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Cosmic Asymmetry

September 11, 2023

Hypothesis is one of the engines that drives scientific progress, and an important part of hypothesis formation is the power of analogy.[1] As George Pólya wrote in his 1945 book, How to Solve It,
"Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements."

An unusual example of analogy in astronomy is the comparison between trees in a forest and the stars in the sky. When you're in a small stand of trees, it's possible to peer through the empty spaces to see what's outside. As the number of trees gets larger, the additional trees block your view of the outside world, and there's a point at which you can't see the outside world at all.

If we consider stars instead of trees, a very large, or infinite, universe will have a star everywhere we look. As a consequence, the night sky should not be dark, but lighted. The distant stars would be dim, but each distant star will cover just a small angular patch of sky. There's a compensating mechanism in which the intensity of light falls as the square of distance, but the surface area of a sphere at that distance is larger by the square of the distance.

The paradox of the dark night sky is called Olbers' paradox. It's named after the German astronomer, Heinrich Wilhelm Matthias Olbers (1758-1840), but Olbers wasn't the first to have this idea.

German astronomer, Heinrich Wilhelm Matthias Olbers

German astronomer, Heinrich Wilhelm Matthias Olbers (1758-1840).

Although Olbers' paradox is named after Olbers, who stated it in 1823, many others deserve some credit, including Johannes Kepler (1571-1630), Edmond Halley (1656-1742), and Jean-Philippe de Cheseaux (1718-1751). Kelvin (1824-1907), who had opinions on many scientific matters, gave one resolution of the paradox in a 1901 paper.

(Lithograph by Rudolf Suhrlandt (1781-1862), via Wikimedia Commons.)

Since the night sky is dark, there's the facile argument that the number of stars is finite, and this was Kepler's argument. As late as the first part of the 20th century, many astronomers still believed that our Milky Way Galaxy was all there was to the universe. Another explanation is that obscuring dust clouds might be the cause. However, thermal equilibrium would eventually cause the dust clouds to glow as brightly as the stars whose energy they absorbed, and this explanation fails.

We now believe that we inhabit a universe of at least 2 trillion galaxies that had a precise origin in an event called the Big Bang 13.787 ± 0.020 billion years ago. At large scale, our universe appears to be both homogeneous and isotropic. This is evidenced by detailed observation of the cosmic microwave background radiation (CMBR) in 1989-1993 by the Cosmic Background Explorer (COBE) satellite observatory. COBE observed the thermal black body spectrum of the remnant radiation of the Big Bang (see figure).

COBE image of the detected small variations in the cosmic microwave background radiation (CMBR)

Cosmic Background Explorer (COBE) false color image of the detected small variation (36 μK between blue and red) in the cosmic microwave background radiation (CMBR). (NASA image of the COBE Science Working Group. Click for larger image.)

While the isotropy of the universe is settled as far as the cosmic microwave background radiation is concerned, scientists always look to understand things from more than one perspective. An interesting example is a feature of the theory of closed timelike curves proposed by mathematician, Kurt Gödel (1906-1978), who is famous for his incompleteness theorem that casts doubt on the possibility of certain mathematical proofs.

Gödel suffered periods of mental instability towards the end of his life, and he seemed to be obsessed with the idea of his mortality. His proposed closed timelike curves would be a means for both the universe and his own self to be reincarnated repeatedly. One consequence of this theory was a preferred spin axis for galaxies. As John Wheeler (1911-2008) explained, Gödel found that observations did not support his theory.[2]
"It turned out that he, himself, had taken out the great atlas of the galaxies and, page after page, had opened it up and looked at each galaxy, determined the direction of its axis, he made a statistics of these numbers, and found there was no preferred direction of rotation..."[2]

Despite such failed attempts, searches for some sort of cosmic asymmetry are still being done. In a recent open access article in the Monthly Notices of the Royal Astronomical Society, Jiamin Hou of the University of Florida (Gainesville, Florida), Zachary Slepian and Robert N. Cahn of Lawrence Berkeley National Laboratory (Berkeley, California) have examined the parity (reflection symmetry) of clusters of galaxies forming a tetrahedron in space when the galaxies serve as vertices joined by connecting lines.[3-5]

A tetrahedron with its four triangular faces is the simplest of all the ordinary convex polyhedra. A regular tetrahedron, with its four identical equilateral triangle faces, has reflection symmetry defined by six bisecting planes, and a tetrahedron with two equal sides will have one such plane. However, the probability is small that a tetrahedron formed from four randomly placed vertices would have any mirror planes; so, in general, tetrahedra can be classified as either clockwise or counter-clockwise (see figure).

