How isotropic is the Universe?

A fundamental assumption in the standard model of cosmology is that the Universe is isotropic on large scales. Breaking this assumption leads to a set of solutions to Einstein's field equations, known as Bianchi cosmologies, only a subset of which have ever been tested against data. For the first time, we consider all degrees of freedom in these solutions to conduct a general test of isotropy using cosmic microwave background temperature and polarization data from Planck. For the vector mode (associated with vorticity), we obtain a limit on the anisotropic expansion of $(\sigma_V/H)_0 < 4.7 \times 10^{-11}$ (95% CI), which is an order of magnitude tighter than previous Planck results that used CMB temperature only. We also place upper limits on other modes of anisotropic expansion, with the weakest limit arising from the regular tensor mode, $(\sigma_{T,\rm reg}/H)_0<1.0 \times 10^{-6}$ (95% CI). Including all degrees of freedom simultaneously for the first time, anisotropic expansion of the Universe is strongly disfavoured, with odds of 121,000:1 against.Comment: 6 pages, 1 figure, v2: replaced with version accepted by PR

3D weak lensing with spin wavelets on the ball

We construct the spin flaglet transform, a wavelet transform to analyze spin signals in three dimensions. Spin flaglets can probe signal content localized simultaneously in space and frequency and, moreover, are separable so that their angular and radial properties can be controlled independently. They are particularly suited to analyzing of cosmological observations such as the weak gravitational lensing of galaxies. Such observations have a unique 3D geometrical setting since they are natively made on the sky, have spin angular symmetries, and are extended in the radial direction by additional distance or redshift information. Flaglets are constructed in the harmonic space defined by the Fourier-Laguerre transform, previously defined for scalar functions and extended here to signals with spin symmetries. Thanks to various sampling theorems, both the Fourier-Laguerre and flaglet transforms are theoretically exact when applied to bandlimited signals. In other words, in numerical computations the only loss of information is due to the finite representation of floating point numbers. We develop a 3D framework relating the weak lensing power spectrum to covariances of flaglet coefficients. We suggest that the resulting novel flaglet weak lensing estimator offers a powerful alternative to common 2D and 3D approaches to accurately capture cosmological information. While standard weak lensing analyses focus on either real or harmonic space representations (i.e., correlation functions or Fourier-Bessel power spectra, respectively), a wavelet approach inherits the advantages of both techniques, where both complicated sky coverage and uncertainties associated with the physical modeling of small scales can be handled effectively. Our codes to compute the Fourier-Laguerre and flaglet transforms are made publicly available.Comment: 24 pages, 4 figures, version accepted for publication in PR

A framework for testing isotropy with the cosmic microwave background

We present a new framework for testing the isotropy of the Universe using cosmic microwave background data, building on the nested-sampling ANICOSMO code. Uniquely, we are able to constrain the scalar, vector and tensor degrees of freedom alike; previous studies only considered the vector mode (linked to vorticity). We employ Bianchi type VII$_h$ cosmologies to model the anisotropic Universe, from which other types may be obtained by taking suitable limits. In a separate development, we improve the statistical analysis by including the effect of Bianchi power in the high-$\ell$, as well as the low-$\ell$, likelihood. To understand the effect of all these changes, we apply our new techniques to WMAP data. We find no evidence for anisotropy, constraining shear in the vector mode to $(\sigma_V/H)_0 < 1.7 \times 10^{-10}$ (95% CL). For the first time, we place limits on the tensor mode; unlike other modes, the tensor shear can grow from a near-isotropic early Universe. The limit on this type of shear is $(\sigma_{T,\rm reg}/H)_0 < 2.4 \times 10^{-7}$ (95% CL).Comment: 11 pages, 6 figures, v3: minor modifications to match version accepted by MNRA

