IfA HomeNbody lss

Non-linear growth of the matter power spectrum P(k)

Related Links:

Baryonic P(k) features
Non-linear P(k) evolution

Virgo Consortium


ECCA Research

The growth of correlations in the matter power spectrum

The fluctuations of the cosmological matter density field grow due to the influence of gravity. Most cosmological models for structure formation assume that the matter fluctuations begin as linear gaussian perturbations on top of the mean matter field. In terms of the Fourier modes, each mode is initially a gaussian-distributed variable and statistically independent of any other mode. As a consequence, the power spectrum (the square of the absolute value of the Fourier density fluctuation) for any given mode is statistically independent of the power spectrum at any other mode.

It was long held that this independence of power spectrum values for differing modes continued to apply even as the density field became non-linear. As a result, the fitting of model predictions of the power spectrum to the measured power spectrum based on galaxy counts assumed independence of the power spectrum values.

In fact gravitational instability will create correlations in the power spectrum values for differing modes. Any fits of models to the non-linear modes requires that these correlations be taken into account. Their neglect would lead to a large over-estimate of the number of degrees-of-freedom used to base the statistical goodness-of-fit of any given model, and so bias the estimates of the cosmological parameters inferred from galaxy surveys.

Return to Gravitational dynamics