One Hundred Years of the Cosmological Constant: from 'Superfluous Stunt' to Dark Energy

We present a centennial review of the history of the term known as the cosmological constant. First introduced to the general theory of relativity by Einstein in 1917 in order to describe a universe that was assumed to be static, the term fell from favour in the wake of the discovery of the expanding universe, only to make a dramatic return in recent times. We consider historical and philosophical aspects of the cosmological constant over four main epochs: (i) the use of the term in static cosmologies (both Newtonian and relativistic); (ii) the marginalization of the term following the discovery of cosmic expansion; (iii) the use of the term to address specific cosmic puzzles such as the timespan of expansion, the formation of galaxies and the redshifts of the quasars; (iv) the re-emergence of the term in today's Lamda-CDM cosmology. We find that the cosmological constant was never truly banished from theoretical models of the universe, but was sidelined by astronomers for reasons of convenience. We also find that the return of the term to the forefront of modern cosmology did not occur as an abrupt paradigm shift due to one particular set of observations, but as the result of a number of empirical advances such as the measurement of present cosmic expansion using the Hubble Space Telescope, the measurement of past expansion using type SN 1a supernovae as standard candles, and the measurement of perturbations in the cosmic microwave background by balloon and satellite. We give a brief overview of contemporary interpretations of the physics underlying the cosmic constant and conclude with a synopsis of the famous cosmological constant problem.Comment: 60 pages, 6 figures. Some corrections, additions and extra references. Accepted for publication the European Physical Journal (H

Einstein's cosmology review of 1933: a new perspective on the Einstein-de Sitter model of the cosmos

We present a first English translation and analysis of a little-known review of relativistic cosmology written by Albert Einstein in late 1932. The article, which was published in 1933 in a book of Einstein papers translated into French, contains a substantial review of static and dynamic relativistic models of the cosmos, culminating in a discussion of the Einstein-de Sitter model. The article offers a valuable contemporaneous insight into Einstein's cosmology in the 1930s and confirms that his interest lay in the development of the simplest model of the cosmos that could account for observation, rather than an exploration of all possible cosmic models. The article also confirms that Einstein did not believe that simplistic relativistic models could give an accurate description of the early universe.Comment: Accepted for publication in the European Physical Journal (H). Includes an English translation of a little-known review of cosmology written by Albert Einstein in 1933. 20 pages, 4 figure

A note on the (1, 1,..., 1) monopole metric

Recently K. Lee, E.J. Weinberg and P. Yi in CU-TP-739, hep-th/9602167, calculated the asymptotic metric on the moduli space of (1, 1, ..., 1) BPS monopoles and conjectured that it was globally exact. I lend support to this conjecture by showing that the metric on the corresponding space of Nahm data is the same as the metric they calculate.Comment: 12 pages, latex, no figures, uses amsmath, amsthm, amsfont

Laplacian modes probing gauge fields

We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying SU(2) lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase. For calorons as classical solutions put on the lattice, the lowest mode localizes one of the constituent monopoles by a maximum and the other one by a minimum, respectively. We introduce adjustable phase boundary conditions in the time direction, under which the role of the monopoles in the mode localization is interchanged. Similar hopping phenomena are observed for thermalized configurations. We also investigate periodic and antiperiodic modes of the adjoint Laplacian for comparison. In the second part we introduce a new Fourier-like low-pass filter method. It provides link variables by truncating a sum involving the Laplacian eigenmodes. The filter not only reproduces classical structures, but also preserves the confining potential for thermalized ensembles. We give a first characterization of the structures emerging from this procedure.Comment: 43 pages, 26 figure

Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras

We prove the existence and associativity of the nonmeromorphic operator product expansion for an infinite family of vertex operator algebras, the triplet W-algebras, using results from P(z)-tensor product theory. While doing this, we also show that all these vertex operator algebras are C_2-cofinite.Comment: 21 pages, to appear in J. Phys. A: Math. Gen.; the exposition is improved and one reference is adde

A note on the index bundle over the moduli space of monopoles

Donaldson has shown that the moduli space of monopoles $M_k$ is diffeomorphic to the space \Rat_k of based rational maps from the two-sphere to itself. We use this diffeomorphism to give an explicit description of the bundle on \Rat_k obtained by pushing out the index bundle from $M_k$. This gives an alternative and more explicit proof of some earlier results of Cohen and Jones.Comment: 9 page

