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The Alternate View

Broken Parity Among Galaxies
by John G. Cramer

Parity symmetry, the fundamental principle that the laws of physics should be the same for an object and its mirror image, is known to be violated in particle physics by weak interaction processes like beta decay. It has been thought that aside from the weak interaction, which acts only at extremely small distances, parity should be a fundamental symmetry of the universe, particularly at the very large scales of cosmology.

However, recent investigations using four-point correlations applied to the observed locations of galaxies show a statistically significant parity violation. This result is still new, and its implications are not completely clear, but this galactic parity symmetry breaking may be connected to the matter-antimatter asymmetry of the Universe. It may also have deep implications for the forces that were acting during the very early inflation phase of the Big Bang.

Before going further, we will need to understand the far-from-obvious assertion that a map of the positions of distant galaxies can somehow show a parity symmetry breaking through deviations from mirror symmetry. Consider the observed positions of four distant galaxies in the sky. In three dimensions, these positions can be considered to form the vertices of a tetrahedron (a three-dimensional solid with four triangles as sides). Now choose one of the tetrahedron’s vertices as a reference point, and label the distances to the other three vertices as r1 for the longest side, r2 for the next side, and r3 for the shortest side. Then, as viewed from the reference vertex, the rotation direction of the progression (r1,r2,r3) must be either clockwise or counterclockwise. If parity symmetry is preserved, the probabilities of these two alternatives should be equal. On the other hand, if there are significantly more clockwise than counterclockwise sequences (or vice versa), then there is a violation of parity symmetry.

Of course, when mapping galaxies from the Earth, we determine two of the location dimensions (up/down and right/left) much better than the third dimension (in/out). However, projecting the tetrahedrons on a plane does not alter the ability to distinguish clockwise from counterclockwise sequences. This is the basis for the four-point correlation functions (4PCF) that is used in the parity-violation analysis.

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In a 6/8/2022 preprint, J. Hou, Z. Slepian, and R. N. Cahn of University of Florida and Lawrence Berkeley National Laboratory reported using 4PCF analysis on the data sets BOSS DR12 LOWZ (z=0.32, number of entries=280,067) and BOSS DR12 CMASS (z=0.57, number of entries=803,112), which tabulate the sky coordinates of luminous red galaxies from the Sloan Digital Sky Survey, where z is the redshift factor.

Using this database of over a million galaxies and taking each galaxy as the vertex of tetrahedrons formed with all the other galaxies of the data set would require analysis of nearly a trillion-trillion such tetrahedra. However, the researchers were able to use a mathematical trick involving spherical harmonic functions to shorten and simplify the calculation and to avoid such an enormous direct processing requirement.

They found that both data sets show significant 4PCF asymmetries, with the LOWZ set showing a parity violation of 3.1 standard deviations and the CMASS set showing a parity violation of 7.1 standard deviations. We note that the physics community normally considers a 5 standard deviation effect to be a valid observation of a new phenomenon.

The observation is partially corroborated by a 7/29/2022 preprint, in which O. H. E. Philcox of Princeton University reported an analysis of the same CMASS data set. However, he used a different analysis technique that showed a parity violation of only 2.9 standard deviations.

In a possibly related 7/29/2020 preprint, L. Shamir of Kansas State University performed an analysis of the apparent spin directions of spiral galaxies. Of course, a spiral galaxy can be recorded as spinning clockwise (CW) or counterclockwise (CCW), depending on the side along its spin axis from which it is viewed. However, analysis of large datasets of spiral galaxies that are imaged well enough to tell their spin direction has shown photometric differences between spiral galaxies with CW and CCW spin patterns.

Shamir analyzed about 6,400 galaxies from the Sloan Digital Sky Survey and found significant asymmetries between the numbers of CW and CCW galaxies, implying an overall parity violation of about 5.4 standard deviations that grows to more than 8 standard deviations for the galaxies with the largest redshifts (z > 0.15).

The overall conclusion from this body of work is that there is statistically significant evidence that in our universe parity symmetry is being violated at the largest scales. The question this result raises is: What could possibly cause this parity violation? There is no plausible known scenario that could connect the manifest parity violation of the weak interaction at the particle level with the locations or spins of galaxies. Therefore, we must look elsewhere.

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The current Standard Model of Cosmology includes a short-duration period of “inflation” at the start of the Big Bang. Inflation was first suggested by Alan Guth in 1980 to address problems with the then-developing Big Bang model of cosmology. It does not follow from the other mathematics of the Big Bang, and so it must be “put in by hand.” Guth was confronting three serious problems inherent in the naive Big Bang model: horizon, flatness, and monopoles.

The horizon problem arises from the fact that separate parts of the Universe go out of speed-of-light contact very early in the Bang and have no further contact, yet we find that they have the same temperature with only small variations, as evidenced by measurements of the cosmic microwave background radiation.

