Ultrasound velocity measurements of the orbital-degenerate frustrated spinel MgV$_2$O$_4$ are performed in the high-purity single crystal which exhibits successive structural and antiferromagnetic phase transitions, and in the disorder-introduced sin
gle crystal which exhibits spin-glass-like behavior. The measurements reveal that two-types of unusual temperature dependence of the elastic moduli coexist in the cubic paramagnetic phase, which are resolved by magnetic-field and disorder sensitivities: huge Curie-type softening with decreasing temperature, and concave temperature dependence with a characteristic minimum. These elastic anomalies suggest the coupling of lattice to coexisting orbital fluctuations and orbital-spin-coupled excitations.
Redshift space distortion (RSD) observed in galaxy redshift surveys is a powerful tool to test gravity theories on cosmological scales, but the systematic uncertainties must carefully be examined for future surveys with large statistics. Here we empl
oy various analytic models of RSD and estimate the systematic errors on measurements of the structure growth-rate parameter, $fsigma_8$, induced by non-linear effects and the halo bias with respect to the dark matter distribution, by using halo catalogues from 40 realisations of $3.4 times 10^8$ comoving $h^{-3}$Mpc$^3$ cosmological N-body simulations. We consider hypothetical redshift surveys at redshifts z=0.5, 1.35 and 2, and different minimum halo mass thresholds in the range of $5.0 times 10^{11}$ -- $2.0 times 10^{13} h^{-1} M_odot$. We find that the systematic error of $fsigma_8$ is greatly reduced to ~5 per cent level, when a recently proposed analytical formula of RSD that takes into account the higher-order coupling between the density and velocity fields is adopted, with a scale-dependent parametric bias model. Dependence of the systematic error on the halo mass, the redshift, and the maximum wavenumber used in the analysis is discussed. We also find that the Wilson-Hilferty transformation is useful to improve the accuracy of likelihood analysis when only a small number of modes are available in power spectrum measurements.
