![]() ![]() ![]() For an extensive discussion of the cosmological Gaussian density field, see. Since M ij = ξ( x i, x j), Equation (71) implies that the statistical nature of the Gaussian density field is completely specified by the two-point correlation function ξ and its linear combination (including its derivative and integral). Here M ij ≡ 〈 δ i δ j〉 is the covariance matrix, and M −1 is its inverse. The cosmological principle is mathematically paraphrased as that the metric of the Universe (in its zero-th order approximation) is given byįor an arbitrary positive integer m. Further details may be easily found in standard cosmology textbooks. The rest of the current section is devoted to a brief review of the homogeneous and isotropic cosmological model. The XRB sources are probably located at redshift z 100h −1 Mpc. The X-ray background (XRB) is likely to be due to sources at high redshift. If the assumption of homogeneity turns out to be wrong, then there are numerous possibilities for inhomogeneous models, and each of them must be tested against the observations.įor that purpose, one needs observational data with good quality and quantity extending up to high redshifts. The practical methodology we adopt is to assume homogeneity and to assess the level of fluctuations relative to the mean, and hence to test for consistency with the underlying hypothesis. Proving the homogeneity of the Universe is particularly difficult as we observe the Universe from one point in space, and we can only deduce isotropy indirectly. Like with any other idea about the physical world, we cannot prove a model, but only falsify it. The anthropic principle is becoming popular again, e.g., in ‘explaining’ the non-zero value of the cosmological constant. The perfect cosmological principle led to the steady state model, which although more symmetric than the (generalized) cosmological principle, was rejected on observational grounds. We note that the ancient Indian principle may be viewed as a sort of ‘fractal model’. Finally, Section 7 is devoted to a summary of the present knowledge of our Universe and our personal view of the future direction of cosmological researche in the new millennium.Ī human being, as he/she is, can exist only in the Universe as it is. We present the latest results from the two currently largest galaxy redshift surveys, 2dF (Two Degree Field) and SDSS (Sloan Digital Sky Survey), in Section 6. Section 5 introduces general relativistic effects which become important especially for galaxies at high redshifts. Nevertheless this is one of the most important ingredients for proper interpretation of galaxy redshift surveys. Our understanding of biasing is still far from complete, and its description is necessarily empirical and very approximate. Next we discuss the spatial biasing of galaxies relative to the underlying dark matter distribution in Section 4. Then we describe the non-Gaussian nature of density fluctuations generated by the nonlinear gravitational evolution of the primordial Gaussian field in Section 3. ![]() We first present a brief overview of the Friedmann model and gravitational instability theory in Section 2. With the above in mind, we will attempt to summarize what we have learned so far from galaxy redshift surveys, and then describe what will be done with future data. In the era of precision cosmology among others, the scientific goals of research using galaxy redshift surveys are gradually shifting from inferring a set of values of cosmological parameters using galaxy as their probes to understanding the origin and evolution of galaxy distribution given a set of parameters accurately determined by the other probes like CMB and supernovae. Still galaxy redshift surveys are of vital importance in cosmology in the 21st century for various reasons: Indeed one may phrase that the modern observational cosmology started with a sort of galaxy redshift survey by Edwin Hubble. Undoubtedly gamma-rays, neutrinos, and gravitational radiation will join the above already crowded list.Īmong those, optical galaxy redshift surveys are the most classical. Nowadays the exploration of the Universe can be performed by a variety of observational probes and methods over a wide range of the wavelengths: the temperature anisotropy map of the cosmic microwave background (CMB), the Hubble diagrams of nearby galaxies and distant Type Ia supernovae, wide-field photometric and spectroscopic surveys of galaxies, the power spectrum and abundances of galaxy clusters in optical and X-ray bands combined with the radio observation through the Sunyaev-Zel’dovich effect, deep surveys of galaxies in sub-mm, infrared, and optical bands, quasar surveys in radio and optical, strong and weak lensing of distant galaxies and quasars, high-energy cosmic rays, and so on. ![]()
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