Bayesian Analysis of Inflation II: Model Selection and Constraints on Reheating

We discuss the model selection problem for inflationary cosmology. We couple ModeCode, a publicly-available numerical solver for the primordial perturbation spectra, to the nested sampler MultiNest, in order to efficiently compute Bayesian evidence. Particular attention is paid to the specification of physically realistic priors, including the parametrization of the post-inflationary expansion and associated thermalization scale. It is confirmed that while present-day data tightly constrains the properties of the power spectrum, it cannot usefully distinguish between the members of a large class of simple inflationary models. We also compute evidence using a simulated Planck likelihood, showing that while Planck will have more power than WMAP to discriminate between inflationary models, it will not definitively address the inflationary model selection problem on its own. However, Planck will place very tight constraints on any model with more than one observationally-distinct inflationary regime -- e.g. the large- and small-field limits of the hilltop inflation model -- and put useful limits on different reheating scenarios for a given model.Comment: ModeCode package available from http://zuserver2.star.ucl.ac.uk/~hiranya/ModeCode/ModeCode (requires CosmoMC and MultiNest); to be published in PRD. Typos fixe

Optimal filters for detecting cosmic bubble collisions

A number of well-motivated extensions of the LCDM concordance cosmological model postulate the existence of a population of sources embedded in the cosmic microwave background (CMB). One such example is the signature of cosmic bubble collisions which arise in models of eternal inflation. The most unambiguous way to test these scenarios is to evaluate the full posterior probability distribution of the global parameters defining the theory; however, a direct evaluation is computationally impractical on large datasets, such as those obtained by the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck. A method to approximate the full posterior has been developed recently, which requires as an input a set of candidate sources which are most likely to give the largest contribution to the likelihood. In this article, we present an improved algorithm for detecting candidate sources using optimal filters, and apply it to detect candidate bubble collision signatures in WMAP 7-year observations. We show both theoretically and through simulations that this algorithm provides an enhancement in sensitivity over previous methods by a factor of approximately two. Moreover, no other filter-based approach can provide a superior enhancement of these signatures. Applying our algorithm to WMAP 7-year observations, we detect eight new candidate bubble collision signatures for follow-up analysis.Comment: 12 pages, 6 figures, replaced to match version accepted by PR

SILC: a new Planck Internal Linear Combination CMB temperature map using directional wavelets

We present new clean maps of the CMB temperature anisotropies (as measured by Planck) constructed with a novel internal linear combination (ILC) algorithm using directional, scale-discretised wavelets --- Scale-discretised, directional wavelet ILC or SILC. Directional wavelets, when convolved with signals on the sphere, can separate the anisotropic filamentary structures which are characteristic of both the CMB and foregrounds. Extending previous component separation methods, which use the frequency, spatial and harmonic signatures of foregrounds to separate them from the cosmological background signal, SILC can additionally use morphological information in the foregrounds and CMB to better localise the cleaning algorithm. We test the method on Planck data and simulations, demonstrating consistency with existing component separation algorithms, and discuss how to optimise the use of morphological information by varying the number of directional wavelets as a function of spatial scale. We find that combining the use of directional and axisymmetric wavelets depending on scale could yield higher quality CMB temperature maps. Our results set the stage for the application of SILC to polarisation anisotropies through an extension to spin wavelets.Comment: 15 pages, 13 figures. Minor changes to match version published in MNRAS. Map products available at http://www.silc-cmb.or

Sparse Inpainting and Isotropy

Sparse inpainting techniques are gaining in popularity as a tool for cosmological data analysis, in particular for handling data which present masked regions and missing observations. We investigate here the relationship between sparse inpainting techniques using the spherical harmonic basis as a dictionary and the isotropy properties of cosmological maps, as for instance those arising from cosmic microwave background (CMB) experiments. In particular, we investigate the possibility that inpainted maps may exhibit anisotropies in the behaviour of higher-order angular polyspectra. We provide analytic computations and simulations of inpainted maps for a Gaussian isotropic model of CMB data, suggesting that the resulting angular trispectrum may exhibit small but non-negligible deviations from isotropy.Comment: 18 pages, 6 figures. v3: matches version published in JCAP; formatting changes and single typo correction only. Code available from http://zuserver2.star.ucl.ac.uk/~smf/code.htm