List of Figures

	Figure 1: A historical time-line showing the major evolutionary stages of our Universe according to the standard model, from the earliest moments of the Planck era to the present. The horizontal axis represents logarithmic time in seconds (or equivalently energy in electron-Volts or temperature in Kelvin), and the solid red line roughly models the radius of the Universe, showing the different rates of expansion at different times: exponential during inflation, shallow power law during the radiation dominated era, and a somewhat steeper power law during the current matter dominated phase.
	Figure 2: Schematic depicting the general sequence of events in the post-recombination Universe. The solid and dotted lines potentially track the Jeans mass of the average baryonic gas component from the recombination epoch at $z ∼ 103$ to the current time. A residual ionization fraction of $nH+ ∕nH ∼ 10− 4$ following recombination allows for Compton interactions with photons to $z ∼ 200$ , during which the Jeans mass remains constant at $5 10 M ⊙$ . The Jeans mass then decreases as the Universe expands adiabatically until the first collapsed structures form sufficient amounts of hydrogen molecules to trigger a cooling instability and produce pop III stars at $z ∼ 20$ . Star formation activity can then reheat the Universe and raise the mean Jeans mass to above $108M ⊙$ . This reheating could affect the subsequent development of structures such as galaxies and the observed Ly $α$ clouds.
	Figure 3: Contour plot of the Bianchi type IX potential $V$ , where $β ±$ are the anisotropy canonical coordinates. Seven level surfaces are shown at equally spaced decades ranging from 10^–1 to 10⁵. For large isocontours ( $V > 1$ ), the potential is open and exhibits a strong triangular symmetry with three narrow channels extending to spatial infinity. For $V < 1$ , the potential closes and is approximately circular for $β ± ≪ 1$ .
	Figure 4: Fractal structure of the transition between reflected and captured states for colliding kink-antikink solitons in the parameter space of impact velocity for a $λ (ϕ2 − 1)2$ scalar field potential. The top image (a) shows the 2-bounce windows in dark with the rightmost region ( $v∕c > 0.25$ ) representing the single-bounce regime above which no captured state exists, and the leftmost white region ( $v∕c < 0.19$ ) representing the captured state below which no reflection windows exist. Between these two marker velocities, there are 2-bounce reflection states of decreasing widths separated by regions of bion formation. Zooming in on the domain outlined by the dashed box, a self-similar structure is apparent in the middle image (b), where now the dark regions represent 3-bounce windows of decreasing widths. Zooming in once again on the boundaries of these 3-bounce windows, a similar structure is found as shown in the bottom image (c) but with 4-bounce reflection windows. This pattern of self-similarity characterized by $n$ -bounce windows is observed at all scales investigated numerically.
	Figure 5: Image sequence of the scalar field from a 2D calculation showing the interaction of two deflagration systems (one planar wall propagating from the right side, and one spherical bubble nucleating from the center). The physical size of the grid is set to 1000 × 1000 fm and resolved by 512 × 512 zones. The run time of the simulation is about two sound crossing times, where the sound speed is $c∕ √3-$ , so the shock fronts leading the condensing phase fronts travel across the grid twice. The hot quark (cold hadron) phases have smaller (larger) scalar field values and are represented by black (color) in the colormap.
	Figure 6: Image sequence of the scalar field from a 2D calculation showing the interaction of two detonation systems (one planar wall propagating from the right side, and one spherical bubble nucleating from the center). The physical size of the grid is set to 1000 × 1000 fm and resolved by 1024 × 1024 zones. The run time of the simulation is about two sound crossing times.
	Figure 7: Image sequence of the scalar field from a 2D calculation showing the interaction of shock and rarefaction waves with a deflagration wall (initiated at the left side) and a detonation wall (starting from the right). A shock and rarefaction wave travel to the right and left, respectively, from the temperature discontinuity located initially at the grid center (the right half of the grid is at a higher temperature). The physical size of the domain is set to 1806.1 × 451.53 fm and resolved by 2048 × 512 zones. The run time of the simulation is about two sound crossing times.
	Figure 8: Historical time-line of the cosmic microwave background radiation showing the start of photon/nuclei combination, the surface of last scattering (SoLS), and the epoch of reionization due to early star formation. The times are represented in years (to the right) and redshift (to the left). Primary anisotropies are collectively attributed to the early effects at the last scattering surface and the large scale Sachs–Wolfe effect. Secondary anisotropies arise from path integration effects, reionization smearing, and higher order interactions with the evolving nonlinear structures at relatively low redshifts.
