Abstract: We propose to install a storage ring at an ISOL-type radioactive beam facility for the first time. Specifically, we intend to setup the heavy-ion, low-energy ring TSR at the HIE-ISOLDE facility in CERN, Geneva. Such a facility will provide a capability for experiments with stored secondary beams that is unique in the world. The envisaged physics programme is rich and varied, spanning from investigations of nuclear ground-state properties and reaction studies of astrophysical relevance, to investigations with highly-charged ions and pure isomeric beams. The TSR might also be employed for removal of isobaric contaminants from stored ion beams and for systematic studies within the neutrino beam programme. In addition to experiments performed using beams recirculating within the ring, cooled beams can also be extracted and exploited by external spectrometers for high-precision measurements. The existing TSR, which is presently in operation at the Max-Planck Institute for Nuclear Physics in Heidelberg, is well-suited and can be employed for this purpose. The physics cases as well as technical details of the existing ring facility and of the beam and infrastructure requirements at HIE-ISOLDE are discussed in the present technical design report.

Abstract: Accurate power spectrum (or correlation function) covariance matrices are a crucial requirement for cosmological parameter estimation from large scale structure surveys. In order to minimize reliance on computationally expensive mock catalogs, it is important to have a solid analytic understanding of the different components that make up a covariance matrix. Considering the matter power spectrum covariance matrix, it has recently been found that there is a potentially dominant effect on mildly non-linear scales due to power in modes of size equal to and larger than the survey volume. This beat coupling effect has been derived analytically in perturbation theory and while it has been tested with simulations, some questions remain unanswered. Moreover, there is an additional effect of these large modes, which has so far not been included in analytic studies, namely the effect on the estimated average density which enters the power spectrum estimate. In this article, we work out analytic, perturbation theory based expressions including both the beat coupling and this local average effect and we show that while, when isolated, beat coupling indeed causes large excess covariance in agreement with the literature, in a realistic scenario this is compensated almost entirely by the local average effect, leaving only similar to 10% of the excess. We test our analytic expressions by comparison to a suite of large N-body simulations, using both full simulation boxes and subboxes thereof to study cases without beat coupling, with beat coupling and with both beat coupling and the local average effect. For the variances, we find excellent agreement with the analytic expressions for k < 0.2 hMpc(-1) at z = 0.5, while the correlation coefficients agree to beyond k = 0.4 hMpc(-1). As expected, the range of agreement increases towards higher redshift and decreases slightly towards z = 0. We finish by including the large-mode effects in a full covariance matrix description for arbitrary survey geometry and confirming its validity using simulations. This may be useful as a stepping stone towards building an actual galaxy (or other tracer's) power spectrum covariance matrix.

Abstract: Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a simple graph, formed by only two nodes. We review the U(N) framework, which provides a powerful tool for the canonical study of this model, and a formulation of the system based on spinors. We consider also the covariant theory, which permits to derive the model from a more complex formulation, paying special attention to the cosmological interpretation of the theory.