Alley coppice—a new system with ancient roots

International audience& Context Current production from natural forests will not satisfy future world demand for timber and fuel wood, and new land management options are required. & Aims We explore an innovative production system that combines the production of short rotation coppice in wide alleys with the production of high-value trees on narrow strips of land; it is an alternative form of alley cropping which we propose to call 'alley coppice'. The aim is to describe this alley coppice system and to illustrate its potential for produc-ing two diverse products, namely high-value timber and ener-gy wood on the same land unit. & Methods Based on a comprehensive literature review, we compare the advantages and disadvantages of the alley cop-pice system and contrast the features with well-known existing or past systems of biomass and wood production. & Results We describe and discuss the basic aspects of alley coppice, its design and dynamics, the processes of competi-tion and facilitation, issues of ecology, and areas that are open for future research. & Conclusion Based on existing knowledge, a solid founda-tion for the implementation of alley coppice on suitable land is presented, and the high potential of this system could be shown

Instanton Moduli for T**3xR

We review the specific problems that arise when studying instantons on a torus. We discuss how the Nahm transformation shows that no exact charge one instanton on T**4 can exist. However, taking one of the directions (the time) to infinity, it can be shown that vacuum to vacuum tunnelling solutions exist. A precise description of the moduli space for T**3xR, studied numerically using lattice techniques, remains an interesting open problem. New is an explicit application of the Nahm transformation to (anti-)selfdual constant curvature solutions on T**4 and a discussion of its properties relevant to instantons on T**3xR.Comment: 12p with 3 figs, uufiles -gz format. Talk at the 29th Int. Symp. on the Theory of Elem. Part., Buckow, 29 Aug.-2 Sept., 1995

Modified Hagedorn formula including temperature fluctuation - Estimation of temperatures at RHIC experiments -

We have systematically estimated the possible temperatures obtained from an analysis of recent data on $p_t$ distributions observed at RHIC experiments. Using the fact that observed $p_t$ distributions cannot be described by the original Hagedorn formula in the whole range of transverse momenta (in particular above 6 GeV/c), we propose a modified Hagedorn formula including temperature fluctuation. We show that by using it we can fit $p_t$ distributions in the whole range and can estimate consistently the relevant temperatures, including their fluctuations.Comment: Some misprints corrected, references updated. To be published in Eur. Phys. J. C (2006

Transit Time Measurement in Indicator Dilution Curves: Overcoming the Missing Ground Truth and Quantifying the Error

The vascular function of a vessel can be qualitatively and intraoperatively checked by recording the blood dynamics inside the vessel via fluorescence angiography (FA). Although FA is the state of the art in proving the existence of blood flow during interventions such as bypass surgery, it still lacks a quantitative blood flow measurement that could decrease the recurrence rate and postsurgical mortality. Previous approaches show that the measured flow has a significant deviation compared to the gold standard reference (ultrasonic flow meter). In order to systematically address the possible sources of error, we investigated the error in transit time measurement of an indicator. Obtaining in vivo indicator dilution curves with a known ground truth is complex and often not possible. Further, the error in transit time measurement should be quantified and reduced. To tackle both issues, we first computed many diverse indicator dilution curves using an in silico simulation of the indicator\u27s flow. Second, we post-processed these curves to mimic measured signals. Finally, we fitted mathematical models (parabola, gamma variate, local density random walk, and mono-exponential model) to re-continualize the obtained discrete indicator dilution curves and calculate the time delay of two analytical functions. This re-continualization showed an increase in the temporal accuracy up to a sub-sample accuracy. Thereby, the Local Density Random Walk (LDRW) model performed best using the cross-correlation of the first derivative of both indicator curves with a cutting of the data at 40% of the peak intensity. The error in frames depends on the noise level and is for a signal-to-noise ratio (SNR) of 20 dB and a sampling rate of f$_{s}$ = 60 Hz at f$^{-1}$$_{s}$⋅0.25(±0.18), so this error is smaller than the distance between two consecutive samples. The accurate determination of the transit time and the quantification of the error allow the calculation of the error propagation onto the flow measurement. Both can assist surgeons as an intraoperative quality check and thereby reduce the recurrence rate and post-surgical mortality