I think the most challenging thing to understand is not the specifically LQC work here but instead the
non-LQC work of Fabian Schmidt which in effect provides the avenue for
pre-inflation effects to have a observable imprint on the (post-inflation) CMB power spectrum.
As they say at the beginning, this non-LQC work is what Ashtekar and Barrau are using. I have highlighted the reference:
==quote Ashtekar Barrau
http://arxiv.org/pdf/1504.07559.pdf ==
Thanks to systematic investigations over the past decade, loop quantum cosmology (LQC) is now sufficiently developed to address these issues. As is common in physics, a more fundamental analysis introduces a new scale at which novel phenomena can occur. In LQC, as we discuss in section 2, because of the underlying quantum geometry, the big bang singularity is resolved and replaced by a quantum bounce. The curvature at the bounce is universal and introduces a
new length scale lLQC. The key new phenomenon is the following: Pre-inflationary LQC dynamics modifies the standard inflationary predictions in a universal way for modes whose wave length at the bounce is larger than l
LQC.
Detailed analysis shows that these correspond either to the longest wave length modes observable today and/or modes whose wave length is larger than the radius of the observable universe but which can couple to the observable modes [2]. Therefore the pre-inflationary dynamics of LQC can have interesting ramifications for the ∼ 3σ anomalies in the Planck data associated with the largest angular scales.
At first reading, this assertion may seem counter-intuitive on two accounts. First, one generally expects quantum gravity effects to modify only the short-distance behavior. How could they have any implications to predictions for the longest wave length modes? Second, it is often claimed that while quantum gravity effects may be conceptually interesting, they will not be relevant for cosmological observations because all they will all be diluted away during inflation. We will now discuss why these expectations are not borne out.
The belief that the pre-inflationary dynamics does not matter stems from the following argument (left panel of FIG. 1). If one evolves the modes that are seen in the CMB back in time using GR, their physical wave lengths λ
phy continue to remain smaller than the curvature radius R
curv all the way to the big bang. The equations governing the evolution of these modes then imply that they propagate as though they were in flat space-time and cannot get excited in the pre-inflationary stage. Therefore, the argument goes, they will be in the Bunch-Davies (BD) vacuum at the onset of inflation.
But in the pre-inflationary calculations, dynamical equations of GR cannot be trusted in the Planck regime; we must use instead a candidate quantum gravity theory. In LQC, if a mode has λ
phy > l
LQC at the bounce, it does experience curvature during pre-inflationary dynamics and can get excited (right panel of FIG. 1). For suitable choices of initial conditions at the bounce, these modes correspond to the largest angular scales seen in the CMB, roughly to l ≤ 30 in the spherical harmonics decomposition of correlation functions.
Thus, the ultraviolet modifications of the background dynamics that cure the big bang singularity can directly influence the infrared behavior of perturbations. These longest wave-length modes, then, will not be in the BD vacuum at the onset of inflation [3, 4]. But why will this fact alter the observable predictions of inflation? Will not these excitations just get washed away during inflation? The answer is in the negative because of the accompanying stimulated emission. Agullo, Navarro-Salas and Parker have shown that if one were to start with a candidate non-BD vacuum at the onset of inflation, the stimulated particle creation would result in certain departures from the standard predictions based on the BD vacuum [5]. The pre-inflationary dynamics of LQC provides specific non-BD initial states at the onset of inflation, thereby streamlining the possibilities, leading to an interplay between the Planck scale physics and observations.
