Annu. Rev. Astron. Astrophys. 1988. 26: 631-86
Copyright © 1988 by . All rights reserved

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The results on large-scale structure presented above cause difficulties for theories of structure formation when considered together with explanations of the structure on smaller scales (galaxy correlations and properties) and the absence of structure in the microwave background. Both the quantitative measure of the clustering of clusters implied by the strong cluster correlation function, with a correlation scale of 25h-1 Mpc, and the suggested bulk velocities on large scales are difficult for most current models to explain.

9.1. Model Parameters

Before summarizing the status of currently discussed models for the formation of structure, I list some of the fundamental parameters that must be assumed for any model. A number of parameters can be adjusted to fit the observations, but this welcome freedom is also a cause of concern in interpreting the significance of the results.

Some of the free parameters are the following:

  1. The value of Omega (0.2 ltapprox Omega ltapprox 1).

  2. The value of the cosmological constant Lambda (Lambda = 0 or neq 0).

  3. The nature of the dark matter (Baryons? Hot dark matter, e.g. ~ 30-eV neutrinos? Cold dark matter, e.g. axions or > keV photinos? Unstable dark matter? Mixture of some of the above? Note that only the baryons and leptons are currently known to exist).

  4. The origin and nature of the initial density fluctuations (Inflation and Gaussian fluctuations? Cosmic strings and non-Gaussian fluctuations? Adiabatic or isothermal? Power-law initial spectrum? What slope?).

  5. The effect of nongravitational processes, which may dominate the model (Explosions? Cosmic strings?).

  6. Does mass follow the observed light? (or is our basic interpretation of observations greatly complicated by some kind of biasing? How is it biased?)

Even with the large choice of parameters available, no single elegant model (i.e. one excluding special combinations of particles, fluctuation spectra, or Lambda neq 0) has yet been proposed that can explain all the observations. Some frustration with available "standard" models motivates new "nonstandard" ideas such as explosions or cosmic strings as a means of explaining the universal structure.

I briefly summarize below the currently available models. For more detailed reviews, see Peebles (1988a, b), Ostriker (1988), White et al. (1987a), Bond (1987), Dekel (1987), Primack et al. (1986), Zeldovich et al. (1982), and references therein.

I divide the models into the following categories:

  1. "Standard" Gaussian Fluctuation Models

  2. Non-Gaussian fluctuation Models

  3. Explosions

9.2. "Standard" Gaussian Fluctuation Models

9.2.1   BARYONIC MATTER   Pure baryonic models of the Universe have not been popular in recent years mainly because of two limitations: the limit imposed on the baryonic mean mass density, Omegab < 0.2, by standard big-bang nucleosynthesis (e.g. review by Audouze 1987), which would then require an open universe (or, alternatively, the consideration of non-standard nucleosynthesis theories; e.g. Audouze 1987); and the observed isotropy limit of the microwave background, T / T < 10-4 on a 4.5' scale (Uson & Wilkinson 1984), which implies density fluctuations too small to form galaxies. However, revived ideas of isocurvature fluctuations in an open baryonic universe have been recently considered (Peebles 1987a, b, 1988a) and the model is now fair game for further investigations. The advantages of "What you see is what you get" (i.e. Omega appeq 0.2 as observed, and only baryons, with no unknown particles) may be more important than the elegance of the solution.

9.2.2   COLD DARK MATTER (CDM)   If one requires that Omega = 1 as demanded by inflation, then CDM is the current leading model [although it was hot dark matter (HDM) just a few years ago . . .]. The assumptions in CDM models are simple and are consistent with inflation, and the number of free parameters is small (White et al. 1987a, b, Blumenthal et al. 1984, and references therein). The model agrees well with observations on small scales when a biased galaxy formation scenario is introduced (Rees 1985, Bardeen et al. 1986, White et al. 1987b, Dekel & Rees 1987). In this scenario, galaxies form only at high-density peaks of the matter distribution, with the galaxy correlation function about 20 times stronger than the underlying mass correlation: xigg(r) appeq 20 xim. Many observations on small scales can then be matched by a biased CDM model (e.g. galaxy correlation function, flat rotation curves of galaxies, Tully-Fisher-type relations for galaxies, velocities on small scale, number density of galaxy clusters; see references above). The large-scale structure results discussed in this review, however, constitute a difficulty for CDM. Considerable evidence for structure on scales gtapprox 30h-1 Mpc has now been accumulated by a number of investigators; this large-scale structure (and velocity) cannot be matched by unadorned CDM models, which do not produce enough power on large scales (gtapprox 20h-1 Mpc). If these largest scale results are confirmed by new and deeper observations, it will be damaging to the simplest CDM models.

