The least-action principle ( LAP ) method is used on four galaxy redshift surveys to measure the density parameter \Omega _ { m } and the matter and galaxy-galaxy power spectra .
The datasets are PSC z , ORS , Mark III and SFI .
The LAP method is applied on the surveys simultaneously , resulting in an overconstrained dynamical system that describes the cosmic overdensities and velocity flows .
The system is solved by relaxing the constraint that each survey imposes upon the cosmic fields .
A least-squares optimization of the errors that arise in the process yields the cosmic fields and the value of \Omega _ { m } that is the best fit to the ensemble of datasets .
The analysis has been carried out with a high-resolution Gaussian smoothing of 500 { km s } ^ { -1 } and over a spherical selected volume of radius 9,000 { km s } ^ { -1 } .
We have assigned a weight to each survey , depending on their density of sampling , and this parameter determines their relative influence in limiting the domain of the overall solution .
The influence of each survey on the final value of \Omega _ { m } , the cosmographical features of the cosmic fields and the power spectra largely depends on the distribution function of the errors in the relaxation of the constraints .
We find that PSC z and Mark III are closer to the final solution than ORS and SFI .
The likelihood analysis yields \Omega _ { m } = 0.37 \pm 0.01 to 1 \sigma level .
PSC z and SFI are the closest to this value , whereas ORS and Mark III predict a somewhat lower \Omega _ { m } .
The model of bias employed is a scale-dependent one , and we retain up to 42 bias coefficients b _ { rl } in the spherical harmonics formalism .
The predicted power spectra are estimated in the range of wavenumbers { { { { { { { { 0.02 h { Mpc } ^ { -1 } \mathrel { \mathchoice { \lower 0.86 pt \vbox { \halign { \cr } $% \displaystyle \hfil < $ \cr$ \displaystyle \hfil \sim$ } } } { \lower 0.86 pt \vbox { \halign { % \cr } $ \textstyle \hfil < $ \cr$ \textstyle \hfil \sim$ } } } { \lower 0.86 pt \vbox { \halign { % \cr } $ \scriptstyle \hfil < $ \cr$ \scriptstyle \hfil \sim$ } } } { \lower 0.86 pt \vbox { % \halign { \cr } $ \scriptscriptstyle \hfil < $ \cr$ \scriptscriptstyle \hfil \sim$ } } } } k% \mathrel { \mathchoice { \lower 0.86 pt \vbox { \halign { \cr } $ \displaystyle \hfil < $ \cr$% \displaystyle \hfil \sim$ } } } { \lower 0.86 pt \vbox { \halign { \cr } $ \textstyle \hfil < $% \cr$ \textstyle \hfil \sim$ } } } { \lower 0.86 pt \vbox { \halign { \cr } $ \scriptstyle \hfil < % $ \cr$ \scriptstyle \hfil \sim$ } } } { \lower 0.86 pt \vbox { \halign { \cr } $% \scriptscriptstyle \hfil < $ \cr$ \scriptscriptstyle \hfil \sim$ } } } } 0.49 h { Mpc% } ^ { -1 } , and we compare these results with measurements recently reported in the literature .