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We develop a method based on the angular distribution on the sky of cosmological parameters to probe the inhomogeneity of large-scale structure and cosmic acceleration. We demonstrate this method on the largest type Ia supernova (SN) data set available to date, as compiled by the Joint Light-curve Analysis (JLA) collaboration and, hence, consider the cosmological parameters that affect the luminosity distance. We divide the supernova sample into equal surface area pixels and estimate the cosmological parameters that minimize the chi-square of the fit to the distance modulus in each pixel, hence producing maps of the cosmological parameters $\{\Omega_{M}, \Omega_{\Lambda}, H_{0}\}.$ In poorly sampled pixels, the measured fluctuations are mostly due to an inhomogeneous coverage of the sky by the SN surveys; in contrast, in well-sampled pixels, the measurements are robust enough to suggest a real fluctuation. We also measure the anisotropy of the parameters by computing the power spectrum of the corresponding maps of the parameters up to $\ell=3.$ For an analytical toy model of an inhomogeneous ensemble of homogeneous pixels, we derive the backreaction term in the deceleration parameter due to the fluctuations of $H_{0}$ across the sky and measure it to be of order $10^{-3}$ times the corresponding average over the pixels in the absence of backreaction. We conclude that, for the toy model considered, backreaction is not a viable dynamical mechanism to emulate cosmic acceleration., Comment: 13 pages, 9 figures: Revised version to be published in A&A (updated)

We use a kinematic parametrisation of the luminosity distance to measure the angular distribution on the sky of time derivatives of the scale factor, in particular the Hubble parameter H_0, the deceleration parameter q_0, and the jerk parameter j_0. We apply a recently published method to complement probing the inhomogeneity of the large-scale structure by means of the inhomogeneity in the cosmic expansion. This parametrisation is independent of the cosmological equation of state, which renders it adequate to test interpretations of the cosmic acceleration alternative to the cosmological constant. For the same analytical toy model of an inhomogeneous ensemble of homogenous pixels, we derive the backreaction term in j_0 due to the fluctuations of {H_0,q_0} and measure it to be of order 10^{-2} times the corresponding average over the pixels in the absence of backreaction. In agreement with that computed using a Lambda CDM parametrisation of the luminosity distance, the backreaction effect on q_0 remains below the detection threshold. Although the backreaction effect on j_0 is about ten times that on q_0, it is also below the detection threshold. Hence backreaction remains unobservable both in q_0 and in j_0., 11 pages, 5 figures: Revised version to be published in A&A. arXiv admin note: text overlap with arXiv:1512.07869

We explore the dynamics and evolution of the Universe at early and late times, focusing on both dark energy and extended gravity models and their astrophysical and cosmological consequences. Modified theories of gravity not only provide an alternative explanation for the recent expansion history of the universe, but they also offer a paradigm fundamentally distinct from the simplest dark energy models of cosmic acceleration. In this review, we perform a detailed theoretical and phenomenological analysis of different modified gravity models and investigate their consistency. We also consider the cosmological implications of well motivated physical models of the early universe with a particular emphasis on inflation and topological defects. Astrophysical and cosmological tests over a wide range of scales, from the solar system to the observable horizon, severely restrict the allowed models of the Universe. Here, we review several observational probes -- including gravitational lensing, galaxy clusters, cosmic microwave background temperature and polarization, supernova and baryon acoustic oscillations measurements -- and their relevance in constraining our cosmological description of the Universe., 94 pages, 14 figures. Review paper accepted for publication in a Special Issue of Symmetry. "Symmetry: Feature Papers 2016". V2: Matches published version, now 79 pages (new format)

We attempt to make a direct measurement of the weak lensing signal from the WMAP 7-year data. We apply the real-space implementation of the optimal quadratic estimator on the maps produced by the W-band Differencing Assemblies. We obtain a weak lensing amplitude parameter of $A_{L}=0.99\pm1.67$ after correcting for several sources of bias. The error budget includes a contribution from the bias removal procedure. Despite the demonstrated insensitivity of the real-space estimator to uncorrelated noise, we conclude that this detection is not statistically significant. We expect that a full-sky, higher-sensitivity experiment such as Planck will allow us to make a more significant measurement., Comment: 19 pages, 8 figures, 3 tables. Revised version to be published in PRD

We present constraints on the primordial power spectrum of adiabatic fluctuations using data from the 2008 Southern Survey of the Atacama Cosmology Telescope (ACT). The angular resolution of ACT provides sensitivity to scales beyond \ell = 1000 for resolution of multiple peaks in the primordial temperature power spectrum, which enables us to probe the primordial power spectrum of adiabatic scalar perturbations with wavenumbers up to k \simeq 0.2 Mpc^{-1}. We find no evidence for deviation from power-law fluctuations over two decades in scale. Matter fluctuations inferred from the primordial temperature power spectrum evolve over cosmic time and can be used to predict the matter power spectrum at late times; we illustrate the overlap of the matter power inferred from CMB measurements (which probe the power spectrum in the linear regime) with existing probes of galaxy clustering, cluster abundances and weak lensing constraints on the primordial power. This highlights the range of scales probed by current measurements of the matter power spectrum., Comment: 10 pages, 5 figures, submitted to ApJ

An incomplete sky coverage poses difficulties in the extraction of the weak lensing information from the CMB. We test the reconstruction of the weak lensing convergence from CMB maps to which masks of point sources have been applied. We use the quadratic estimator with a kernel with finite support acting in real space for a Planck simulation. We recover the lensing signal without significant loss of power or addition of spurious correlations, thus showing that masking defected pixels does not affect the reconstruction of the weak lensing convergence in real space.

We report the first detection of the gravitational lensing of the cosmic microwave background through a measurement of the four-point correlation function in the temperature maps made by the Atacama Cosmology Telescope. We verify our detection by calculating the levels of potential contaminants and performing a number of null tests. The resulting convergence power spectrum at 2-degree angular scales measures the amplitude of matter density fluctuations on comoving length scales of around 100 Mpc at redshifts around 0.5 to 3. The measured amplitude of the signal agrees with Lambda Cold Dark Matter cosmology predictions. Since the amplitude of the convergence power spectrum scales as the square of the amplitude of the density fluctuations, the 4-sigma detection of the lensing signal measures the amplitude of density fluctuations to 12%., Comment: 4 pages, 4 figures, replaced title and author list with version accepted by Physical Review Letters. Likelihood code can be downloaded from http://bccp.lbl.gov/~sudeep/ACTLensLike.html