Evaluating the standard model of cosmology in light of large-scale anomalies in the cosmic microwave background

The establishment of the standard model of cosmology represents great observational and theoretical achievements; at the same time, possible deviations from the standard model are sought. In this thesis, two anomalies are studied:\ud \ud The late-time integrated Sachs-Wolfe effect---a few percent of the total temperature fluctuations generated by evolving gravitational potentials---is a signature of dark energy in a spatially flat universe. Its strongest detection comes from the average microwave background temperature in the sky directions of superclusters and supervoids seen in the Sloan Digital Sky Survey, which is claimed to be larger than expected. We compute the maximum expected average temperature signal by treating the signal due to large-scale structures as a Gaussian random field, and including correlations between different physical contributions to the temperature fluctuations and between different redshift ranges of the evolving gravitational potentials. Our model confirms that the observed average temperatures are unexpectedly large, but reduces the statistical significance of this discrepancy. Comparing with other measurements, none of which has yielded a detection with the same large discrepancy, our work suggests that a large signal is less unusual to occur than previously thought. \ud \ud The latter anomaly refers to a 7% asymmetry of fluctuation power between two halves of the sky found in full-sky maps of the microwave background temperature field. A common phenomenological model for this asymmetry is an overall dipole modulation of statistically isotropic fluctuations, which produces particular off-diagonal correlations between multipole coefficients. We compute these correlations and construct estimators for the amplitude and direction of the dipole modulation. Applying these estimators to various cut-sky temperature maps from Planck and WMAP data shows consistency with a dipole modulation, differing from a null signal at 2.5sigma, with an amplitude and direction consistent with previous fits based on the temperature fluctuation power. The signal is scale dependent, with a statistically significant amplitude at angular scales larger than 2 degrees. Future measurements of microwave background polarization and gravitational lensing can increase the significance of the signal. If the signal is not a statistical fluke in an isotropic Universe, it requires new physics beyond the standard model of cosmology