	Figure 9: Temperature fluctuations ( $ΔT ∕T$ ) in the CMBR due to the primary Sachs–Wolfe (SW) effect and secondary integrated SW, Doppler, and Thomson scattering effects in a critically closed model. The top two plates are results with no reionization and baryon fractions 0.02 (plate 1, $∘ ∘ 4 × 4$ , $−5 ΔT ∕T\|rms = 2.8 × 10$ ), and 0.2 (plate 2, $∘ ∘ 8 × 8$ , $−5 ΔT ∕T \|rms = 3.4 × 10$ ). The bottom two plates are results from an “early and gradual” reionization scenario of decaying neutrinos with baryon fraction 0.02 (plate 3, $4∘ × 4∘$ , $ΔT ∕T \|rms = 1.3 × 10−5$ ; and plate 4, $8∘ × 8∘$ , $ΔT ∕T \|rms = 1.4 × 10−5$ ). If reionization occurs, the scattering probability increases and anisotropies are damped with each scattering event. At the same time, matter structures develop large bulk motions relative to the comoving background and induce Doppler shifts on the CMB. The imprint of this effect from last scattering can be a significant fraction of primary anisotropies.
	Figure 10: Secondary anisotropies from the proper motion of galaxy clusters across the sky and Rees–Sciama effects are presented in the upper-left image over $8∘ × 8∘$ in a critically closed Cold Dark Matter model. The corresponding column density of matter over the same region ( $z = 0.43$ , $Δz = 0.025$ ) is displayed in the upper-right, clearly showing the dipolar nature of the proper motion effect. Anisotropies arising from decaying potentials in an open $Ω = 0.3$ model over a scale of $8∘ × 8∘$ are shown in the bottom left image, along with the gravitational potential over the same region ( $z = 0.33$ , $Δz = 0.03$ ) in the bottom right, demonstrating a clear anti-correlation. Maximum temperature fluctuations in each simulation are $ΔT ∕T = (5 × 10− 7, 1.0 × 10− 6)$ respectvely. Secondary anisotropies are dominated by decaying potentials at large scales, but all three sources (decaying potential, proper motion, and R-S) produce signatures of order 10^–6.
	Figure 11: Distribution of the gas density at redshift $z = 3$ from a numerical hydrodynamics simulation of the Ly $α$ forest with a CDM spectrum normalized to second year COBE observations, Hubble parameter of $h = 0.5$ , a comoving box size of 9.6 Mpc, and baryonic density of $Ωb = 0.06$ composed of 76% hydrogen and 24% helium. The region shown is 2.4 Mpc (proper) on a side. The isosurfaces represent baryons at ten times the mean density and are color coded to the gas temperature (dark blue = 3 × 10⁴ K, light blue = 3 × 10⁵ K). The higher density contours trace out isolated spherical structures typically found at the intersections of the filaments. A single random slice through the cube is also shown, with the baryonic overdensity represented by a rainbow-like color map changing from black (minimum) to red (maximum). The He⁺ mass fraction is shown with a wire mesh in this same slice. To emphasize fine structure in the minivoids, the mass fraction in the overdense regions has been rescaled by the gas overdensity wherever it exceeds unity.
	Figure 12: Two different model simulations of cosmological sheets are presented: a six species model including only atomic line cooling (left), and a nine species model including also hydrogen molecules (right). The evolution sequences in the images show the baryonic overdensity and gas temperature at three redshifts following the initial collapse at $z = 5$ . In each figure, the vertical axis is 32 kpc long (parallel to the plane of collapse) and the horizontal axis extends to 4 Mpc on a logarithmic scale to emphasize the central structures. Differences in the two cases are observed in the cold pancake layer and the cooling flows between the shock front and the cold central layer. When the central layer fragments, the thickness of the cold gas layer in the six (nine) species case grows to 3 (0.3) kpc and the surface density evolves with a dominant transverse mode corresponding to a scale of approximately 8 (1) kpc. Assuming a symmetric distribution of matter along the second transverse direction, the fragment masses are approximately 10⁷ (10⁵) solar masses.