1. PREFACE: THE FRONTIER OF SMALL-SCALE STRUCTURE

The detection of cosmic microwave background (CMB) anisotropies (Bennett et al. 1996; de Bernardis et al. 2000; Hanany et al. 2000) confirmed the notion that the present large-scale structure in the universe originated from small-amplitude density fluctuations at early times. Due to the natural instability of gravity, regions that were denser than average collapsed and formed bound objects, first on small spatial scales and later on larger and larger scales. The present-day abundance of bound objects, such as galaxies and X-ray clusters, can be explained based on an appropriate extrapolation of the detected anisotropies to smaller scales. Existing observations with the Hubble Space Telescope (e.g., Steidel et al. 1996; Madau et al. 1996; Chen et al. 1999; Clements et al. 1999) and ground-based telescopes (Lowenthal et al. 1997; Dey et al. 1998; Hu et al. 1998, 1999; Spinrad et al. 1998; Steidel et al. 1999), have constrained the evolution of galaxies and their stellar content at z 6. However, in the bottom-up hierarchy of the popular Cold Dark Matter (CDM) cosmologies, galaxies were assembled out of building blocks of smaller mass. The elementary building blocks, i.e., the first gaseous objects to form, acquired a total mass of order the Jeans mass (~ 10⁴ M), below which gas pressure opposed gravity and prevented collapse (Couchman & Rees 1986; Haiman & Loeb 1997; Ostriker & Gnedin 1996). In variants of the standard CDM model, these basic building blocks first formed at z ~ 15-30.

An important qualitative outcome of the microwave anisotropy data is the confirmation that the universe started out simple. It was by and large homogeneous and isotropic with small fluctuations that can be described by linear perturbation analysis. The current universe is clumpy and complicated. Hence, the arrow of time in cosmic history also describes the progression from simplicity to complexity (see Figure 1). While the conditions in the early universe can be summarized on a single sheet of paper, the mere description of the physical and biological structures found in the present-day universe cannot be captured by thousands of books in our libraries. The formation of the first bound objects marks the central milestone in the transition from simplicity to complexity. Pedagogically, it would seem only natural to attempt to understand this epoch before we try to explain the present-day universe. Historically, however, most of the astronomical literature focused on the local universe and has only been shifting recently to the early universe. This violation of the pedagogical rule was forced upon us by the limited state of our technology; observation of earlier cosmic times requires detection of distant sources, which is feasible only with large telescopes and highly-sensitive instrumentation.

Figure 1. Milestones in the evolution of the universe from simplicity to complexity. The ``end of the dark ages'' bridges between the recombination epoch probed by microwave anisotropy experiments (z ~ 103) and the horizon of current observations (z ~ 5-6).

For these reasons, advances in technology are likely to make the high redshift universe an important frontier of cosmology over the coming decade. This effort will involve large (30 meter) ground-based telescopes and will culminate in the launch of the successor to the Hubble Space Telescope, called Next Generation Space Telescope (NGST). Figure 2 shows an artist's illustration of this telescope which is currently planned for launch in 2009. NGST will image the first sources of light that formed in the universe. With its exceptional sub-nJy (1 nJy = 10^-32erg cm^-2 s^-1 Hz^-1) sensitivity in the 1-3.5 µm infrared regime, NGST is ideally suited for probing optical-UV emission from sources at redshifts 10, just when popular Cold Dark Matter models for structure formation predict the first baryonic objects to have collapsed.

Figure 2. Artist's illustration of one of the current designs (GSFC) of the Next Generation Space Telescope. More details about the telescope can be found at http://ngst.gsfc.nasa.gov/.

The initial mass function of the first stars and black holes is therefore determined by a simple set of initial conditions (although subsequent generations of stars are affected by feedback from photoionization heating and metal enrichment). While the early evolution of the seed density fluctuations can be fully described analytically, the collapse and fragmentation of nonlinear structure must be simulated numerically. The first baryonic objects connect the simple initial state of the universe to its complex current state, and their study with hydrodynamic simulations (e.g., Abel et al. 1998a, Abel, Bryan, & Norman 2000; Bromm, Coppi, & Larson 1999) and with future telescopes such as NGST offers the key to advancing our knowledge on the formation physics of stars and massive black holes.

