The dynamics of background evolution and structure formation in phase space: a semi-cosmographic reconstruction

TL;DR

This paper introduces a semi-cosmographic method to analyze background evolution and structure formation in phase space, fitting observational data without assuming a specific dark energy model, revealing deviations from Lambda-CDM at low redshifts.

Contribution

It develops a novel semi-cosmographic framework that reconstructs cosmological functions and phase trajectories directly from data, avoiding predefined dark energy models.

Findings

Detected deviations from Lambda-CDM at low redshifts.

Identified key redshifts for future observational focus.

Reconstructed phase space trajectories consistent with current data.

Abstract

The Baryon Acoustic Oscillation (BAO) feature, imprinted in the transverse and radial clustering of dark matter tracers, enables the simultaneous measurement of the angular diameter distance $D_A(z)$ and the Hubble parameter $H(z)$ at a given redshift. Further, measuring the redshift space anisotropy (RSD) allows us to measure the combination $f_8(z)\equiv f\sigma_8(z)$. Motivated by this, we simultaneously study the dynamics of background evolution and structure formation in an abstract phase space of dynamical quantities: $ x = H_0 D_A/c$, $p = dx/dz$, and $f_8$. We adopt a semi-cosmographic approach, whereby we do not pre-assume any specific dark energy model to integrate the dynamical system. The Luminosity distance is expanded as a Pad\'e rational approximation in the variable $(1+z)^{1/2}$. The dynamical system is solved by using a semi-cosmographic equation of state, which incorporates the dark matter density parameter along with the parameters of the Pad\'e expansion. The semi-cosmographic $D_A(z), H(z)$ and $f\sigma_8(z)$, thus obtained, are fitted with BAO and RSD data from the SDSS IV. The reconstructed phase trajectories in the $3D$ $(x,p,f_8)$ space are used to reconstruct some diagnostics of background cosmology and structure formation. At low redshifts, a discernible departure from the $\Lambda$CDM model is observed. The geometry of the phase trajectories in the projected spaces allows us to identify three key redshifts where future observations may be directed for a better understanding of cosmic tensions and anomalies.