We study the coherent temperature and polarization patterns produced in homogeneous but anisotropic cosmological models. We show results for all Bianchi types with a Friedman-Robertson-Walker limit (i.e. Types I, V, VII$_{0}$, VII$_{h}$ and IX) to il
lustrate the range of possible behaviour. We discuss the role of spatial curvature, shear and rotation in the geodesic equations for each model and establish some basic results concerning the symmetries of the patterns produced. We also give examples of the time-evolution of these patterns in terms of the Stokes parameters $I$, $Q$ and $U$.
We calculate the temperature and polarization patterns generated in anisotropic cosmological models drawn from the Bianchi classification. We show that localized features in the temperature pattern, perhaps similar to the cold spot observed in the Wi
lkinson Microwave Anisotropy Probe (WMAP) data, can be generated in models with negative spatial curvature, i.e. Bianchi types V and VII$_{h}$. Both these models also generate coherent polarization patterns. In Bianchi VII$_h$, however, rotation of the polarization angle as light propagates along geodesics can convert E modes into B modes but in Bianchi V this is not necessarily the case. It is in principle possible, therefore, to generate localized temperature features without violating existing observational constraints on the odd-parity component of the polarization of the cosmic microwave background.
We present a simple heuristic model to demonstrate how feedback related to the galaxy formation process can result in a scale-dependent bias of mass versus light, even on very large scales. The model invokes the idea that galaxies form initially in l
ocations determined by the local density field, but the subsequent formation of galaxies is also influenced by the presence of nearby galaxies that have already formed. The form of bias that results possesses some features that are usually described in terms of stochastic effects, but our model is entirely deterministic once the density field is specified. Features in the large-scale galaxy power spectrum (such as wiggles that might in an extreme case mimic the effect of baryons on the primordial transfer function) could, at least in principle, arise from spatial modulations of the galaxy formation process that arise naturally in our model. We also show how this fully deterministic model gives rise to apparently stochasticity in the galaxy distribution.
Scale transformations have played an extremely successful role in studies of cosmological large-scale structure by relating the non-linear spectrum of cosmological density fluctuations to the linear primordial power at longer wavelengths. Here we gen
eralize this approach to investigate the usefulness of scale transformations for nonlinear higher-order statistics, specifically the bispectrum. We find that the bispectrum predicted by perturbation theory at tree-level can be rescaled to match the results of full numerical simulations in the weakly and intermediately nonlinear regimes, especially at high redshifts, with an accuracy that is surprising given the simplicity of the procedure used. This discovery not only offers a simple practical way of calculating the matter bispectrum, but also suggests that scale transformations may yet yield even deeper insights into the physics of hierarchical clustering.