The first light from stars and quasars ended the ``dark ages'' <sup>(2)</sup> of the universe and initiated a ``renaissance of enlightenment'' in the otherwise fading glow of the microwave background (see Figure 1). It is easy to see why the mere conversion of trace amounts of gas into stars or black holes at this early epoch could have had a dramatic effect on the ionization state and temperature of the rest of the gas in the universe. Nuclear fusion releases ~ 7 × 10⁶ eV per hydrogen atom, and thin-disk accretion onto a Schwarzschild black hole releases ten times more energy; however, the ionization of hydrogen requires only 13.6 eV. It is therefore sufficient to convert a small fraction, ~ 10^-5 of the total baryonic mass into stars or black holes in order to ionize the rest of the universe. (The actual required fraction is higher by at least an order of magnitude [Bromm, Kudritzky, & Loeb 2000] because only some of the emitted photons are above the ionization threshold of 13.6 eV and because each hydrogen atom recombines more than once at redshifts z 7). Recent calculations of structure formation in popular CDM cosmologies imply that the universe was ionized at z ~ 7-12 (Haiman & Loeb 1998, 1999b, c; Gnedin & Ostriker 1997; Chiu & Ostriker 2000; Gnedin 2000a). Current observations are at the threshold of probing this epoch of reionization, given the fact that galaxies and quasars at redshifts ~ 6 are being discovered (Fan et al. 2000; Stern et al. 2000). One of these sources is a bright quasar at z = 5.8 whose spectrum is shown in Figure 3. The plot indicates that there is transmitted flux short-ward of the Ly wavelength at the quasar redshift. The optical depth at these wavelengths of the uniform cosmic gas in the intergalactic medium is however (Gunn & Peterson 1965),

(1)

where H 100h km s^-1 Mpc^-1 _m^1/2 (1 + z_s)^3/2 is the Hubble parameter at the source redshift z_s, f = 0.4162 and = 1216Å are the oscillator strength and the wavelength of the Ly transition; n_{H I}(z_s) is the neutral hydrogen density at the source redshift (assuming primordial abundances); _m and _b are the present-day density parameters of all matter and of baryons, respectively; and x_{H I} is the average fraction of neutral hydrogen. In the second equality we have implicitly considered high redshifts (see equations (9) and (10) in Section 2.1). Modeling of the transmitted flux (Fan et al. 2000) implies _s < 0.5 or x_{H I} 10^-6, i.e., the low-density gas throughout the universe is fully ionized at z = 5.8! One of the important challenges for future observations will be to identify when and how the intergalactic medium was ionized. Theoretical calculations (see Section 6.3.1) imply that such observations are just around the corner.

Figure 3. Optical spectrum of the highest-redshift known quasar at z = 5.8, discovered by the Sloan Digital Sky Survey (Fan et al. 2000).

Figure 4 shows schematically the various stages in a theoretical scenario for the history of hydrogen reionization in the intergalactic medium. The first gaseous clouds collapse at redshifts ~ 20-30 and fragment into stars due to molecular hydrogen (H₂) cooling. However, H₂ is fragile and can be easily dissociated by a small flux of UV radiation. Hence the bulk of the radiation that ionized the universe is emitted from galaxies with a virial temperature 10⁴ K, where atomic cooling is effective and allows the gas to fragment (see the end of Section 3.3 for an alternative scenario).

Figure 4. Stages in the reionization of hydrogen in the intergalactic medium.

Since recent observations confine the standard set of cosmological parameters to a relatively narrow range, we assume a CDM cosmology with a particular standard set of parameters in the quantitative results in this review. For the contributions to the energy density, we assume ratios relative to the critical density of _m = 0.3, = 0.7, and _b = 0.045, for matter, vacuum (cosmological constant), and baryons, respectively. We also assume a Hubble constant H₀ = 70 km s^-1Mpc^-1, and a primordial scale invariant (n = 1) power spectrum with ₈ = 0.9, where ₈ is the root-mean-square amplitude of mass fluctuations in spheres of radius 8 h^-1 Mpc. These parameter values are based primarily on the following observational results: CMB temperature anisotropy measurements on large scales (Bennett et al. 1996) and on the scale of ~ 1° (Lange et al. 2000; Balbi et al. 2000); the abundance of galaxy clusters locally (Viana & Liddle 1999; Pen 1998; Eke, Cole, & Frenk 1996) and as a function of redshift (Bahcall & Fan 1998; Eke, Cole, Frenk, & Henry 1998); the baryon density inferred from big bang nucleosynthesis (see the review by Tytler et al. 2000); distance measurements used to derive the Hubble constant (Mould et al. 2000; Jha et al. 1999; Tonry et al. 1997); and indications of cosmic acceleration from distances based on type Ia supernovae (Perlmutter et al. 1999; Riess et al. 1998).

This review summarizes recent theoretical advances in understanding the physics of the first generation of cosmic structures. Although the literature on this subject extends all the way back to the sixties (Saslaw & Zipoy 1967, Peebles & Dicke 1968, Hirasawa 1969, Matsuda et al. 1969, Hutchins 1976, Silk 1983, Palla et al. 1983, Lepp & Shull 1984, Couchman 1985, Couchman & Rees 1986, Lahav 1986), this review focuses on the progress made over the past decade in the modern context of CDM cosmologies.

² The use of this term in the cosmological context was coined by Sir Martin Rees. Back.