; here is a sample: Einstein Still Rules Says Fermi Telescope Team, and New Way to Measure Curvature of Space Could Unite Gravity Theory.

Two Astronomy Cast episodes are worth a special listen, Einstein’s Theory of Special Relativity, and Einstein’s Theory of General Relativity.

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