The multipole moments of the power spectrum of large scale structure , observed in redshift space , are calculated for a finite sample volume including the effects of both the linear velocity field and geometry .
A variance calculation is also performed including the effects of shot noise .
The sensitivity with which a survey with the depth and geometry of the Sloan Digital Sky Survey ( SDSS ) can measure cosmological parameters \Omega _ { 0 } and b _ { 0 } ( the bias ) or \lambda _ { 0 } ( the cosmological constant ) and b _ { 0 } is derived through fitting power spectrum moments to the large scale structure in the linear regime in a way which is independent of the evolution of the galaxy number density .
A fiducial model is assumed and the region of parameter space which can then be excluded to a given confidence limit is determined .
In the absence of geometric and evolutionary effects , the ratios of multipole moments ( in particular the zeroth and second ) , are degenerate for models of constant \beta \approx \Omega ^ { 0.6 } / b _ { 0 } .
However , this degeneracy is broken by the Hubble expansion , so that in principle \Omega _ { 0 } and b _ { 0 } may be measured separately by a deep enough galaxy redshift survey ( [ Nakamura , Matsubara , & Suto ( 1997 ) ] ) .
We find that for surveys of the approximate depth of the SDSS no restrictions can be placed on \Omega _ { 0 } at the 99 % confidence limit when a fiducial open , \Omega _ { 0 } = 0.3 model is assumed and bias is unconstrained .
At the 95 % limit , \Omega _ { 0 } < .85 is ruled out .
Furthermore , for this fiducial model , both flat ( cosmological constant ) and open models are expected to reasonably fit the data .
For flat , cosmological constant models with a fiducial \Omega _ { 0 } = 0.3 , we find that models with \Omega _ { 0 } > 0.48 are ruled out at the 95 % confidence limit regardless of the choice of the bias parameter , and open models can not fit the data even at the 99 % confidence limit .
We also find significant deviations in \beta from the naive estimate for both fiducial models .
Thus , we conclude for the SDSS that linear evolution-free statistics alone can strongly distinguish between \Omega _ { 0 } = 1 and low matter density models only in the case of the fiducial cosmological constant model .
For the open model , \Omega _ { 0 } = 1 is only at best only nominally excluded unless \Omega _ { 0 } < 0.3 .