_{s}, they can improve limits on the tensor amplitude ratio r. They claim ultimately 0.5% constraints on r may be possible, which is much lower than previously thought.

If all they are getting from the LSS observation is a measurement of A

_{s}, I don't see how they can possibly get such a good limit on r from CMB scales 10 < l < 40. If you assume perfect knowledge of all the cosmological parameters (except r), the cosmic variance limit is around 0.05 - see e.g.

http://cosmologist.info/notes/tensors.ps

- so how can you do better with a much worse than perfect measurement of A

_{s}?

Maybe I misunderstood, but there does seem to be a clear statement in the paper about how they actually made Fig. 1 or what is happening with cosmic variance. The only way out I can think of to get better constraints than expected is if the value of A

_{s}you get is larger than you would expect from the measured CMB power. In this case I could imagine r would get squeezed to be as small as possible, but only at the expense of the r=0 model still not fitting very well.

Other comments:

* r is defined implicitly, presumably as some C

_{l}ratio at large scales (otherwise the CMB observation would not measure A

_{s}(1+r). Note that some people (e.g. me) usually quote values for primordial amplitude ratios A

_{t}/ A

_{s}which are different.

* The amplitude enters 3 times in equations 5,6, via A

_{s}, Δ

_{R}

^{2}and Φ. Presumably they only want it once, which requires odd definitions of Δ

_{R}

^{2}and Φ where the amplitude is scaled out.

* On page 2 they state that the tensor perturbations are generated at recombination or before. I don't think this is correct: the effect of tensors is to induce anisotropies because you are looking at the smooth recombination surface through distorting gravitational waves entering the horizon along the line of sight. The contributions from recombination are small on large scales (comparable to the polarization signal, which does only come from recombination and reionization).