Looking Down the Light Cone: Can Deep Redshift Surveys Alone Measure the Power Spectrum?

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We analyze the window functions for the spherical harmonic mode estimators of all--sky, volume limited surveys considering evolutionary effects along the past light--cone which include the deviation of the distance scale from a linear relationship with redshift, linear peculiar velocity corrections, and linear evolution of the density perturbations. The spherical harmonic basis functions are considered because they correspond most closely to the symmetries of typical survey geometries and of the light--cone effects we consider. Our results show substantial broadening of the windows over that expected by ignoring light--cone effects, indicating the difficulty of measuring the power spectrum independently from cosmology. We suggest that because of light--cone effects, deep redshift surveys should either be analyzed in conjunction with CMBR data which determines the cosmological parameters, or by using a Bayesian likelihood scheme in which varying cosmological parameters and a simple parameterization of the primordial power spectrum are assumed as the priors, so that observed data can be mapped from redshift to real space. The derived power spectrum can then be compared to underlying models of fluctuation generation and growth in structure formation to evaluate both these models and the cosmological priors.