Abstract
We consider the effects of entanglement in the initial quantum state of scalar and tensor fluctuations during inflation. We allow the gauge-invariant scalar and tensor fluctuations to be entangled in the initial state and compute modifications to the various cosmological power spectra. We compute the angular power spectra (Cl's) for some specific cases of our entangled state and discuss what signals one might expect to find in CMB data. This entanglement also can break rotational invariance, allowing for the possibility that some of the large scale anomalies in the CMB power spectrum might be explained by this mechanism.
Highlights
The use of excited states based on the BD state
The non-trivial transformations of the tensor perturbations under the rotation group allow for the breaking of rotational invariance; such breaking is constrained by current data, but might still be large enough to explain some of the large scale anomalies [25] found in the CMB temperature anisotropy maps
To give a clearer picture of how much these compute the angular power spectra (Cl’s) differ from those of the ΛCDM model, we plot the difference of the zero-entanglement best fit Cl and our model’s Cl, with non-zero entanglement, on top of the binned residual data given by Planck (figs.(1b, 2b, 3b)
Summary
In order to describe the entanglement between the scalar perturbation ζ and the tensor perturbations γij, we use Schrodinger picture field theory [28,29,30] in this subsection (though for another viewpoint on the states constructed in ref.[23] see ref.[31]) This entails constructing the Hamiltonian for the ζ-γij system as well as giving the wave-functional Ψ[ζ, γij] which will solve the Schrodinger equation coming from the Hamiltonian. In the absence of any interactions in the Hamiltonian it is consistent to factorize the wavefunctional into a product of wave-functions for each momentum mode: ψk [ζk Such that kernel Ck(σ)(τ ) = 0 sets the entanglement between tensor and scalar modes. Using eq(2.19) we can rewrite these equations in terms of the variables:
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