Limits on the primordial fluctuation spectrum: void sizes and anisotropy of the cosmic microwave background radiation

• Published in: Monthly notices of the Royal Astronomical Society 1993-12, Vol.265 (3), p.681-688
• Main Authors: Piran, T., Lecar, M., Goldwirth, D. S., da Costa, L. Nicolaci, Blumenthal, G. R.
• Format: Article
• Language: English
• Subjects: Astronomy; cosmic microwave background; Cosmology; Earth, ocean, space; Exact sciences and technology; galaxies: clustering; Galaxy groups, clusters, and superclusters. Large-scale structure of the universe; large-scale structure of Universe; Mathematical and relativistic aspects of cosmology. Quantum cosmology; Stellar systems. Galactic and extragalactic objects and systems. The universe; Superclusters. Large-scale structure of the universe (including voids, pancakes, great wall, etc.)
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/265.3.681

We suggest the use of the typical appearance of voids on a scale of 5000 km s–1 in the galaxy distribution to estimate the power spectrum on this scale. We use a simple model for the gravitational formation of voids, and we compare the results with the matter fluctuations as constrained by the CMBR observations by COBE. We find that a power spectrum $P(k)\propto k^{n}$ with n ≈ 1.25 is compatible both with COBE and with the gravitational growth of large voids in an Ω = 1 universe. A Harrison–Zel’dovich spectrum, n = 1, normalized to produce the observed CMBR fluctuations, does not have enough power for gravitational growth of voids with a diameter of 5000 km s–1in an Ω = 1 universe. Such a spectrum would be compatible if (i) void diameters were smaller (3500 km s–1), the voids were shallower or the voids were rare (we assume that the Universe is void-filled), (ii) Ω < 1 (i.e. the Universe is open), (iii) galaxies do not trace matter on very large scales, or (iv) the voids do not grow gravitationally.