We calculate the scalar power spectrum generated by sourced fluctuations due to coupling between the scalar field, which holds most of the energy density of the universe, and a gauge field for a general FLRW metric. For this purpose we calculate the curvature perturbation to second order in the presence of gauge fields, and show that the gauge fields behave like an additional potential term. We then apply the analysis to the case of slow-contraction. Due to the interaction between the scalar field and gauge fields additional 'sourced' tensor and scalar spectra are generated. The resulting spectra are chiral, slightly blue and arbitrarily close to scale invariance. The only difference between the tensor and scalar spectra is the coupling constant with an O(1) numerical coefficient, and some momentum space polarization vectors. As a result the tilt of the spectra are the same. For the nearly scale invariant case, the momentum integration gives the same leading contribution. Hence, r 1 where the deviation from unity is controlled by the deviation from scale invariance, and is not in agreement with CMB observations. Deviating considerably from near scale invariance, and considering a bluer tilt with n T > 0.12, the model cannot account for CMB observations, but can be detected by LIGO and/or LISA in the future.

Black hole entropy has been shown by 't Hooft to diverge at the horizon. The region near the horizon is in a thermal state, so entropy is linear to energy which consequently also diverges. We find a similar divergence for the energy of the reduced density matrix of relativistic and non-relativistic field theories, extending previous results in quantum mechanics. This divergence is due to an infinitely sharp division between the observable and unobservable regions of space, and it stems from the position/momentum uncertainty relation in the same way that the momentum fluctuations of a precisely localized quantum particle diverge. We show that when the boundary between the observable and unobservable regions is smoothed the divergence is tamed. We argue that the divergence of black hole entropy can also be interpreted as a consequence of position/momentum uncertainty, and that 't Hooft's brick wall tames the divergence in the same way, by smoothing the boundary.Comment: Added clarifications and explanation

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Scattering phenomena affect light propagation through any kind of medium from free space to biological tissues. Finding appropriate strategies to increase the robustness to scattering is the common requirement in developing both communication protocols and imaging systems. Recently, structured light has attracted attention due to its seeming scattering resistance in terms of transmissivity and spatial behavior. Moreover, correlation between optical polarization and orbital angular momentum (OAM), which characterizes the so-called vector vortex beams (VVBs) states, seems to allow for the preservation of the polarization pattern. We extend the analysis by investigating both the spatial features and the polarization structure of vectorial optical vortexes propagating in scattering media with different concentrations. Among the observed features, we find a sudden swift decrease in contrast ratio for Gaussian, OAM, and VVB modes for concentrations of the adopted scattering media exceeding 0.09%. Our analysis provides a more general and complete study on the propagation of structured light in dispersive and scattering media.

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