Dark Energy, Expansion History And Non-Gaussianity From The Topology Of The Large-Scale Structure Of The Universe

Mathematics – Logic

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Scientific paper

Constraining different cosmological models and the dark energy equation of state (DE EoS) is usually achieved by analyzing the primordial fluctuations through the power spectrum or the correlation function, or by studying the expansion of the Universe measured with standard candles, rulers (i.e. Baryon Acoustic Oscillations), or populations; the comoving-distance/redshift relation is then used to reconstruct the global expansion history.
As a new alternative method, we propose to adopt the one-dimensional large-scale topology as a cosmic standard ruler, based on the fact that the pattern of the galaxy distribution should be maintained in the course of time on large scales.
In particular, by considering pencil beam surveys and by examining the scale-dependence of the level crossing statistics in different redshift intervals, it is possible to reconstruct the expansion history of the Universe and thus to measure the cosmological parameters governing its expansion. The main parameters and the DE EoS can be estimated by requiring that the rate of level crossings in the radial distribution is constant in time across different redshift intervals, through an iterative minimization procedure. The scale dependence of the one-dimensional level crossings, being an intrinsic topological quantity, is a robust standard ruler, resistant against non-linear gravitational evolution, galaxy biasing, and redshift-space distortions. The technique introduced here is particularly relevant for current and next generation redshift surveys such as BOSS, Wiggle-Z and HETDEX, and will also be used to study primordial non-Gaussianity - in synergy with the Cosmic Microwave Background analysis.

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