The Standard Cosmology

These lectures provide an introductory review of big bang cosmology. I discuss the expanding Friedmann-Robertson-Walker universe, summarizing the observational evidence which has led to its adoption as the `standard' cosmological model and reviewing its basic properties. Subsequent lectures provide an overview of the early universe. The final lectures give an introduction to the inflationary universe, beginning with the motivating puzzles of the standard cosmology (the horizon and flatness problems) and ending with the inflationary production of quantum field fluctuations and their possible role in seeding the large-scale structure of the Universe.Comment: 49 pages, uuencoded postscript file (includes 7 figures), Fermilab-Conf-94/090-

Perturbations in a coupled scalar field cosmology

I analyze the density perturbations in a cosmological model with a scalar field coupled to ordinary matter, such as one obtains in string theory and in conformally transformed scalar-tensor theories. The spectrum of multipoles on the last scattering surface and the power spectrum at the present are compared with observations to derive bounds on the coupling constant and on the exponential potential slope. It is found that the acoustic peaks and the power spectrum are strongly sensitive to the model parameters. The models that best fit the galaxy spectrum and satisfy the cluster abundance test have energy density $\Omega_{\phi}\simeq 0.1$ and a scale factor expansion law $a\sim t^{p}, p\simeq 0.68$.Comment: 13 pages, 9 figures, minor revision, now figures are embedded in tex

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

Loop Corrections in Non-Linear Cosmological Perturbation Theory II. Two-point Statistics and Self-Similarity

We calculate the lowest-order non-linear contributions to the power spectrum, two-point correlation function, and smoothed variance of the density field, for Gaussian initial conditions and scale-free initial power spectra, $P(k) \sim k^n$. These results extend and in some cases correct previous work in the literature on cosmological perturbation theory. Comparing with the scaling behavior observed in N-body simulations, we find that the validity of non-linear perturbation theory depends strongly on the spectral index $n$. For $n<-1$, we find excellent agreement over scales where the variance \sigma^2(R) \la 10; however, for $n \geq -1$, perturbation theory predicts deviations from self-similar scaling (which increase with $n$) not seen in numerical simulations. This anomalous scaling suggests that the principal assumption underlying cosmological perturbation theory, that large-scale fields can be described perturbatively even when fluctuations are highly non-linear on small scales, breaks down beyond leading order for spectral indices $n \geq -1$. For $n < -1$, the power spectrum, variance, and correlation function in the scaling regime can be calculated using dimensional regularization.Comment: 48 pages, 19 figures, uses axodraw.sty; also available at http://fnas08.fnal.gov

Lensing and high-z supernova surveys

Gravitational lensing causes the distribution of observed brightnesses of standard candles at a given redshift to be highly non-gaussian. The distribution is strongly, and asymmetrically, peaked at a value less than the expected value in a homogeneous Robertson-Walker universe. Therefore, given any small sample of observations in an inhomogeneous universe, the most likely observed luminosity is at flux values less than the Robertson-Walker value. This paper explores the impact of this systematic error due to lensing upon surveys predicated on measuring standard candle brightnesses. We re-analyze recent results from the high-z supernova team (Riess et al. 1998), both when most of the matter in the universe is in the form of compact objects (represented by the empty-beam expression, corresponding to the maximal case of lensing), and when the matter is continuously distributed in galaxies. We find that the best-fit model remains unchanged (at Omega_m=0, Omega_Lambda=0.45), but the confidence contours change size and shape, becoming larger (and thus allowing a broader range of parameter space) and dropping towards higher values of matter density, Omega_m (or correspondingly, lower values of the cosmological constant, Omega_Lambda). These effects are slight when the matter is continuously distributed. However, the effects become considerably more important if most of the matter is in compact objects. For example, neglecting lensing, the Omega_m=0.5, Omega_Lambda=0.5 model is more than 2 sigma away from the best fit. In the empty-beam analysis, this cosmology is at 1 sigma.Comment: 11 pages, 3 ps figures. uses aaspp4.sty. accepted to ApJ Letters. includes analysis of lensing due to matter continuously distributed in galaxie

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