I have read a handful of old articles from mid 2013 expressing that the Universe may, in fact, be curved.


My question is how is the apparent "lopsidedness" of the CMB Radiation explained in a flat universe model?

I understand that the vast majority of the evidence indicates a spatially flat universe, but I would like to know if there is any merit to these claims:
enter image description here
The temperature of the cosmic microwave background radiation fluctuates more on one side of the sky (the right side of this projection) than on the opposite side, a sign that space might be curved.

  • $\begingroup$ The Liddle paper referred to in the first link is here: arxiv.org/abs/1306.5698 . The second link doesn't seem to me to be relevant to the question. the vast majority of the evidence indicates a flat (Minkowski) universe No, the evidence points toward spatial flatness, but there is no viable cosmological model in which the universe is modeled as Minkowski space, which is a completely flat spacetime, not just a spatially flat one. $\endgroup$
    – user4552
    Oct 27, 2014 at 20:02
  • $\begingroup$ Ironically, I had originally put Euclidean instead of Minkowski as I was, indeed, referring to only spacial dimensions. @Danu was the one that changed it to Minkowski. $\endgroup$
    – Goodies
    Oct 27, 2014 at 20:44
  • 1
    $\begingroup$ !! My mistake! Sorry! @BenCrowell and OP. I have corrected my error. Don't know how that happened ;) $\endgroup$
    – Danu
    Oct 27, 2014 at 20:49
  • $\begingroup$ So @BenCrowell, that paper describes the Universe as Open, not Flat? I was curious as to if there are spatially flat models that do describe these anomalies. $\endgroup$
    – Goodies
    Oct 27, 2014 at 20:59

1 Answer 1


From here:

Before proceeding, it should be mentioned that the statistical significance of the result is still under debate. While the asymmetry is significant at the ≳3σ level, some question whether it is simply a consequence of the “look-elsewhere” effect: i.e., we test for all kinds of anomalies in the CMB, and the investigated parameter space is so vast that it’s no surprise that, by chance, one of the parameters shows a positive result. Cosmological models make statistical predictions about the distribution of temperature fluctuations on an ensemble of CMB skies, but we have only one CMB sky to observe. Therefore, if the observed asymmetry is a statistical fluke, we are stuck with it because there is no way to increase the statistics on this particular measurement. But if the asymmetry is real and not just a statistical fluke, then it is extremely important. It may well be a remnant of the preinflationary Universe!

The dipole anisotropy in the power spectrum seems real (not the doppler dipole, but rather the one discussed in these articles). Alright, that's out of the way. This observation needs to be interpreted to get any further, though.

One possibility is that this is just a $3\sigma$ excursion from the expected isotropy. Without a statistical sample of additional Universes to observe, we have no way of knowing for sure. And as the article points out, if you look at enough parameters, eventually you'd actually be surprised if you didn't find one off by a couple of $\sigma$.

Another interpretation is that the Universe is a little bit curved (in the "Open" direction, i.e. negatively). This depends on the model some theorists are proposing being at least broadly correct. However, for the moment, this class of models offers no other presently testable predictions. I'm sure the theorists are working on more predictions that are testable, and CMB observers are working on measuring the predictions that have been made (the signal is supposed to be very faint, and the measurement is very difficult). But for the moment no other tested predictions means that this is just another class of theories, and there is no compelling reason to prefer it over the usual flat Universe model. In fact, I would prefer the flat model as it has less parameters and also explains the observations (even though I have to live with a $3\sigma$ statistical anomaly).

The same article also mentions that the anomaly is seen in the two hemispheres roughly separated by the ecliptic, which is somewhat worrying. Alignment with the ecliptic, or galactic equator, or other preferred direction, to me is suggestive of some uncorrected systematic effect. Not to say that this can't be a real anomaly because it's aligned with the ecliptic, but it's worrying...

So to sum up, there doesn't seem to be any compelling evidence for an open Universe. There is this anomaly in the isotropy of the power spectrum, but it's not so large that it couldn't just be happenstance. If the proposed curvaton model makes some additional predictions (differing from the predictions of the usual cosmology) that are later borne out by observation, that would be more strongly suggestive of an Open geometry.


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