Fast and Reliable Time Delay Estimation of Strong Lens Systems Using Method of Smoothing and Cross-Correlation

The observable time delays between the multiple images of strong lensing systems with time variable sources can provide us with some valuable information to probe the expansion history of the Universe. Estimation of these time delays can be very challenging due to complexities of the observed data where there are seasonal gaps, various noises and systematics such as unknown microlensing effects. In this paper we introduce a novel approach to estimate the time delays for strong lensing systems implementing various statistical methods of data analysis including the method of smoothing and cross-correlation. The method we introduce in this paper has been recently used in TDC0 and TDC1 Strong Lens Time Delay Challenges and has shown its power in reliable and precise estimation of time delays dealing with data with different complexities.Comment: 23 pages, 9 figures, 3 tables, discussions extended, references added, results unchanged, matches final version published in Ap

Unveiling acoustic physics of the CMB using nonparametric estimation of the temperature angular power spectrum for Planck

Estimation of the angular power spectrum is one of the important steps in Cosmic Microwave Background (CMB) data analysis. Here, we present a nonparametric estimate of the temperature angular power spectrum for the Planck 2013 CMB data. The method implemented in this work is model-independent, and allows the data, rather than the model, to dictate the fit. Since one of the main targets of our analysis is to test the consistency of the $\Lambda$CDM model with Planck 2013 data, we use the nuisance parameters associated with the best-fit $\Lambda$CDM angular power spectrum to remove foreground contributions from the data at multipoles $\ell \geq50$. We thus obtain a combined angular power spectrum data set together with the full covariance matrix, appropriately weighted over frequency channels. Our subsequent nonparametric analysis resolves six peaks (and five dips) up to $\ell \sim1850$ in the temperature angular power spectrum. We present uncertainties in the peak/dip locations and heights at the $95\%$ confidence level. We further show how these reflect the harmonicity of acoustic peaks, and can be used for acoustic scale estimation. Based on this nonparametric formalism, we found the best-fit $\Lambda$CDM model to be at $36\%$ confidence distance from the center of the nonparametric confidence set -- this is considerably larger than the confidence distance ($9\%$) derived earlier from a similar analysis of the WMAP 7-year data. Another interesting result of our analysis is that at low multipoles, the Planck data do not suggest any upturn, contrary to the expectation based on the integrated Sachs-Wolfe contribution in the best-fit $\Lambda$CDM cosmology.Comment: 15 pages, 8 figures, 2 table

Evolution of the Cosmic Microwave Background power spectrum across Wilkinson Microwave Anisotropy Probe data releases: A nonparametric analysis

Using a nonparametric function estimation methodology, we present a comparative analysis of the Wilkinson Microwave Anisotropy Probe (WMAP) 1-, 3-, 5-, and 7-year data releases for the cosmic microwave background (CMB) angular power spectrum with respect to the following key questions. (1) How well is the power spectrum determined by the data alone? (2) How well is the ΛCDM model supported by a model-independent, data-driven analysis? (3) What are the realistic uncertainties on peak/dip locations and heights? Our results show that the height of the power spectrum is well determined by data alone for multipole l approximately less than 546 (1-year), 667 (3-year), 804 (5-year), and 842 (7-year data). We show that parametric fits based on the ΛCDM model are remarkably close to our nonparametric fits in l-regions where data are sufficiently precise. In contrast, the power spectrum for an HΛCDM model is progressively pushed away from our nonparametric fit as data quality improves with successive data realizations, suggesting incompatibility of this particular cosmological model with respect to the WMAP data sets. We present uncertainties on peak/dip locations and heights at the 95% (2σ) level of confidence and show how these uncertainties translate into hyperbolic "bands" on the acoustic scale (lA ) and peak shift (Φ m ) parameters. Based on the confidence set for the 7-year data, we argue that the low-l upturn in the CMB power spectrum cannot be ruled out at any confidence level in excess of about 10% (≈0.12σ). Additional outcomes of this work are a numerical formulation for minimization of a noise-weighted risk function subject to monotonicity constraints, a prescription for obtaining nonparametric fits that are closer to cosmological expectations on smoothness, and a method for sampling cosmologically meaningful power spectrum variations from the confidence set of a nonparametric fit

Evolution of the CMB Power Spectrum Across WMAP Data Releases: A Nonparametric Analysis

Using a nonparametric function estimation methodology, we present a comparative analysis of the WMAP 1-, 3-, 5-, and 7-year data releases for the CMB angular power spectrum with respect to the following key questions: (a) How well is the power spectrum determined by the data alone? (b) How well is the $\Lambda$CDM model supported by a model-independent, data-driven analysis? (c) What are the realistic uncertainties on peak/dip locations and heights? Our results show that the height of the power spectrum is well determined by data alone for multipole l approximately less than 546 (1-year), 667 (3-year), 804 (5-year), and 842 (7-year data). We show that parametric fits based on the $\Lambda$CDM model are remarkably close to our nonparametric fits in $l$-regions where data are sufficiently precise. In contrast, the power spectrum for an H$\Lambda$CDM model gets progressively pushed away from our nonparametric fit as data quality improves with successive data realizations, suggesting incompatibility of this particular cosmological model with respect to the WMAP data sets. We present uncertainties on peak/dip locations and heights at the 95% ($2 \sigma$) level of confidence, and show how these uncertainties translate into hyperbolic "bands" on the acoustic scale ($l_A$) and peak shift ($\phi_m$) parameters. Based on the confidence set for the 7-year data, we argue that the low-l up-turn in the CMB power spectrum cannot be ruled out at any confidence level in excess of about 10% ($\approx 0.12 \sigma$). Additional outcomes of this work are a numerical formulation for minimization of a noise-weighted risk function subject to monotonicity constraints, a prescription for obtaining nonparametric fits that are closer to cosmological expectations on smoothness, and a method for sampling cosmologically meaningful power spectrum variations from the confidence set of a nonparametric fit