Other testable predictions of CDM include flat rotation curves of galaxies to very large scales (~ 0.5h-1 Mpc) (Frenk et al. 1985), the existence of matter in voids (due to the requirement of a biased galaxy formation process in which matter is considerably less clumped than galaxies), and a highly isotropic microwave background on large scales (T / T < 10-5). Observations of falling rotation curves at scales ltapprox 0.5h-1 Mpc, or strong limits on the emptiness of some voids, or a detection of fluctuations T / T gtapprox 10-5 in the microwave background on large scales [e.g. see Davies et al. (1987) for a possible detection] would also constitute serious difficulties for CDM.

9.2.3   HOT DARK MATTER (HDM)   HDM models with matter in the form of massive neutrinos that can account for some of the large-scale structure observations (pancakes, filaments, voids; Zeldovich et al. 1982) were abandoned a few years ago when N-body simulations and analytic models suggested that it would be difficult to form galaxies at high redshifts without overproducing clusters and large-scale structure. However, HDM with antibiasing, i.e. suppressing galaxy formation at high-density regions, may still be a possibility (e.g. Braun et al. 1987), although large peculiar velocities and excessive X-ray emission from massive clusters may still be problems for this model (White et al. 1984).

9.2.4   HYBRID SCENARIOS   Hybrid scenarios attempt to combine, in a somewhat ad hoc manner, CDM models on small scales and HDM models on large scales (e.g. Barnes et al. 1985, Dekel 1984, Dekel & Aarseth 1984). In these scenarios, galaxies and large-scale structure may form from different components of the density fluctuation. The model can involve two types of dark matter (baryonic and nonbaryonic) or two types of initial fluctuations (adiabatic and isothermal) [e.g. see Blumenthal et al. (1988) for an open hybrid model with CDM and baryons]. While the hybrid picture may succeed in reproducing several observations on both small and large scales, the number of model parameters is large, and their choice is ad hoc rather than naturally based on first principles.

9.3. Non-Gaussian Fluctuation Models

9.3.1   COSMIC STRINGS   A rather different method of producing large-scale density fluctuations without producing large thermal fluctuations is the use of non-Gaussian statistics. The recently suggested cosmic strings model (Vilenkin 1985, Albrecht & Turok 1985, Turok 1985) uses the latter to induce the density fluctuations. Cosmic strings are curvature singularities that are born with a topology of random walks. They turn into closed loops, which later break into multiple smaller loops in a scale-free fashion, leading to a scale-invariant fluctuation spectrum. Matter is then accreted onto the loops to form galaxies and clusters. The loop-loop correlation function appears to reproduce the universal correlation function discussed in Section 4, with a power law of r-2 (Albrecht & Turok 1985, Turok 1985). This model offers a natural way to account for the large-scale structure observations while keeping a rather isotropic microwave background. More detailed calculations are needed, however, before any conclusions can be reached regarding this model (e.g. Bouchet & Bennett 1988, Turok 1988).

9.4 Explosions

A fundamentally different approach to the formation of structure is provided by a model with powerful explosions (Ostriker & Cowie 1981, Ikeuchi 1981). In this model, which is a natural extension of the theory of how some stars form in the interstellar medium, structure is not produced by small density fluctuations in the early Universe but rather from explosions of first-generation objects, which help gravity in forming further galaxies and clusters. The blast waves produced by the explosions push the gas out of an evacuated area: the shells expand, cool, and fragment into a new generation of galaxies. Individual "bubbles" of galaxies formed in this manner, typically of ~ 10h-1 Mpc radius, can interact with each other to form clusters, superclusters, and still larger voids (Ostriker 1986). The model predicts a morphological appearance that is indeed similar to that observed in recent galaxy redshift surveys (Section 7). The cluster correlation function can also be reproduced by such a shell model (Bahcall et al. 1988a, Weinberg et al. 1988; Section 5.2). At the same time the isotropy of the microwave background is preserved, since the structure is formed after decoupling in a way that will not produce significant fluctuations in the background. High peculiar velocities on large scales (~ 60h-1 Mpc) may be a problem for explosions; however, the coherence length of the galaxy velocity field is still under investigation (Section 8). A recent variation on the explosion picture is the use of magnetized superconducting cosmic strings that can give rise to explosionlike phenomena (Ostriker et al. 1986). For recent reviews of the explosion model, see Ostriker (1986, 1988).

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