Power Index in the Measurement of the Variance from a Gaussian Field
Abstract
The rms fluctuation (variance) σ of a cosmic field α(x) is an important measure to quantify the initial fluctuation of the universe and is usually determined by the formula σ^{2}=<α(x)^{2}>. We investigate the necessity of using this specific formula, under the assumption that the initial fluctuation is randomGaussiandistributed. We calculate the expected finitevolume effect on σ obtained from a general formula <α^{m}>. We find that although the finitevolume effect is minimal at the conventional choice m=2, it is almost insensitive to m around m=1~3. Therefore we can reduce the relative contribution of tail parts, which might be considerably contaminated by other effects (such as measurement errors), at a very small sacrifice of the finitevolume effect.
 Publication:

The Astrophysical Journal
 Pub Date:
 May 1999
 DOI:
 10.1086/307153
 Bibcode:
 1999ApJ...516..527S
 Keywords:

 COSMOLOGY: THEORY;
 COSMOLOGY: LARGESCALE STRUCTURE OF UNIVERSE;
 Cosmology: Theory;
 Cosmology: LargeScale Structure of Universe