Power Index in the Measurement of the Variance from a Gaussian Field

Details Power Index in the Measurement of the Variance from a Gaussian Field Power Index in the Measurement of the Variance from a Gaussian Field

May 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999apj...516..527s&link_type=abstract

The Astrophysical Journal, Volume 516, Issue 2, pp. 527-529.

Astronomy and Astrophysics

Astronomy

2

Cosmology: Theory, Cosmology: Large-Scale Structure Of Universe

Scientific paper

The rms fluctuation (variance) sigma of a cosmic field alpha(x) is an important measure to quantify the initial fluctuation of the universe and is usually determined by the formula sigma^2=alpha(x)^2. We investigate the necessity of using this specific formula, under the assumption that the initial fluctuation is random-Gaussian-distributed. We calculate the expected finite-volume effect on sigma obtained from a general formula |alpha|^m. We find that although the finite-volume 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 finite-volume effect.

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