Chaotic inflation limits for non-minimal models with a Starobinsky attractor

We investigate inflationary attractor points by analyzing non-minimally coupled single field inflation models in two opposite limits; the `flat' limit in which the first derivative of the conformal factor is small and the `steep' limit, in which the first derivative of the conformal factor is large. We consider a subset of models that yield Starobinsky inflation in the steep conformal factor, strong coupling, limit and demonstrate that they result in chaotic inflation in the opposite flat, weak coupling, limit. The suppression of higher order powers of the inflaton field in the potential is shown to be related to the flatness condition on the conformal factor. We stress that the chaotic attractor behaviour in the weak coupling limit is of a different, less universal, character than the Starobinsky attractor. Agreement with the COBE normalisation cannot be obtained in both attractor limits at the same time and in the chaotic attractor limit the scale of inflation depends on the details of the conformal factor, contrary to the strong coupling Starobinsky attractor.Comment: v2: 4 figures added, refs added, minor textual change

Properties of Causal Holographic Information

Causal holographic information [1] is a variant of the Ryu-Takayanagi proposal for the entanglement entropy of a spatial region in the context of AdS/CFT, but with the bulk surface defined by causality rather than extremality. We investigate the properties of causal holographic information, focusing in particular on the universal coefficient of the logarithmically divergent term. We find that this coefficient contains a novel conformal invariant that cannot be written as an integral of local quantities. By considering higher curvature corrections in the bulk, we identify the coefficient of the a and c central charges in 4 dimensions. Finally, we speculate about which CFT quantity could correspond to the causal holographic information

Vacua and correlators in hyperbolic de Sitter space

We study the power - and bi -spectrum of vacuum fluctuations in a hyperbolic section of de Sitter space, comparing two states of physical interest: the Bunch-Davies and hyperbolic vacuum. We introduce a one -parameter family of de Sitter hyperbolic sections and their natural vacua, and identify a limit in which it reduces to the planar section and the corresponding Bunch -Davies vacuum state. Selecting the Bunch -Davies vacuum for a massless scalar field implies a mixed reduced density matrix in a hyperbolic section of de Sitter space. We stress that in the Bunch -Davies state the hyperbolic de Sitter $n$-point correlation functions have to match the planar de Sitter $n$-point correlation functions. The expressions for the planar and hyperbolic Bunch -Davies correlation functions only appear different because of the transformation from planar to hyperbolic coordinates. Initial state induced deviations from the standard inflationary predictions are instead obtained by considering the pure hyperbolic vacuum, as we verify explicitly by computing the power - and bi -spectrum. For the bi -spectrum in the hyperbolic vacuum we find that the corrections as compared to the standard Bunch -Davies result are not enhanced in specific momentum configurations and strongly suppressed for momenta large compared to the hyperbolic curvature scale. We close with some final remarks, in particular regarding the implications of these results for more realistic inflationary bubble scenarios.Comment: Added references, removed typos, added author, extensions in first section and conclusions. 34 pages, 4 figure

Casting Shadows on Holographic Reconstruction

In the context of the AdS/CFT correspondence, we study several holographic probes that relate information about the bulk spacetime to CFT data. The best-known example is the relation between minimal surfaces in the bulk and entanglement entropy of a subregion in the CFT. Building on earlier work, we identify "shadows" in the bulk: regions that are not illuminated by any of the bulk probes we consider, in the sense that the bulk surfaces do not pass through these regions. We quantify the size of the shadow in the near horizon region of a black hole and in the vicinity of a sufficiently dense star. The existence of shadows motivates further study of the bulk-boundary dictionary in order to identify CFT quantities that encode information about the shadow regions in the bulk. We speculate on the interpretation of our results from a dual field theory perspective.Comment: 42 pages, 38 figure

Speckle-scale focusing in the diffusive regime with time reversal of variance-encoded light (TROVE)

Focusing of light in the diffusive regime inside scattering media has long been considered impossible. Recently, this limitation has been overcome with time reversal of ultrasound-encoded light (TRUE), but the resolution of this approach is fundamentally limited by the large number of optical modes within the ultrasound focus. Here, we introduce a new approach, time reversal of variance-encoded light (TROVE), which demixes these spatial modes by variance encoding to break the resolution barrier imposed by the ultrasound. By encoding individual spatial modes inside the scattering sample with unique variances, we effectively uncouple the system resolution from the size of the ultrasound focus. This enables us to demonstrate optical focusing and imaging with diffuse light at an unprecedented, speckle-scale lateral resolution of ~5 µm

Translation correlations in anisotropically scattering media

Controlling light propagation across scattering media by wavefront shaping holds great promise for a wide range of communications and imaging applications. However, finding the right wavefront to shape is a challenge when the mapping between input and output scattered wavefronts (i.e. the transmission matrix) is not known. Correlations in transmission matrices, especially the so-called memory-effect, have been exploited to address this limitation. However, the traditional memory-effect applies to thin scattering layers at a distance from the target, which precludes its use within thick scattering media, such as fog and biological tissue. Here, we theoretically predict and experimentally verify new transmission matrix correlations within thick anisotropically scattering media, with important implications for biomedical imaging and adaptive optics.Comment: main article (18 pages) and appendices (6 pages