Fluctuating geometries, q-observables, and infrared growth in inflationary spacetimes

Infrared growth of geometrical fluctuations in inflationary spacetimes is investigated. The problem of gauge-invariant characterization of growth of perturbations, which is of interest also in other spacetimes such as black holes, is addressed by studying evolution of the lengths of curves in the geometry. These may either connect freely falling "satellites," or wrap non-trivial cycles of geometries like the torus, and are also used in diffeomorphism- invariant constructions of two-point functions of field operators. For spacelike separations significantly exceeding the Hubble scale, no spacetime geodesic connects two events, but one may find geodesics constrained to lie within constant-time spatial slices. In inflationary geometries, metric perturbations produce significant and growing corrections to the lengths of such geodesics, as we show in both quantization on an inflating torus and in standard slow-roll inflation. These become large, signaling breakdown of a perturbative description of the geometry via such observables, and consistent with perturbative instability of de Sitter space. In particular, we show that the geodesic distance on constant time slices during inflation becomes non-perturbative a few e-folds after a given scale has left the horizon, by distances \sim 1/H^3 \sim RS, obstructing use of such geodesics in constructing IR-safe observables based on the spatial geometry. We briefly discuss other possible measures of such geometrical fluctuations.Comment: 33 pages, 2 figures, latex; v2: typos corrected, references improve

Cosmological diagrammatic rules

A simple set of diagrammatic rules is formulated for perturbative evaluation of ``in-in" correlators, as is needed in cosmology and other nonequilibrium problems. These rules are both intuitive, and efficient for calculational purposes.Comment: 7 pages, 3 figure

Nonlocality vs. complementarity: a conservative approach to the information problem

A proposal for resolution of the information paradox is that "nice slice" states, which have been viewed as providing a sharp argument for information loss, do not in fact do so as they do not give a fully accurate description of the quantum state of a black hole. This however leaves an information *problem*, which is to provide a consistent description of how information escapes when a black hole evaporates. While a rather extreme form of nonlocality has been advocated in the form of complementarity, this paper argues that is not necessary, and more modest nonlocality could solve the information problem. One possible distinguishing characteristic of scenarios is the information retention time. The question of whether such nonlocality implies acausality, and particularly inconsistency, is briefly addressed. The need for such nonlocality, and its apparent tension with our empirical observations of local quantum field theory, may be a critical missing piece in understanding the principles of quantum gravity.Comment: 11 pages of text and figures, + references. v2 minor text. v3 small revisions to match final journal versio

Enhancing the tensor-to-scalar ratio in simple inflation

We show that in theories with a nontrivial kinetic term the contribution of the gravitational waves to the CMB fluctuations can be substantially larger than that is naively expected in simple inflationary models. This increase of the tensor-to-scalar perturbation ratio leads to a larger B-component of the CMB polarization, thus making the prospects for future detection much more promising. The other important consequence of the considered model is a higher energy scale of inflation and hence higher reheating temperature compared to a simple inflation.Comment: 9 pages, 1 figure and references are added, discussion is slightly extended, published versio

Low-scale Quintessential Inflation

In quintessential inflationary model, the same master field that drives inflation becomes, later on, the dynamical source of the (present) accelerated expansion. Quintessential inflationary models require a curvature scale at the end of inflation around $10^{-6}M_{\rm P}$ in order to explain the large scale fluctuations observed in the microwave sky. If the curvature scale at the end of inflation is much smaller than $10^{-6}M_{\rm P}$, the large scale adiabatic mode may be produced thanks to the relaxation of a scalar degree of freedom, which will be generically denoted, according to the recent terminology, as the curvaton field. The production of the adiabatic mode is analysed in detail in the case of the minimal quintessential inflationary model originally proposed by Peebles and Vilenkin.Comment: 25 pages; 5 figure

Dipeptidyl peptidase IV inhibitors in diabetes: more than inhibition of glucagon-like peptide-1 metabolism?

Inhibitors of the protease dipeptidyl peptidase IV (DPP-IV) are promising new drugs for the treatment of type 2 diabetes. They are thought to act by inhibiting the breakdown of glucagon-like peptide-1 and, thereby, selectively enhancing insulin release under conditions when it is physiologically required. These drugs are selective for DPP-IV, but the enzyme itself has a broad range of substrates other than glucagon-like peptide-1. Other high affinity substrates of DPP-IV including peptide YY may also play a role in the regulation of energy homeostasis. Moreover, DPP-IV is also known as CD26 and considered to be a moonlighting protein because it has a wide range of other functions unrelated to energy homeostasis, e.g. in immunity. The potential role of DPP-IV inhibition on substrates other than glucagon-like peptide-1 in diabetes patients remains to be elucidated

Semiclassical relations and IR effects in de Sitter and slow-roll space-times

We calculate IR divergent graviton one-loop corrections to scalar correlators in de Sitter space, and show that the leading IR contribution may be reproduced via simple semiclassical consistency relations. One can likewise use such semiclassical relations to calculate leading IR corrections to correlators in slow-roll inflation. The regulated corrections shift the tensor/scalar ratio and consistency relation of single field inflation, and non-gaussianity parameters averaged over very large distances. For inflation of sufficient duration, for example arising from a chaotic inflationary scenario, these corrections become of order unity. First-order corrections of this size indicate a breakdown of the perturbative expansion, and suggest the need for a non-perturbative description of the corresponding regime. This is analogous to a situation argued to arise in black hole evolution, and to interfere with a sharp perturbative calculation of "missing information" in Hawking radiation.Comment: 32 pages, 2 figures; v2: running of spectral index included and other minor changes; v3: minor changes to agree with published versio

Tracking Curvaton(s)?

The ratio of the curvaton energy density to that of the dominant component of the background sources may be constant during a significant period in the evolution of the Universe. The possibility of having tracking curvatons, whose decay occurs prior to the nucleosynthesis epoch, is studied. It is argued that the tracking curvaton dynamics is disfavoured since the value of the curvature perturbations prior to curvaton decay is smaller than the value required by observations. It is also argued, in a related context, that the minimal inflationary curvature scale compatible with the curvaton paradigm may be lowered in the case of low-scale quintessential inflation.Comment: 20 pages, 4figure

Diagrammatic approach to non-Gaussianity from inflation

We present Feynman type diagrams for calculating the n-point function of the primordial curvature perturbation in terms of scalar field perturbations during inflation. The diagrams can be used to evaluate the corresponding terms in the n-point function at tree level or any required loop level. Rules are presented for drawing the diagrams and writing down the corresponding terms in real space and Fourier space. We show that vertices can be renormalised to automatically account for diagrams with dressed vertices. We apply these rules to calculate the primordial power spectrum up to two loops, the bispectrum including loop corrections, and the trispectrum.Comment: 17 pages, 13 figures. v2: Comments and references added, v3: Introduction expanded, subsection on evaluating loop diagrams added, minor errors corrected, references adde