cristo said:
... do you have an idea how much that prediction has changed since 2011? Has this k* parameter been constrained by other observations to make a meaningful prediction of B mode spectrum, or is it the case that the spectrum can be fit by choosing a value of this parameter?
It's a good question! I don't know. I'll take a look at the recent invited review paper by those same authors. With luck they will mention that k parameter and give us some larger context.
http://inspirehep.net/record/1255638?ln=en
Observational issues in loop quantum cosmology
A. Barrau (LPSC, Grenoble & IHES, Bures-sur-Yvette) , T. Cailleteau (Penn State U., University Park, IGC) , J. Grain (Orsay, IAS & Orsay) , J. Mielczarek (Jagiellonian U. & Warsaw, Inst. Nucl. Studies)
Abstract: Quantum gravity is sometimes considered as a kind of metaphysical speculation. In this review, we show that, although still extremely difficult to reach, observational signatures can in fact be expected. The early universe is an invaluable laboratory to probe "Planck scale physics". Focusing on Loop Quantum Gravity as one of the best candidate for a non-perturbative and background-independant quantization of gravity, we detail some expected features.
75 pages, invited topical review for
Classical and Quantum Gravity
The relevant passages start around page 56 (and the 2010 paper does NOT seem to have been outmoded! It is reference [76] and they often cite that reference "for details".) My concern to get an up-to-date source does not, in this case, seem to matter. Sometimes it makes a difference but maybe in this instance it doesn't.
I'll quote some, starting on page 56.
==review paper Feb. 2014 Classical and Quantum Gravity==
The primordial component of the B-mode angular power spectrum is determined by the five following parameters: k
*, R, n
T, T/S and the reionization optical-depth τ. This set of parameters will be denoted θ
i hereafter. There values are not fixed as this is precisely those parameters that can be constrained by a potential observation of the B-modes. The other cosmological parameters will be fixed to the WMAP 7-yr best fit, and the lensing-induced B-modes will be fixed to the standard prediction. The case of τ should be briefly discussed. Its value is already constrained by measurements of the TT, TE and EE angular power spectra. However, this parameter is potentially degenerated with the other cosmological parameters, k
*, R, n
T, T/S. It is therefore worth letting this parameter free from the perspective of exploring its degeneracies with e.g. k
* and R and evaluate how such degeneracies could affect the estimation of k
* and R from CMB measurements.
When compared to standard cosmology, the set of cosmological parameters is therefore enlarged by adding two phenomenological parameters, k
* and R, parametrizing the LQC-induced distortions of the primordial power spectrum. The parameters k
*, R, n
T, T/S encode all the physics taking place in the primordial universe. They allow for a phenomenological description of the primordial power spectrum. The constraints that one can set on those four parameters can finally be translated into constraints on fundamental parameters of the model using:
[Here are given 4 equations (176) thru (179) determining those 4 quantities in terms of model parameters]
==endquote==
The following paragraphs look interesting. I'll look the over some more and post again later today.