## A Test of the Cosmological Principle using Quasars

I’m not getting much time these days to even think about cosmology but Subir Sarkar drew my attention to an intriguing paper by his team so I thought I’d share it here. Here is the abstract and author list:

I find this an intriguing result because I’ve often wondered about the dipole anisotropy of the cosmic microwave background might not be exclusively kinematic in origin and whether they might also be a primordial contribution. The dipole (180°) variation corresponds to a ΔT/T of order 10^{-3}, which a hundred times larger than the variation on any other angular scale. This is what it looks like:

This is usually interpreted as being due to the motion of the observer through a frame in which the cosmic microwave background is completely isotropic. A simple calculation then gives the speed of this motion using ΔT/T ≈ v/c. This motion is assumed to be generated by gravitational interaction with local density fluctuations rather than being due to anything truly cosmological (i.e. of primordial origin).

The features in the cosmic microwave background temperature pattern on smaller angular scales (the quadrupole, octopole, etc…) , which have ΔT/T of order 10^{-5} are different in that they are dominated by primordial density fluctuations. There should be a primordial dipole at some level, but the fact that these other harmonic modes have such low amplitudes and the assumption that the primordial dipole should be of the same order, combined with the fact that the CMB dipole does indeed roughly line up with the dipole expected to be generated by local inhomogeneities, has led to the widespread belief that this intrinsic dipole is negligible. This analysis suggests that it might not be.

What the authors have done is study the anisotropy of a large sample of quasars (going out to redshifts of order three) finding the dipole to be larger than that of the CMB. Note however that the sample does not cover the whole sky because of a mask to remove regions wherein AGN are hard to observe:

As well as the mask there are other possible systematics that might be at play, which I am sure will be interrogated when the paper is peer-reviewed which, as far as I know, is not yet the case.

P.S. I might just quibble a little bit about the last sentence of the abstract. We know that the Universe violates the cosmological principle even in the standard model: with scale-invariant perturbations there is no scale at which the Universe is completely homogeneous. The question is really how much and in what way it is violated. We seem to be happy with 10^{-5} but not with 10^{-3}…

Update: On 23rd October Subir will be giving a talk about this an participating in a debate. For more details, see here.

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October 8, 2020 at 3:17 pm

“I’ve often wondered about the dipole anisotropy of the cosmic microwave background might not be exclusively kinematic in origin and whether they might also be a primordial contribution”I’m not a CMB guy, but my understanding is that it would be very strange if there were not a primordial contribution, but it would be expected to be of the same order of mangitude as the other multipoles and hence swamped by the kinematic dipole.

One idea which I had but gave up on trying to figure out in detail due to lack of knowledge and the shortness of life: could the low quadrupole be an artefact of the removal of the dipole, especially if there are unexpected correlations as the axis of evil demonstrates for higher multipoles?

If anyone publishes a paper based on this idea, at least mention me in the acknowledgements. 🙂

October 8, 2020 at 3:21 pm

I actually talked a lot about that specific idea with Pavel Naselsky last time I was in Copenhagen. Perhaps I should dust off the notes…

October 8, 2020 at 4:01 pm

A few years ago, I discussed it via email with some CMB folks, but none of them thought that it had anything to it.

October 9, 2020 at 7:23 am

Peter:From the point of view of general relativity, a nonkinematic dipole is readily obtainable from foreground inhomogeneity on scales of tens of Mpc. There’s no need for something exotic on the surface of last scattering.Although the only evidence for a notion of statistical homogeneity occurs on scales > 100/h Mpc, the FLRW assumption is usually applied below this scale. That is implicit in treating the dipole only with special relativity. In GR differential expansion on scales < 100/h Mpc will not always be reducible to FLRW plus a boost. See arXiv:1512.07364 [JCAP 06 (2016) 035].

A purely kinematic dipole relative to an isotropic CMB has a specific expansion in powers of

v/c. Whatever the nature of the dipole, if it is assumed to be purely kinematic but is not in reality then there will be deviations from thev/cexpansion in the higher CMB multipoles giving rise to large angle anisotropies which would be deemed anomalous – particularly the quadrupole. We gave an expression for the nonkinematic terms in eq (2.3), (2.4) of arXiv:1512.07364. Furthermore, we presented specific realistic examples using LTB and Szekeres toy models for foreground structures in an asymptotically FLRW universe (on > 100/h Mpc scales).While the Planck team published a paper arXiv:1303.5087 [A&A 571 (2014) A27] claiming to verify the kinematic nature of the transformation to the CMB frame (through special relativistic aberration and modulation) the conclusion works only for small angles only. If one looks at large angles then the putative boost direction moves across the sky to point in the direction of the “modulation dipole anomaly”. While this in itself is not a proof of our hypothesis, it is consistent with it.

