Mathematics – Logic
Scientific paper
Jan 2012
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012aas...21931204w&link_type=abstract
American Astronomical Society, AAS Meeting #219, #312.04
Mathematics
Logic
Scientific paper
Motivated by the roughly log-normal probability density distribution function (PDF) of the small scale density field, we develop cosmological perturbation theory for the power spectrum of a logarithmically transformed density field with the formalism which is developed in the context of the cosmological renormalized perturbation theory. Compared with the standard perturbation theory, our approach help to regulate the convergence behavior of the perturbation series, and of the Taylor series expansion we use for the logarithmic mapping. The perturbation calculation achieved good agreement with simulation results. Then we consider the topology of the iso-density contour of the density field, especially the genus. The genus is relatively insensitive to nonlinear gravitational evolution, clustering bias and redshift distortion, and is approximately conserved over time as structures grow in Einstein's general relativity, hence it can be used as a robust standard ruler for cosmological measurements. However, in modified gravity models where structures grow with different rates on different scales, the genus should change over time, and therefore it can be used to test the gravity models on large scales. We studied the case of the f(R) theory, DGP brane-world theory as well as phenomenological models. We also forecast how the modified gravity models can be constrained with optical/IR or 21cm surveys in the near future.
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