4.1. The Origin of the Fluctuation Spectrum
We do not yet have an adequate understanding for the origin of the power spectrum of Primordial Density Fluctuations. Therefore it is usually assumed that primordial density fluctuations with an initial power spectrum (k) kn were present at some initial time ti either as part of the initial conditions of the Universe or having formed through some causal process which presumably would specify n and/or their amplitude. The case n = + 1 is generally referred to as the Harrison-Zeldovich spectrum, after the individuals who advocate its use on the grounds that this was the power spectrum that did the least violence to the geometry of spacetime on any scale.
The "natural" Harrison-Zeldovich spectrum of fluctuations may not be so natural. In inflationary cosmologies the emergent spectrum of fluctuations depends on the details of the fields that cause the inflation (Kofman and Linde, 1987; Kofman and Pogosyan, 1988; Kofman and Blumenthal, 1989; Matarrese, Ortolan and Lucchin, 1989; Hodges, Blumenthal, Kofman and Primack, 1990; Salopek and Bond, 1991). These papers discuss specific models for the generation of power law spectra, spectra that are non-Gaussian and even non-power law spectra. The non-power law spectra are of interest partly because we see here a direct influence of the parameters of microscopic physics on large scale cosmic structure.
The issue is very contentious. For example, the Kofman and Linde (1987) idea that inflation driven by multiple scalar fields might create non-Gaussian fluctuations has been disputed by Hodges (1989). (See also Hodges and Blumenthal, 1990). In an analytically solvable case Barrow and Coles (1990) find that although non-Gaussian fluctuations can be generated, they become Gaussian as a state of exponential expansion is attained. Nevertheless, power law spectra with index different than 1 (Harrison-Zeldovich) can be created.
Peebles (1989) discusses the origin of isocurvature fluctuations in the inflationary scenarios. The question of the origin of isothermal perturbations as a consequence of the baryongenesis process at very early epochs is discussed by Barrow, Copeland, Kolb and Liddle (1991).