Tetrahedrons showing parity and Robert's Quartet

In the tetrahedrons pictured, each vertex represents a galaxy. Choosing the topmost galaxy as the primary, there are three vectors pointing from it to the other vertices. Viewing the tetrahedron from the topmost galaxy looking down, the direction from smallest to largest side determines a clockwise or counter-clockwise rotation. The leftmost here is clockwise.

On the right is an image of a tetrahedral arrangement of galaxies known as Robert's Quartet. This compact clusters of galaxies composed of NGC 87, NGC 88, NGC 89, and NGC 92 is approximately 160 million light-years away in the constellation, Phoenix. It was discovered by John Herschel (1792-1871) on September 30, 1834.

(Left and center images created using Inkscape. The rightmost image is a European Southern Observatory image from Wikimedia Commons. Click for larger image.)

Oliver Philcox, an astrophysicist at Columbia University (New York, New York) published a study in Physical Review D in September, 2022, in which he considered galaxies to be vertices of tetrahedra.[5] Philcox found a small imbalance in the numbers of tetrahedra of each parity (clockwise or counter-clockwise rotation).[5] Cahn decided to look for such parity violation in a million galaxies as cataloged in the Sloan Digital Sky Survey and luminous red galaxies of its Baryon Oscillation Spectroscopic Survey twelfth data release.[3-5]

For analysis, Cahn's team used the 4-point correlation function (4PCF) to ascertain an imbalance between such tetrahedra and their mirror images.[3-4] The million galaxy dataset yielded nearly 1024 tetrahedra.[5] The result was a parity imbalance that exceeded 7.1 standard deviations (seven-sigma), a very definitive result.[3-5] Five sigma is the standard for discovery in particle physics.

If there is a true cosmological asymmetry, it must arise from an epoch of the expansion of space known as inflation.[3-4] During inflation,the universe rapidly expanded to 1026 times its original size, and small quantum fluctuations of particles were amplified to affect the density of matter. The denser regions continued to gravitationally coalesce to produce the galaxies and large-scale structure we see today.[5]

As they say, "extraordinary claims require extraordinary evidence." Cahn and his colleagues have examined many possible sources of systematic error in their study, and they've found none that contradicts their finding of cosmic asymmetry.[3-4] The authors write that this 4PCF approach is a possible approach to examining details of the inflation epoch when augmented with data from newer galaxy surveys, such as the presently 14 million galaxies of the Dark Energy Spectroscopic Instrument (DESI) survey.[3-4] The pattern found for the cosmic microwave background radiation should also contain parity-violating correlations.[5]


  1. Dedre Gentner and Michael Jeziorski, "Historical Shifts in the Use of Analogy In Science," Technical Report No. 498, Center for the Study of Reading, University of Illinois at Urbana-Champaign, April 1990 (via Northwestern University).
  2. John Wheeler - Kurt Gödel and the Closed Time-like Line, YouTube video by Web of Stories - Life Stories of Remarkable People, Oct 6, 2017.
  3. Jiamin Hou, Zachary Slepian, and Robert N Cahn, "Measurement of parity-odd modes in the large-scale 4-point correlation function of Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey twelfth data release CMASS and LOWZ galaxies," Monthly Notices of the Royal Astronomical Society, vol. 522, no. 4 (July 2023), pp. 5701-5739, https://doi.org/10.1093/mnras/stad1062
  4. Jiamin Hou, Zachary Slepian, and Robert N. Cahn, "Measurement of Parity-Odd Modes in the Large-Scale 4-Point Correlation Function of SDSS BOSS DR12 CMASS and LOWZ Galaxies," arXiv, June 23, 2023, https://doi.org/10.48550/arXiv.2206.03625.
  5. Katie McCormick, "Asymmetry Detected in the Distribution of Galaxies," Quanta Magazine, December 5, 2022.

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