Observational Constraints on the Spectral Index

Abstract

We address the possibility of bounding the spectral index $n$ of primordial density fluctuations, using both the cosmic microwave background (cmb) anisotropy and data on galaxies and clusters. Each piece of galaxy and cluster data is reduced to a value of $\sigma (R)$ (the linearly evolved {\em rms} density contrast with top hat smoothing on scale $R$) which allows data on different scales to be readily compared. As a preliminary application, we normalise the spectrum using the ten degree variance of the COBE data, and then compare the prediction with a limited sample of low energy data, for the MDM model with various values of $n$, ${\Omega }_{\nu }$ and $h$. With $h=.5$, the data constrain the spectral index to the range $0.7\lsim n \lsim 1.2$. If gravitational waves contribute to the cmb anisotropy with relative strength $R=6(1-n)$ (as in some models of inflation), the lower limit on $n$ is increased to about $0.85$. The uncertainty in $h$ widens this band by about $0.1$ at either end.

11 pages. Revised version with an extended text and comments on damped Lyman alpha systems. Latex file for the text, plus a ps file for the two figures

References in corpus (6)

• On Determining the Spectrum of Primordial Inhomogeneity from the COBE DMR Sky Maps: II. Results of Two Year Data Analysis
• Damped Lyman Alpha Systems and Galaxy Formation
• Amplitude of Primeval Fluctuations from Cosmological Mass Density Reconstructions
• A Simple Model of Large Scale Structure Formation
• Constraints on the Models for Structure Formation from the Abundance of Damped Lyman Alpha Systems
• Mapping Moderate Redshift Cluster

Cited by in corpus (1)

• Spectral Analysis of Microwave Background Perturbations Induced by Cosmic Strings