I have looked into the question of whether we could test alternative models directly on CMB data, and had discussions with Francois Bouchet (a Planck PI) a few years ago. Unfortunately the empirical modeling of the galaxy foreground appears to intimately tied in with the dipole subtraction which makes this highly nontrivial.

We were led to study these issues firstly on account of the observation that the spherically averaged Hubble expansion on > 5): arXiv:1201.5371 [Phys Rev D 88 (2013) 083529]. If one does arbitrary boosts to try to find a frame in which the expansion is most uniform then given a lack of peculiar velocity data in the Zone of Avoidance, one cannot distinguish the local group frame from frames related by a boost in the plane of the galaxy. All such frames could be the “most uniform frame”: arXiv:1503.04192 [MNRAS 457 (2016) 3285; 463 (2016) 3113].

Kraljic and Sarkar (arXiv:1607.07377 [JCAP 10 (2016) 016]) subsequently showed that our results on the spherically averaged Hubble expansion could also be reproduced with FLRW + Newtonian N-body with a sufficiently large bulk flow. One then gets into the problem of how unusual are such large bulk flows, and different observations not agreeing. The latest result with quasars is a very strong signal that something is amiss in the standard approach.

Thus we consider it promising to continue with a hypothesis which is consistent with known physics, and our best theory of gravity, even if it is not popular.

October 10, 2020 at 11:38 am

The size of this “excess dipole” is very small, ~ 10^-3, so I would be highly suspicious about possible thermal effects in the WISE spacecraft which are not mentioned in the paper.

I can think of three: firstly there’s the obvious ~ 7 percent January-June difference in solar heating.

Secondly, WISE uses a “sun-synchronous” polar orbit which is inclined ~ 98 deg from the equator and precesses once per year so the orbit pole points near the Sun. The telescope looks “up” away from the earth scanning great circles. There is a possible “6am/6pm” effect, i.e. going down Arctic to Antarctic is at 6am local time , going up is 6pm local time (or vice versa), so the Earth is order 10K warmer on the 6pm side and there’s 15 percent more Earth heating.

Third: the radio transmitter probably turns on at specific locations w.r.t. Earth over the ground-station, creating heat.

All these partially average out over the scan-pattern, but they may not cancel precisely.

While it would take a lot of modelling to work this out in any detail, in principle any of these could leak into a tiny residual of the size observed.

October 10, 2020 at 7:11 pm

Hi Will,

Thanks for your interest in our paper.

Taking all the sources in a 10 degree radius around the found dipole and anti-dipole, the mean value of the mean observation MJD (i.e. the mean of the MJD values for all individual observations that went into each catalog source) is 57,230 for the pole and 57,229 for the anti-pole, each with a standard error (stdv/sqrtN) of 1 day. So the data at the pole (where we see the strongest excess) and the anti-pole (where we see the strongest decrement) are *consistent* with having the same mean observation epoch, 2015 July 27. The corresponding temperature of the instrument was about 74.5 K:

So, it is unlikely that the found dipole is induced by a temperature difference. Hope that assuages your concern.

Nathan Secrest – on behalf of the authors

PS: Subir comments: Will, since you emphasise our “very small” ~10^-3 signal, are you not also concerned about satellite measurements of the *much smaller* fluctuations in the CMB? Planck was of course at L2 rather than on a Sun-synchronous polar orbit like WISE – but the HFI sub-K bolometric detectors suffered serious damage by cosmic rays (arXiv:1403.6592, arXiv:1404.1305). There was indeed “a lot of modelling” done to “to work this out in detail” (arXiv:1303.5071). Our signal may not be precision cosmology but we believe it is accurate cosmology!

November 5, 2020 at 1:12 pm

[…] may recall that I recently posted about a paper by Subir Sarkar and collaborators. Here is the abstract and author […]