CMB or nucleosynthesis as empirical tests of gravitation by radiation?

[bcrowell]

General relativity predicts that electromagnetic fields contribute to the stress-energy tensor, and that they therefore have gravitational fields. Kreuzer (1968) did laboratory experiments that were interpreted by Will (1976) as confirmation of this prediction in the case of the static electric fields of nuclei. The precision of the test was later improved by orders of magnitude by Bartlett and Van Buren (1986) based on lunar laser ranging.

But these are all tests of static electric fields in nuclei. Is there any direct empirical test of GR's prediction in the case of electromagnetic radiation? A test of the static case does not trivially imply a test of the radiation case, since the distinction between radiation and non-radiation fields is generally covariant.

The early universe was radiation-dominated. Do CMB observations allow us to probe early enough times so that if GR was wrong about this, discrepancies would have shown up? Radiation-dominated cosmologies are one of the standard closed-form solutions of the FRW equations, but I'm not clear on whether any of the features of these models can actually be tested empirically. The CMB comes from the surface of last scattering, which was at about 400,000 yr. The switch-over from radiation-dominated to matter-dominated happened at about 2,000 yr. Based on those figures, which differ by a factor of about 100, I'd kind of crudely expect that gravitation by radiation would perturb observable features of the CMB by no more than 1% or something...?

How about nucleosynthesis, which probes times as early as 100 s? Is our knowledge of nucleosynthesis too crude to test this prediction of GR?

-Ben

Kreuzer, Phys. Rev. 169 (1968) 1007. I've written a description here: http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html
Will, “Active mass in relativistic gravity: Theoretical interpretation of the Kreuzer experiment,” Ap. J. 204 (1976) 234, available online at adsabs.harvard.edu. A broader review of experimental tests of general relativity is given in Will, “The Confrontation between General Relativity and Experiment,” relativity.livingreviews.org/Articles/lrr-2006-3/.
Bartlett and Van Buren, Phys. Rev. Lett. 57 (1986) 21. The result is summarized in section 3.7.3 of the review by Will.

 

[Chalnoth]

I'm pretty sure big bang nucleosynthesis is currently our best check of the relationship between gravity and radiation. The CMB might also place some constraints on this, but since it was emitted much later, long after normal matter became the dominant form of energy density, it's probably not that much of a constraint.

 

[Ich]

There's an "expansion rate parameter" S=H'/H, where H is the standard model Hubble parameteer, and H' is the parameter you run the calculations with. Unless I'm completely mistaken, that would mean S=1.33 if expansion were matter-dominated back then.
There seem to be constraints on S under certain assumptions that exclude this scenario. See http://arxiv.org/ftp/arxiv/papers/0712/0712.1100.pdf" , p. 472ff and p. 488.

 

[bcrowell]

There's an "expansion rate parameter" S=H'/H, where H is the standard model Hubble parameteer, and H' is the parameter you run the calculations with. Unless I'm completely mistaken, that would mean S=1.33 if expansion were matter-dominated back then.
There seem to be constraints on S under certain assumptions that exclude this scenario. See http://arxiv.org/ftp/arxiv/papers/0712/0712.1100.pdf" , p. 472ff and p. 488.

Thanks, Ich! That's exactly what I was looking for!

-Ben

 

[BillSaltLake]

There is still a problem-- the only "independent" measurement of total mass+energy density at a known time is at the CMB last scattering surface, t = 379,000yr. The BBN data give us a photon:baryon ratio of 4.2-4.7 x10^-10 (see http://arxiv.org/PS_cache/arxiv/pdf/0808/0808.2818v1.pdf and read this from the overlap graphs). I would think that the ⁷Li data have a systematic error, but if right, then the total density at t = 379,000yr was only ~80% of the critical density. LCDM requires a ratio of 6.2x10^-10.

 

[Chalnoth]

There is still a problem-- the only "independent" measurement of total mass+energy density at a known time is at the CMB last scattering surface, t = 379,000yr. The BBN data give us a photon:baryon ratio of 4.2-4.7 x10^-10 (see http://arxiv.org/PS_cache/arxiv/pdf/0808/0808.2818v1.pdf and read this from the overlap graphs). I would think that the ⁷Li data have a systematic error, but if right, then the total density at t = 379,000yr was only ~80% of the critical density. LCDM requires a ratio of 6.2x10^-10.

Well, I'm pretty sure that the abundances of the other light elements, which do accord with the prediction, are good enough for the determination that radiation gravitates as expected.

But obviously it is an open question at this point whether or not there are other exotic physics going on in the early universe. It would be really exciting if this observational discrepancy was real and not just a function of our lack of understanding of these particular stars. But I'm not holding my breath.

If it so happens that there is some other observational discrepancy in a completely and utterly unrelated area (such as results at the LHC), and a new model explains both the Lithium abundance and these other results, then we might have something interesting. Until then, the default assumption remains the most viable: it's an observational error.