POWER INDEX IN THE MEASUREMENT OF THE VARIANCE FROM A GAUSSIAN FIELD

摘要

The rms fluctuation (variance) σ of a cosmic field α(χ) is an important measure to quantify the initial fluctuation of the universe and is usually determined by the formula σ~2 =〈α(χ)~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 σ obtained from a general formula〈 |α|~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.