Steps toward the power spectrum of matter. III. The primordial spectrum

Observed power spectrum of matter found in Papers I and II is compared with analytical power spectra. Spatially flat cold and mixed dark matter models with cosmological constant and open models are considered. The primordial power spectrum of matter is determined using the power spectrum of matter and the transfer functions of analytical models. The primordial power spectrum has a break in amplitude. We conclude that a scale-free primordial power spectrum is excluded if presently available data on the distribution of clusters and galaxies represent the true mass distribution of the Universe.Comment: LaTex (sty files added), 22 pages, 5 PostScript figures embedded, Astrophysical Journal (accepted

Power Spectra for Cold Dark Matter and its Variants

The bulk of recent cosmological research has focused on the adiabatic cold dark matter model and its simple extensions. Here we present an accurate fitting formula that describes the matter transfer functions of all common variants, including mixed dark matter models. The result is a function of wavenumber, time, and six cosmological parameters: the massive neutrino density, number of neutrino species degenerate in mass, baryon density, Hubble constant, cosmological constant, and spatial curvature. We show how observational constraints---e.g. the shape of the power spectrum, the abundance of clusters and damped Lyman-alpha systems, and the properties of the Lyman-alpha forest--- can be extended to a wide range of cosmologies, including variations in the neutrino and baryon fractions in both high-density and low-density universes.Comment: 20 pages, LaTeX, 4 figures. Submitted to ApJ. Electronic versions of the fitting formula, as well as simple codes to output cosmological quantities (e.g. sigma_8) as a function of parameters and illustrative animations of parameter dependence, are available at http://www.sns.ias.edu/~whu/transfer/transfer.htm

Contractions of Low-Dimensional Lie Algebras

Theoretical background of continuous contractions of finite-dimensional Lie algebras is rigorously formulated and developed. In particular, known necessary criteria of contractions are collected and new criteria are proposed. A number of requisite invariant and semi-invariant quantities are calculated for wide classes of Lie algebras including all low-dimensional Lie algebras. An algorithm that allows one to handle one-parametric contractions is presented and applied to low-dimensional Lie algebras. As a result, all one-parametric continuous contractions for the both complex and real Lie algebras of dimensions not greater than four are constructed with intensive usage of necessary criteria of contractions and with studying correspondence between real and complex cases. Levels and co-levels of low-dimensional Lie algebras are discussed in detail. Properties of multi-parametric and repeated contractions are also investigated.Comment: 47 pages, 4 figures, revised versio

A built-in scale in the initial spectrum of density perturbations: evidence from cluster and CMB data

We calculate temperature anisotropies of the cosmic microwave background (CMB) for several initial power spectra of density perturbations with a built-in scale suggested by recent optical data on the spatial distribution of rich clusters of galaxies. Using cosmological models with different values of spectral index, baryon fraction, Hubble constant and cosmological constant, we compare the calculated radiation power spectrum with the CMB temperature anisotropies measured by the Saskatoon experiment. We show that spectra with a sharp peak at 120 h^{-1} Mpc are in agreement with the Saskatoon data. The combined evidence from cluster and CMB data favours the presence of a peak and a subsequent break in the initial matter power spectrum. Such feature is similar to the prediction of an inflationary model where an inflaton field is evolving through a kink in the potential.Comment: LaTex style, 9 pages, 3 PostScript figures embedded, accepted by J. Exper. Theor. Phy

The Formation of Cosmic Structures in a Light Gravitino Dominated Universe

We analyse the formation of cosmic structures in models where the dark matter is dominated by light gravitinos with mass of $100$ eV -- 1 keV, as predicted by gauge-mediated supersymmetry (SUSY) breaking models. After evaluating the number of degrees of freedom at the gravitinos decoupling ($g_*$), we compute the transfer function for matter fluctuations and show that gravitinos behave like warm dark matter (WDM) with free-streaming scale comparable to the galaxy mass scale. We consider different low-density variants of the WDM model, both with and without cosmological constant, and compare the predictions on the abundances of neutral hydrogen within high-redshift damped Ly--$\alpha$ systems and on the number density of local galaxy clusters with the corresponding observational constraints. We find that none of the models satisfies both constraints at the same time, unless a rather small $\Omega_0$ value (\mincir 0.4) and a rather large Hubble parameter (\magcir 0.9) is assumed. Furthermore, in a model with warm + hot dark matter, with hot component provided by massive neutrinos, the strong suppression of fluctuation on scales of \sim 1\hm precludes the formation of high-redshift objects, when the low--$z$ cluster abundance is required. We conclude that all different variants of a light gravitino DM dominated model show strong difficulties for what concerns cosmic structure formation. This gives a severe cosmological constraint on the gauge-mediated SUSY breaking scheme.Comment: 28 pages,Latex, submitted for publication to Phys.Rev.

Large Scale Structure and Supersymmetric Inflation without Fine Tuning

We explore constraints on the spectral index $n$ of density fluctuations and the neutrino energy density fraction $\Omega_{HDM}$, employing data from a variety of large scale observations. The best fits occur for $n\approx 1$ and $\Omega_{HDM} \approx 0.15 - 0.30$, over a range of Hubble constants $40-60$ km s$^{-1}$ Mpc$^{-1}$. We present a new class of inflationary models based on realistic supersymmetric grand unified theories which do not have the usual `fine tuning' problems. The amplitude of primordial density fluctuations, in particular, is found to be proportional to $(M_X /M_P)^2$, where $M_X (M_P)$ denote the GUT (Planck) scale, which is reminiscent of cosmic strings! The spectral index $n = 0.98$, in excellent agreement with the observations provided the dark matter is a mixture of `cold' and `hot' components.Comment: LaTEX, 14 pp. + 1 postscript figure appende

Reconstructing the Inflaton Potential --- an Overview

We review the relation between the inflationary potential and the spectra of density (scalar) perturbations and gravitational waves (tensor perturbations) produced, with particular emphasis on the possibility of reconstructing the inflaton potential from observations. The spectra provide a potentially powerful test of the inflationary hypothesis; they are not independent but instead are linked by consistency relations reflecting their origin from a single inflationary potential. To lowest-order in a perturbation expansion there is a single, now familiar, relation between the tensor spectral index and the relative amplitude of the spectra. We demonstrate that there is an infinite hierarchy of such consistency equations, though observational difficulties suggest only the first is ever likely to be useful. We also note that since observations are expected to yield much better information on the scalars than on the tensors, it is likely to be the next-order version of this consistency equation which will be appropriate, not the lowest-order one. If inflation passes the consistency test, one can then confidently use the remaining observational information to constrain the inflationary potential, and we survey the general perturbative scheme for carrying out this procedure. Explicit expressions valid to next-lowest order in the expansion are presented. We then briefly assess the prospects for future observations reaching the quality required, and consider a simulated data set that is motivated by this outlook.Comment: 69 pages standard LaTeX plus 4 postscript figures. Postscript version of text in landscape format (35 pages) available at http://star-www.maps.susx.ac.uk/papers/infcos_papers.html Modifications are a variety of updates to discussion and reference