The flatness problem is related to the observation, made with ever-increasing accuracy, that the curvature parameter V (omega) of the Universe is precisely V=1. This means that the energy content of the Universe is just right to fit in the crack between positive curvature from excess mass leading to eventual re-collapse from the pull of gravity and negative curvature from excess kinetic energy of expansion.

The monopoles problem arises from the prediction by most particle-physics models that the extreme temperatures of the early Big Bang should have produced floods of massive exotic particles, including magnetic monopoles. While most of the other massive exotics would have long since decayed into more normal particles (electrons, protons, neutrinos, photons . . .), magnetic monopoles cannot do that. They have a single magnetic charge that is either an isolated “north” or “south” magnetic pole. Because of that magnetic charge, the monopoles are “stuck” in their configuration and cannot decay to lighter particles, since no magnetically charged lighter particles exist. Therefore, monopoles in significant numbers should still be present in today’s universe. However, all experimental searches for magnetic monopoles have been negative. Inflation stretches, smooths, and homogenizes the early universe, eliminating all three of these problems.

In Guth’s inflation scenario, the size of the Universe is supposed to grow exponentially by a factor of about 1026 under the brief influence of something called “the infalton field,” a force that vanished after doing its job and about which little is known. The inflation scenario, while solving Big Bang problems, has not yet been reinforced by any observations. It should have produced intense gravitational radiation, which should have led to distinctive patterns in the polarization of the cosmic microwave background. However, despite a false alarm in 2014 by the BICEP2 Collaboration (see Alternate View 174 in the October 2014 issue of Analog), no evidence of those polarization patterns has ever been found, and the inflation scenario remains unsubstantiated. The observation of the parity violation in the locations of galaxies could change that and could constitute evidence for a certain form of inflation.

In the past two decades, a few theorists have speculated on the possibility that the “inflaton field” responsible for inflation of the early Universe may also have been responsible for the manifest dominance of matter over antimatter in the present Universe. This would require the inflaton field to include some special forces that have built-in asymmetric treatment of right-handed antimatter vs. left-handed matter particles, leading to today’s matter-antimatter asymmetry. One form of this effect is called Chern-Simons gravity.

These speculations have lead to an interesting scenario: the quantum fluctuations present in the era of inflation should produce intense gravitational radiation, which, because of the action of Chern-Simons gravity, will favor one polarization state of the created gravitational waves over the other. Since gravitational waves carry angular momentum, Chern-Simons gravity will also favor the angular momentum vector pointing along rather than against the direction of the wave motion as a parity violation.

As the Universe cools and matter emerges, the gravitational wave polarization favors some matter distributions over their mirror images, spreads angular momentum asymmetrically, and thereby could produce a primordial asymmetry and spatial parity violation. As the first stars and galaxies form, this asymmetry would be reflected in the locations and spins of the galaxies formed.

The exact mechanisms by which the gravitational wave polarization preference becomes a spatial parity violation are still being investigated, but the scenario looks plausible and promising. The case that Chern-Simons gravity effects during the Big-Bang era of inflation lead to the matter-antimatter asymmetry as well as the galactic parity violations, if validated, would solve one of the deep mysteries of cosmology and at the same time would provide the needed experimental validation of the inflation scenario.

Things are looking up on the cosmological front. Watch this column for further developments.



Parity Violation in Galaxy Locations:

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: 2206.03625v1 [astro-ph.CO] 8 Jun 2022;

Oliver H. E. Philcox, “Probing Parity-Violation with the Four-Point Correlation Function of BOSS Galaxies,” arXiv:2206.04227v2 [astro-ph.CO] 29 Jul 2022.

Parity Violation in Galaxy Spin:

Lior Shamir, “Patterns of galaxy spin directions in SDSS and Pan-STARRS show parity violation and multipoles,” Astrophysics and Space Science 365, 136 (2020); arXiv:2007.16116v1 [astro-ph.CO] 29 Jul 2020.

Chern-Simons Gravity Theory

and CP Violations:

Stephon H.S Alexander, Michael E. Peskin, and M. M. Sheikh-Jabbari, “Leptogenesis from Gravity Waves in Models of Inflation,” Phys. Rev. Letters 96, 081301 (2006); arXiv:hep-th/0403069v4;

Arthur Lue, Limin Wang, and Marc Kamionkowski, “Cosmological Signature of New Parity-Violating Interactions,” Phys. Rev. Letters 83, 1506 (1999); arXiv:astro-ph/9812088v2.



John G. Cramer’s 2016 nonfiction book describing his transactional interpretation of quantum mechanics, The Quantum Handshake—Entanglement, Nonlocality, and Transactions, (Springer, January 2016) is available online as a hardcover or eBook at: or Editions of John’s hard SF novels Twistor and Einstein’s Bridge are available online at: and Electronic reprints of 207 or more “The Alternate View” columns written by John G. Cramer and previously published in Analog are currently available online at:

Copyright © 2023 John G. Cramer

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