Loop Corrections in Non-Linear Cosmological Perturbation Theory

Using a diagrammatic approach to Eulerian perturbation theory, we analytically calculate the variance and skewness of the density and velocity divergence induced by gravitational evolution from Gaussian initial conditions, including corrections *beyond* leading order. Except for the power spectrum, previous calculations in cosmological perturbation theory have been confined to leading order (tree level)-we extend these to include loop corrections. For scale-free initial power spectra, the one-loop variance \sigma^2 = \sigma^2_l + 1.82 \sigma^4_l and the skewness S_3 = 34/7 + 9.8 \sigma^2_l, where \sigma_l is the rms fluctuation of the linear density field. We also compute loop corrections to the variance, skewness, and kurtosis for several non-linear approximation schemes, where the calculation can be easily generalized to 1-point cumulants of higher order and arbitrary number of loops. We find that the Zel'dovich approximation gives the best approximation to the loop corrections of exact perturbation theory, followed by the Linear Potential approximation (LPA) and the Frozen Flow approximation (FFA), in qualitative agreement with the relative behavior of tree-level results. In LPA and FFA, loop corrections are infrared divergent for spectral indices n < 0; this is related to the breaking of Galilean invariance in these schemes.Comment: 53 pages, uuencoded and gzipped postscript file, 20 figures, 25 tables, also available at http://fnas08.fnal.gov/cumu.u

Weak Gravitational Lensing by Voids

We consider the prospects for detecting weak gravitational lensing by underdensities (voids) in the large-scale matter distribution. We derive the basic expressions for magnification and distortion by spherical voids. Clustering of the background sources and cosmic variance are the main factors which limit in principle the detection of lensing by voids. We conclude that only voids with radii larger than $\sim 100$ \hm have lensing signal to noise larger than unity.Comment: 12 pages, 7 figures, uses mn-1_4.sty file, submitted to MNRA

Constraining Dark Energy with Clusters: Complementarity with Other Probes

The Figure of Merit Science Working Group (FoMSWG) recently forecast the constraints on dark energy that will be achieved prior to the Joint Dark Energy Mission (JDEM) by ground-based experiments that exploit baryon acoustic oscillations, type Ia supernovae, and weak gravitational lensing. We show that cluster counts from on-going and near-future surveys should provide robust, complementary dark energy constraints. In particular, we find that optimally combined optical and Sunyaev-Zel'dovich effect cluster surveys should improve the Dark Energy Task Force (DETF) figure of merit for pre-JDEM projects by a factor of two even without prior knowledge of the nuisance parameters in the cluster mass-observable relation. Comparable improvements are achieved in the forecast precision of parameters specifying the principal component description of the dark energy equation of state parameter as well as in the growth index gamma. These results indicate that cluster counts can play an important complementary role in constraining dark energy and modified gravity even if the associated systematic errors are not strongly controlled.Comment: 6 pages, 3 figures, accepted to Phys. Rev. D. Discussion section adde

Halo Model Analysis of Cluster Statistics

We use the halo model formalism to provide expressions for cluster abundances and bias, as well as estimates for the correlation matrix between these observables. Off-diagonal elements due to scatter in the mass tracer scaling with mass are included, as are observational effects such as biases/scatter in the data, detection rates (completeness), and false detections (purity). We apply the formalism to a hypothetical volume limited optical survey where the cluster mass tracer is chosen to be the number of member galaxies assigned to a cluster. Such a survey can strongly constrain $\sigma_8$ ($\Delta\sigma_8\approx 0.05$), the power law index $\alpha$ where $= 1+(m/M_1)^\alpha$ ($\Delta\alpha\approx0.03$), and perhaps even the Hubble parameter ($\Delta h\approx 0.07$). We find cluster abundances and bias not well suited for constraining $\Omega_m$ or the amplitude $M_1$. We also find that without bias information $\sigma_8$ and $\alpha$ are degenerate, implying constraints on the former are strongly dependent on priors used for the latter and vice-versa. The degeneracy stems from an intrinsic scaling relation of the halo mass function, and hence it should be present regardless of the mass tracer used in the survey.Comment: 27 pages, 11 figures, references adde

Cosmological constraints on pseudo-Nambu-Goldstone bosons

Particle physics models with pseudo-Nambu-Goldstone bosons (PNGBs) are characterized by two mass scales: a global spontaneous symmetry breaking scale, f, and a soft (explicit) symmetry breaking scale, Lambda. General model insensitive constraints were studied on this 2-D parameter space arising from the cosmological and astrophysical effects of PNGBs. In particular, constraints were studied arising from vacuum misalignment and thermal production of PNGBs, topological defects, and the cosmological effects of PNGB decay products, as well as astrophysical constraints from stellar PNGB emission. Bounds on the Peccei-Quinn axion scale, 10(exp 10) GeV approx. = or less than f sub pq approx. = or less than 10(exp 10) to 10(exp 12) GeV, emerge as a special case, where the soft breaking scale is fixed at Lambda sub QCD approx. = 100 MeV

Cosmic microwave background and large-scale structure constraints on a simple quintessential inflation model

We derive constraints on a simple quintessential inflation model, based on a spontaneously broken Phi^4 theory, imposed by the Wilkinson Microwave Anisotropy Probe three-year data (WMAP3) and by galaxy clustering results from the Sloan Digital Sky Survey(SDSS). We find that the scale of symmetry breaking must be larger than about 3 Planck masses in order for inflation to generate acceptable values of the scalar spectral index and of the tensor-to-scalar ratio. We also show that the resulting quintessence equation-of-state can evolve rapidly at recent times and hence can potentially be distinguished from a simple cosmological constant in this parameter regime.Comment: 5 pages, 2 figure