At linear order in cosmological perturbations, departures from the growth in the cosmological standard model can be quantified in terms of two functions of redshift $z$ and Fourier number $k$. Previous studies have performed principal component forec
asts for several choices of these two functions, based on expected capabilities of upcoming large structure surveys. It is typically found that there will be many well-constrained degrees of freedom. However, not all and, probably most, of these degrees of freedom were physical if the parametrization had allowed for an arbitrary $k$-dependence. In this paper, we restrict the $k$-dependence to that allowed in local theories of gravity under the quasi-static approximation, i.e. ratios of polynomials in $k$, and identify the best constrained features in the ($z$,$k$)-dependence of the commonly considered functions $mu$ and $gamma$ as measured by an LSST-like weak lensing survey. We estimate the uncertainty in the measurements of the eigenmodes of modified growth. We find that imposing the theoretical prior on $k$-dependence reduces the number of degrees of freedom and the covariance between parameters. On the other hand, imaging surveys like LSST are not as sensitive to the $z$-dependence as they are to the $k$-dependence of the modified growth functions. This trade off provides us with, more or less, the same number of well-constrained eigenmodes (with respect to our prior) as found before, but now these modes are physical.
Cosmic Microwave Background (CMB) polarization B-modes induced by Faraday Rotation (FR) can provide a distinctive signature of primordial magnetic fields because of their characteristic frequency dependence and because they are only weakly damped on
small scales. FR also leads to mode-coupling correlations between the E and B type polarization, and between the temperature and the B-mode. These additional correlations can further help distinguish magnetic fields from other sources of B-modes. We review the FR induced CMB signatures and present the constraints on primordial magnetism that can be expected from upcoming CMB experiments. Our results suggest that FR of CMB will be a promising probe of primordial magnetic fields.
We develop an efficient, non-parametric Bayesian method for reconstructing the time evolution of the dark energy equation of state w(z) from observational data. Of particular importance is the choice of prior, which must be chosen carefully to minimi
se variance and bias in the reconstruction. Using a principal component analysis, we show how a correlated prior can be used to create a smooth reconstruction and also avoid bias in the mean behaviour of w(z). We test our method using Wiener reconstructions based on Fisher matrix projections, and also against more realistic MCMC analyses of simulated data sets for Planck and a future space-based dark energy mission. While the accuracy of our reconstruction depends on the smoothness of the assumed w(z), the relative error for typical dark energy models is <10% out to redshift z=1.5.
The next generation of weak lensing surveys will trace the evolution of matter perturbations and gravitational potentials from the matter dominated epoch until today. Along with constraining the dynamics of dark energy, they will probe the relations
between matter overdensities, local curvature, and the Newtonian potential. We work with two functions of time and scale to account for any modifications of these relations in the linear regime from those in the LCDM model. We perform a Principal Component Analysis (PCA) to find the eigenmodes and eigenvalues of these functions for surveys like DES and LSST. This paper builds on and significantly extends the PCA analysis of Zhao et al. (2009) in several ways. In particular, we consider the impact of some of the systematic effects expected in weak lensing surveys. We also present the PCA in terms of other choices of the two functions needed to parameterize modified growth on linear scales, and discuss their merits. We analyze the degeneracy between the modified growth functions and other cosmological parameters, paying special attention to the effective equation of state w(z). Finally, we demonstrate the utility of the PCA as an efficient data compression stage which enables one to easily derive constraints on parameters of specific models without recalculating Fisher matrices from scratch.
Cosmic string networks generate cosmological perturbations actively throughout the history of the universe. Thus, the string sourced anisotropy of the cosmic microwave background is not affected by Silk damping as much as the anisotropy seeded by inf
lation. The spectrum of perturbations generated by strings does not match the observed CMB spectrum on large angular scales (l<1000) and is bounded to contribute no more than 10% of the total power on those scales. However, when this bound is marginally saturated, the anisotropy created by cosmic strings on small angular scales l>2000 will dominate over that created by the primary inflationary perturbations. This range of angular scales in the CMB is presently being measured by a number of experiments; their results will test this prediction of cosmic string networks soon.
We test General Relativity (GR) using current cosmological data: the cosmic microwave background (CMB) from WMAP5 (Komatsu et al. 2009), the integrated Sachs-Wolfe (ISW) effect from the cross-correlation of the CMB with six galaxy catalogs (Giannanto
nio et al. 2008), a compilation of supernovae Type Ia (SNe) including the latest SDSS SNe (Kessler et al. 2009), and part of the weak lensing (WL) data from CFHTLS (Fu et al. 2008, Kilbinger et al. 2009) that probe linear and mildly non-linear scales. We first test a model where the effective Newtons constant, mu, and the ratio of the two gravitational potentials, eta, transit from the GR value to another constant at late times; in this case, we find that standard GR is fully consistent with the combined data. The strongest constraint comes from the ISW effect which would arise from this gravitational transition; the observed ISW signal imposes a tight constraint on a combination of mu and eta that characterizes the lensing potential. Next, we consider four pixels in time and space for each function mu and eta, and perform a Principal Component Analysis (PCA) finding that seven of the resulting eight eigenmodes are consistent with GR within the errors. Only one eigenmode shows a 2-sigma deviation from the GR prediction, which is likely to be due to a systematic effect. However, the detection of such a deviation demonstrates the power of our time- and scale-dependent PCA methodology when combining observations of structure formation and expansion history to test GR.
