FRW Universe Models in Conformally Flat Spacetime Coordinates. II: Universe models with negative and vanishing spatial curvature

We deduce general expressions for the line element of universe models with negative and vanishing spatial curvature described by conformally flat spacetime coordinates. The empty Milne universe model and models with dust, radiation and vacuum energy are exhibited. Discussing the existence of particle horizons we show that there is continual creation of space, matter and energy when conformal time is used in Friedmann-Robertson-Walker models with negative spatial curvature.Comment: 25 pages, 12 figure

Planck-LFI: Design and Performance of the 4 Kelvin Reference Load Unit

The LFI radiometers use a pseudo-correlation design where the signal from the sky is continuously compared with a stable reference signal, provided by a cryogenic reference load system. The reference unit is composed by small pyramidal horns, one for each radiometer, 22 in total, facing small absorbing targets, made of a commercial resin ECCOSORB CR (TM), cooled to approximately 4.5 K. Horns and targets are separated by a small gap to allow thermal decoupling. Target and horn design is optimized for each of the LFI bands, centered at 70, 44 and 30 GHz. Pyramidal horns are either machined inside the radiometer 20K module or connected via external electro-formed bended waveguides. The requirement of high stability of the reference signal imposed a careful design for the radiometric and thermal properties of the loads. Materials used for the manufacturing have been characterized for thermal, RF and mechanical properties. We describe in this paper the design and the performance of the reference system.Comment: This is an author-created, un-copyedited version of an article accepted for publication in JINST. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at [10.1088/1748-0221/4/12/T12006]. 14 pages, 34 figure

Planck-LFI radiometers' spectral response

The Low Frequency Instrument (LFI) is an array of pseudo-correlation radiometers on board the Planck satellite, the ESA mission dedicated to precision measurements of the Cosmic Microwave Background. The LFI covers three bands centred at 30, 44 and 70 GHz, with a goal bandwidth of 20% of the central frequency. The characterization of the broadband frequency response of each radiometer is necessary to understand and correct for systematic effects, particularly those related to foreground residuals and polarization measurements. In this paper we present the measured band shape of all the LFI channels and discuss the methods adopted for their estimation. The spectral characterization of each radiometer was obtained by combining the measured spectral response of individual units through a dedicated RF model of the LFI receiver scheme. As a consistency check, we also attempted end-to-end spectral measurements of the integrated radiometer chain in a cryogenic chamber. However, due to systematic effects in the measurement setup, only qualitative results were obtained from these tests. The measured LFI bandpasses exhibit a moderate level of ripple, compatible with the instrument scientific requirements.Comment: 16 pages, 9 figures, this paper is part of the Prelaunch status LFI papers published on JINST: http://www.iop.org/EJ/journal/-page=extra.proc5/jins

Distributional versions of Littlewood's Tauberian theorem

We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We apply these Tauberian results to deduce a number of Tauberian theorems for power series where Ces\`{a}ro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.Comment: 15 page

Investigating dietary life histories and mobility of children buried in St Gertrude Church Cemetery, Riga, Latvia (15th– 17th centuries AD)

Carbon and nitrogen isotope profiles were obtained from incremental dentine analysis of 19 non‐adults from a cemetery in Riga, Latvia. The research compared the life histories and diet between people buried in two mass graves and the general cemetery. The δ13C profiles of several children from the mass graves were similar but did not resemble the patterns seen in children from the general cemetery, suggesting that they probably represented a different population group. The rise in δ15N values towards the end of the life of four individuals from one mass grave suggests they were victims of an historically documented famine

Theorems on shear-free perfect fluids with their Newtonian analogues

In this paper we provide fully covariant proofs of some theorems on shear-free perfect fluids. In particular, we explicitly show that any shear-free perfect fluid with the acceleration proportional to the vorticity vector (including the simpler case of vanishing acceleration) must be either non-expanding or non-rotating. We also show that these results are not necessarily true in the Newtonian case, and present an explicit comparison of shear-free dust in Newtonian and relativistic theories in order to see where and why the differences appear.Comment: 23 pages, LaTeX. Submitted to GR

Planck pre-launch status: Low Frequency Instrument calibration and expected scientific performance

We give the calibration and scientific performance parameters of the Planck Low Frequency Instrument (LFI) measured during the ground cryogenic test campaign. These parameters characterise the instrument response and constitute our best pre-launch knowledge of the LFI scientific performance. The LFI shows excellent $1/f$ stability and rejection of instrumental systematic effects; measured noise performance shows that LFI is the most sensitive instrument of its kind. The set of measured calibration parameters will be updated during flight operations through the end of the mission.Comment: Accepted for publications in Astronomy and Astrophysics. Astronomy & Astrophysics, 2010 (acceptance date: 12 Jan 2010

Rare region effects at classical, quantum, and non-equilibrium phase transitions

Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions, and in systems with correlated disorder. In some cases, rare regions can actually completely destroy the sharp phase transition by smearing. This topical review presents a unifying framework for rare region effects at weakly disordered classical, quantum, and nonequilibrium phase transitions based on the effective dimensionality of the rare regions. Explicit examples include disordered classical Ising and Heisenberg models, insulating and metallic random quantum magnets, and the disordered contact process.Comment: Topical review, 68 pages, 14 figures, final version as publishe

Dimensionless cosmology

Although it is well known that any consideration of the variations of fundamental constants should be restricted to their dimensionless combinations, the literature on variations of the gravitational constant $G$ is entirely dimensionful. To illustrate applications of this to cosmology, we explicitly give a dimensionless version of the parameters of the standard cosmological model, and describe the physics of Big Bang Neucleosynthesis and recombination in a dimensionless manner. The issue that appears to have been missed in many studies is that in cosmology the strength of gravity is bound up in the cosmological equations, and the epoch at which we live is a crucial part of the model. We argue that it is useful to consider the hypothetical situation of communicating with another civilization (with entirely different units), comparing only dimensionless constants, in order to decide if we live in a Universe governed by precisely the same physical laws. In this thought experiment, we would also have to compare epochs, which can be defined by giving the value of any {\it one} of the evolving cosmological parameters. By setting things up carefully in this way one can avoid inconsistent results when considering variable constants, caused by effectively fixing more than one parameter today. We show examples of this effect by considering microwave background anisotropies, being careful to maintain dimensionlessness throughout. We present Fisher matrix calculations to estimate how well the fine structure constants for electromagnetism and gravity can be determined with future microwave background experiments. We highlight how one can be misled by simply adding $G$ to the usual cosmological parameter set