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 DA(z) and the Hubble parameter H(z) at a given redshift. Further, measuring the redshift space anisotropy (RSD) allows us to measure the combination f8(z) ≡ fσ8(z). Motivated by this, we simultaneously study the dynamics of background evolution and structure formation in an abstract phase space of dynamical quantities , , and f8. 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 Padé rational approximation in the variable . 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 Padé expansion. The semi-cosmographic DA(z), H(z) and fσ8(z), thus obtained, are fitted with BAO and RSD data from the SDSS IV. The reconstructed phase trajectories in the 3D (x, p, f8) space are used to reconstruct some diagnostics of background cosmology and structure formation. At low redshifts, a discernible departure from the ΛCDM 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.