Title: Cosmology with Weak Lensing Peaks
Description: Recent studies have shown that the number counts of peaks in weak lensing (WL) surveys contain significant cosmological information. Motivated by this finding, in the first part of the thesis, we address two questions: (i) what is the physical origin of WL peaks; and (ii) how much information do the peaks contain beyond the traditional cosmological WL observable (the power spectrum). To investigate the first question, we use a suite of ray-tracing N-body simulations, in which we identify individual dark matter halos. We study the halos' contribution to the peaks. We find that high peaks are typically dominated by a single massive halo, while low peaks are created by galaxy shape noise, but with an important contribution from a line-of-sight projection of typically 4-8 halos. For the second question, we first compare the cosmological peak count distributions to those in a Gaussian random field. We find significant differences, both in the peak-count distributions themselves, as well as in how the distributions depend on cosmology, demonstrating that the peaks contain non-Gaussian information.

To explicitly quantify the information content of the peaks beyond the power spectrum, we use the Fisher matrix method to forecast errors in the three-dimensional parameters space (σ_8, w, Ω_m). We find that when we combine the peaks and the power spectrum, the marginalized errors are a factor of about two smaller than from power spectrum alone. In the second part of the thesis, we address a major theoretical systematic error: the presence of baryons -- not included in the N-body simulations -- can affect the WL statistics (both peaks and power spectrum), and the inferred cosmological parameters. We apply a simplified model, which mimics the cooling and condensation of baryons at the centers of dark matter halos. In particular, we manually steepen the density profile of each dark matter halo identified in the N-body simulations, and repeat the ray-tracing procedure create WL maps in mock "baryonic'' universes. We then compare the peak count distributions and power spectra in these baryonic models to those from the pure DM models.

We find that there is a large increase in the number of high peaks, but low peaks -- which contain most of the cosmological information -- are robust to baryons. Similarly, we find that the high--l power spectrum is increased, but the change in the low--l power spectrum is relatively modest. We then utilize a Monte Carlo approach to compute the joint, and in general, biased constraints on σ_8, w, Ω_m when the baryonic model is fit by the pure DM models. We find that: (i) constraints obtained from low peaks are nearly unbiased; (ii) high peaks yield large biases, but in different directions in parameter space than the biases from the power spectrum. Our first finding suggests it may be advantageous to use low peaks for analysis until the baryonic processes are better understood. However, our second finding suggests the possibility of "self-calibration'': simultaneously fitting astrophysical "nuisance'' parameters (describing lensing halo profiles) with cosmological parameters.