Physics welcomes the idea that space contains energy whose gravitational effect approximates that of Einstein's cosmological constant, \ensuremath{\Lambda}; today the concept is termed dark energy or quintessence. Physics also suggests that dark energy could be dynamical, allowing for the arguably appealing picture of an evolving dark-energy density approaching its natural value, zero, and small now because the expanding universe is old. This would alleviate the classical problem of the curious energy scale of a millielectron volt associated with a constant \ensuremath{\Lambda}. Dark energy may have been detected by recent cosmological tests. These tests make a good scientific case for the context, in the relativistic Friedmann-Lema\^{\i}tre model, in which the gravitational inverse-square law is applied to the scales of cosmology. We have well-checked evidence that the mean mass density is not much more than one-quarter of the critical Einstein--de Sitter value. The case for detection of dark energy is not yet as convincing but still serious; we await more data, which may be derived from work in progress. Planned observations may detect the evolution of the dark-energy density; a positive result would be a considerable stimulus for attempts at understanding the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.

/pdf/the-cosmological-constant-and-dark-energy-1w78acsak0.pdf

The Cosmological Constant and Dark Energy

https://www.physics.rutgers.edu/grad/690/Padmanabhan-2003.pdf

Cosmological constant—the weight of the vacuum

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001. Apart from providing several examples of possible covariant generalizations, we study a particular construction based on light-sheets, motivated in similar spirit to the covariant entropy bound underlying the holographic principle. In particular, we argue that the entanglement entropy associated with a specified region on the boundary in the context of the AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. We demonstrate our construction with several examples to illustrate its reduction to the holographic entanglement entropy proposal in static spacetimes. We further show how this proposal may be used to understand the time evolution of entanglement entropy in a time varying QFT state dual to a collapsing black hole background. Finally, we use our proposal to argue that the Euclidean wormhole geometries with multiple boundaries should be regarded as states in a non-interacting but entangled set of QFTs, one associated to each boundary.

/pdf/a-covariant-holographic-entanglement-entropy-proposal-7emwnougsz.pdf

A covariant holographic entanglement entropy proposal

Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution

Traversable wormholes have traditionally been viewed as intrinsically topological entities in some multiply connected spacetime. Here, we show that topology is too limited a tool to accurately characterize a generic traversable wormhole: in general one needs geometric information to detect the presence of a wormhole, or more precisely to locate the wormhole throat. For an arbitrary static spacetime we shall define the wormhole throat in terms of a 2–dimensional constant-time hypersurface of minimal area. (Zero trace for the extrinsic curvature plus a “flare–out” condition.) This enables us to severely constrain the geometry of spacetime at the wormhole throat and to derive generalized theorems regarding violations of the energy conditions—theorems that do not involve geodesic averaging but nevertheless apply to situations much more general than the spherically symmetric Morris–Thorne traversable wormhole. [For example: the null energy condition (NEC), when suitably weighted and integrated over the wormhole throat, must be violated.] The major technical limitation of the current approach is that we work in a static spacetime—this is already a quite rich and complicated system.

Geometric structure of the generic static traversable wormhole throat

It is by now apparent that topology is too crude a tool to accurately characterize a generic traversable wormhole. In two earlier papers we developed a complete characterization of generic but static traversable wormholes, and in the present paper extend the discussion to arbitrary time-dependent (dynamical) wormholes. A local definition of a wormhole throat, free from assumptions about asymptotic flatness, symmetries, future and past null infinities, embedding diagrams, topology, and even time dependence is developed that accurately captures the essence of what a wormhole throat is, and where it is located. Adapting and extending a suggestion due to Page, we define a wormhole throat to be a marginally anti-trapped surface, that is, a closed two-dimensional spatial hypersurface such that one of the two future-directed null geodesic congruences orthogonal to it is just beginning to diverge. Typically a dynamic wormhole will possess {ital two} such throats, corresponding to the two orthogonal null geodesic congruences, and these two throats will not coincide (though they do coalesce into a single throat in the static limit). The divergence property of the null geodesics at the marginally anti-trapped surface generalizes the {open_quotes}flare-out{close_quotes} condition for an arbitrary wormhole. We derive theorems regarding violations of the nullmore » energy condition (NEC) at and near these throats and find that, even for wormholes with arbitrary time dependence, the violation of the NEC is a generic property of wormhole throats. We also discuss wormhole throats in the presence of fully antisymmetric torsion and find that the energy condition violations {ital cannot} be dumped into the torsion degrees of freedom. Finally by means of a concrete example we demonstrate that even temporary suspension of energy-condition violations is incompatible with the flare-out property of dynamic throats. {copyright} {ital 1998} {ital The American Physical Society}« less

http://cds.cern.ch/record/346083/files/9802046.pdf

Dynamic wormholes, anti-trapped surfaces, and energy conditions

We extend previous proofs that violations of the null energy condition are a generic and universal feature of traversable wormholes to completely nonsymmetric time-dependent wormholes. We show that the analysis can be phrased purely in terms of local geometry at and near the wormhole throat, and we do not have to make any technical assumptions about asymptotic flatness or other global properties. A key aspect of the analysis is the demonstration that time-dependent wormholes have two throats, one for each direction through the wormhole, and that the two throats coalesce only for the case of a static wormhole.

Null Energy Condition in Dynamic Wormholes

We present the first results of a self-consistent solution of the semiclassical Einstein field equations corresponding to a Lorentzian wormhole coupled to a quantum scalar field. The specific solution presented here represents a wormhole connecting two asymptotically spatially flat regions. In general, the diameter of the wormhole throat, in units of the Planck length, can be arbitrarily large, depending on the values of the scalar coupling $\ensuremath{\xi}$ and the boundary values for the shape and redshift functions. In all cases we have considered, there is a fine structure in the form of Planck-scale oscillations or ripples superimposed on the solutions.

Self-Consistent Wormhole Solutions of Semiclassical Gravity

In a closed system an irreversible enantioselective autocatalysis coupled to a mutual inhibition reaction, corresponding to a fast and low exergonic formation of the heterochiral dimer which reverts to the monomers in the final reaction work-up, yields absolute asymmetric synthesis even in the absence of chiral polarizations. This is due to the very high chiral amplifications of the initial small statistical deviations from the ideal racemic composition. Moreover, this system is sensitive to very small chiral polarizations (energy differences between transition states below the mJ mol−1 range). This behaviour can also be observed in reversible exergonic reactions, because the racemization time scale is substantially longer than that of the transformation of the initial reagents. The effect of the presence of other reactions likely to occur (i.e. non-catalytic transformations, non-enantioselective catalysis and homodimer formation) is discussed. Even if these decrease the sensitivity of the network in several chemical scenarios, the emergence of kinetically controlled spontaneous symmetry breaking is not hindered. These features, together with the response of the system to a sequential reaction procedure, suggest that a similar type of network is at the heart of the Soai reaction.

David Hochberg

Papers

Geometric structure of the generic static traversable wormhole throat

Dynamic wormholes, anti-trapped surfaces, and energy conditions

Null Energy Condition in Dynamic Wormholes

Self-Consistent Wormhole Solutions of Semiclassical Gravity

Frank Model and Spontaneous Emergence of Chirality in Closed Systems