Why can primordial tensor perturbations of the CMB be ascribed to gravitational waves? Is this attribution unique, or are there other mechanisms that could lead to the excitation of tensor modes?

In an explanation I have read recently that gravitational waves turn the E-modes into the now observed B-modes somehow, but I don't understand this. So can somebody give a more detailed explanation of this interaction of gravitational waves with the CMB?

LaTeX and equations are welcome and appreciated :-)

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    $\begingroup$ You should first of all quote the papers you are referring to. $\endgroup$
    – Py-ser
    Mar 18, 2014 at 5:34
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    $\begingroup$ @Py-ser it was mentioned somewhere in a physics blog and I am looking for papers or direct explanations (in an answer) that explain it further. $\endgroup$
    – Dilaton
    Mar 18, 2014 at 6:33
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    $\begingroup$ Then you should refer to that forum, or article, or whatever gives a context :) For the moment take a look at this preposterousuniverse.com/blog/2014/03/16/… $\endgroup$
    – Py-ser
    Mar 18, 2014 at 7:02
  • $\begingroup$ I found astrobites.org/2018/10/30/… an interesting read, although there is nothing about E-modes there. $\endgroup$
    – B--rian
    May 11, 2021 at 14:40
  • $\begingroup$ I also found arxiv.org/abs/2007.04241 and arxiv.org/abs/2007.04241 - is that going into the right direction? $\endgroup$
    – B--rian
    May 12, 2021 at 10:31

1 Answer 1


Gravitational waves themselves are modeled as tensor perturbations of the metric. Einstein first derived gravitational waves from a linearly perturbed Minkowski metric. Ringdown analysis of compact binary black hole mergers is done in the context of the perturbed Kerr metric (see section 5 of this). Therefore, mathematically, tensor perturbations are gravitational waves.

So, if you have tensor perturbations of a metric used to model cosmology, you then have a type of gravitational waves that are cosmologically relevant. An example are "primordial" gravitational waves that could appear in the cosmic microwave background (CMB) due time-varying quadrupole moments (and higher order currents) of the early Universe matter-energy distribution. There are also scalar density perturbations that are possible.

Inflationary models of early Universe cosmology offer an explanation for primordial gravitational waves, and if detected as a gravitational wave background would provide observational support for inflation.

The claim that B-modes were observed in the BICEP2 experiment were not confirmed confidently, and later the Planck experiment showed that the BICEP2 results can be explained by cosmic dust. Therefore, it is generally accepted that B-mode oscillations in the CMB have not been observed. For an explanation of what B-modes and E-modes are, please see here.

Joint detections using space based gravitational wave interferometers, pulsar timing arrays, and CMB probes in the future may provide measurements of the primordial gravitational wave background.


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