The minimal volume orientable hyperbolic 2-cusped 3-manifolds

We prove that the Whitehead link complement and the (-2, 3, 8) pretzel link complement are the minimal volume orientable hyperbolic 3-manifolds with two cusps, with volume 3.66... = 4 x Catalan's constant. We use topological arguments to establish the existence of an essential surface which provides a lower bound on volume and strong constraints on the manifolds that realize that lower bound.Comment: 10 pages, 5 figures, incorporated referees comments, includes hyperref link

Figures of merit for present and future dark energy probes

We compare current and forecasted constraints on dynamical dark energy models from Type Ia supernovae and the cosmic microwave background using figures of merit based on the volume of the allowed dark energy parameter space. For a two-parameter dark energy equation of state that varies linearly with the scale factor, and assuming a flat universe, the area of the error ellipse can be reduced by a factor of ~10 relative to current constraints by future space-based supernova data and CMB measurements from the Planck satellite. If the dark energy equation of state is described by a more general basis of principal components, the expected improvement in volume-based figures of merit is much greater. While the forecasted precision for any single parameter is only a factor of 2-5 smaller than current uncertainties, the constraints on dark energy models bounded by -1<w<1 improve for approximately 6 independent dark energy parameters resulting in a reduction of the total allowed volume of principal component parameter space by a factor of ~100. Typical quintessence models can be adequately described by just 2-3 of these parameters even given the precision of future data, leading to a more modest but still significant improvement. In addition to advances in supernova and CMB data, percent-level measurement of absolute distance and/or the expansion rate is required to ensure that dark energy constraints remain robust to variations in spatial curvature.Comment: 9 pages, 7 figures; submitted to Phys. Rev.

S-parameter and vector decay constant in QCD with eight fundamental fermions

SU(3) gauge theory with eight massless fundamental fermions seems to be near the conformal boundary, and is a candidate theory of walking technicolor. Along the series of study by LatKMI collaboration using HISQ fermions, S-parameter and vector decay constant, which provide important constraints in the model of electroweak symmetry breaking, are calculated for this theory. Use of various volumes allows a systematic investigation of finite volume effects. A strong sensitivity of the S-parameter to the volume is found.Comment: 7 pages, 7 figures, Proceedings of the 33rd International Symposium on Lattice Field Theory, July 14-18, 2015, Kobe, Japa

Relativistic Mean-Field Hadronic Models under Nuclear Matter Constraints

Relativistic mean-field (RMF) models have been widely used in the study of many hadronic frameworks because of several important aspects not always present in nonrelativistic models, such as intrinsic Lorentz covariance, automatic inclusion of spin, appropriate saturation mechanism for nuclear matter, causality and, therefore, no problems related to superluminal speed of sound. With the aim of identifying the models which best satisfy well known properties of nuclear matter, we have analyzed $263$ parameterizations of seven different types of RMF models under three different sets of constraints related to symmetric nuclear matter, pure neutron matter, symmetry energy, and its derivatives. One of these (SET1) is formed of the same constraints used in a recent work [M. Dutra et al., Phys. Rev. C 85, 035201 (2012)] in which we analyzed $240$ Skyrme parameterizations. The results pointed to $2$ models consistent with all constraints. By using another set of constraints, namely, SET2a, formed by the updated versions of the previous one, we found $4$ models approved simultaneously. Finally, in the third set, named SET2b, in which the values of the constraints are more restrictive, we found $3$ consistent models. Another interesting feature of our analysis is that the results change dramatically if we do not consider the constraint regarding the volume part of the isospin incompressibility ($K_{\tau,\rm v}$). In this case, we have $35$ approved models in SET2a and $30$ in SET2b.Comment: 63 pages, 3 figures and 9 tables. Version accepted for publication in PR