1 Introduction Loop Quantum Cosmology (LQC) has established a robust framework for resolving the Big Bang singularity through a quantum bounce 3, 4. The Agullo–Ashtekar–Nelson (AAN) dressed metric framework 5, 6 extends perturbation theory through the bounce, producingpredictions for the primordial power spectrum that can be confronted with CMB observations. A structural feature shared by all LQC perturbation frameworks is the assumption thatthe pre-bounce background state is purely isotropic FLRW. This factorization is not anapproximation — the intertwiner degrees of freedom encoding the shape of the quantumgeometry at each spin-network vertex are eliminated before quantization by exact impositionof isotropy 9. In the full LQG theory the pre-bounce quantum geometry is described by a spin-networkstate |Γ,je,ιv⟩ carrying both edge spins and vertex intertwiners. At a four-valent vertexwith all edge spins j = 1 2, the intertwiner Hilbert space Hint(12, 12, 12, 12) is two-dimensional,spanned by the singlet |k=0⟩ (isotropic tetrahedron shape) and the triplet-recoupled state|k=1⟩ (anisotropic shape excitation). Standard LQC retains only |k=0⟩. The weight |β|2 ofthe excited state |k=1⟩ is a genuine quantum gravity initial condition, not derivable fromLQC. We emphasize the precise sense in which this is true. The full kinematic LQG Hilbertspace admits superselection sectors and the intertwiner label is in general gauge-dependent;in standard LQC this sector is eliminated before quantization by exact SU(2) symmetryreduction, so |β|2 does not survive as an independent degree of freedom in the reducedtheory. In the present paper |β|2 is therefore proposed as an effective parameter motivatedby the LQG quantum tetrahedron geometry 11: it encodes the pre-bounce shape excitationthat would be present in the full theory but is projected out by the LQC symmetry reduction.The coupling of |β|2 to the macroscopic Bianchi I shear is derived from first principles inSection 4.3 via a four-step coarse-graining argument; the form factor ˜f =2 is an algebraic consequence of the SU(2) Casimir eigenvalue, not an assumption.We argue this discarded degree of freedom is physically active. For a general pre-bounceintertwiner state |ι⟩ = α|k=0⟩+β|k=1⟩, we derive (Section 4.3) that Σ2 = ˜f|β|2 with ˜f= 2exact from first principles, via the coarse-graining map established in Section 4. This couplingenters the Bianchi I effective Hamiltonian and generates a shear energy density ρshear ∝|β|2 cos2(¯µc). The bounce profile F(η) = F0 sech2(η/ηB)tanh2(η/ηB) is proven exact on thekinetic-dominated trajectory (Section 5.2), not assumed. This correction propagates throughthe LQCbounce, modifies the dressed metric, and leaves a specific band-pass signature in theprimordial power spectrum. The signal peaks at the bounce scale k∗ = 1/ηB and is observablein the CMB for inflationary models on a specific constraint curve in the (Ninf, V 1/4inf ) plane.
Hillard et al. (Thu,) studied this question.