Cosmography by orthogonalized logarithmic polynomials

Abstract

Cosmography is a powerful tool for investigating the Universe kinematic and then for reconstructing the dynamics in a model-independent way. However, recent new measurements of supernovae Ia and quasars have populated the Hubble diagram up to high redshifts (z ∼ 7.5) and the application of the traditional cosmographic approach has become less straightforward due to the large redshifts implied. Here we investigate this issue through an expansion of the luminosity distance–redshift relation in terms of orthogonal logarithmic polynomials. In particular, we point out the advantages of a new procedure called orthogonalization, and we show that such an expansion provides a very good fit in the whole z = 0 ÷ 7.5 range to both real and mock data obtained assuming various cosmological models. Moreover, although the cosmographic series is tested well beyond its convergence radius, the parameters obtained expanding the luminosity distance–redshift relation for the Lambda cold dark matter (ΛCDM) model are broadly consistent with the results from a fit of mock data obtained with the same cosmological model. This provides a method for testing the reliability of a cosmographic function to study cosmological models at high redshifts, and it demonstrates that the logarithmic polynomial series can be used to test the consistency of the ΛCDM model with the current Hubble diagram of quasars and supernovae Ia. We confirm a strong tension (at > 4σ) between the concordance cosmological model and the Hubble diagram at z > 1.5. This tension is dominated by the contribution of quasars at z > 2 and also starts to be present in the few supernovae Ia observed at z > 1.

Quasar cosmology: dark energy evolution and spatial curvature

“…Risaliti & Lusso 2015. These expectations have already been confirmed in Bargiacchi et al (2021), where the same sample of QSOs (without the inclusion of BAO) is used for a cosmographic test of the flat ΛCDM model, with an improved estimation of the cosmographic free parameters, compared to the use of less updated QSO samples. It is worth mentioning some of the assumptions used in the cosmological analyses before moving on.…”

“…Deviations from the spatially flat ΛCDM model would imply important theoretical and observational consequences and a change in our current understanding of cosmic evolution (e.g. Capozziello et al 2020), and are also observed at higher redshifts in the combined quasars (QSOs) and SNe Ia Hubble-Lemaître diagram, with a statistical significance of 3-4σ Lusso et al 2019Lusso et al , 2020Bargiacchi et al 2021). Such a joint analysis makes use of the observed non-linear relation between the ultraviolet and the X-ray luminosity in QSOs (e.g.…”

Cosmographic approach to Running Vacuum dark energy models: new constraints using BAOs and Hubble diagrams at higher redshifts

“…( 11), we first calculate the luminosity distance and then the distance modulus. In parallel way, one can use the logarithmic expansion of the luminosity distance in terms of redshift Bargiacchi et al 2019;Lusso et al 2019).…”

Constraining the anisotropy of the Universe with the X-ray and UV fluxes of quasars

“…Unlike the well-constraint from the 2015 quasar compilation, the 2020 quasar compilation gives a weak constraint on the dipole parameters. It appears that there is a tension at the 3σ -4σ confidence level between the cosmographic fit of the 2020 quasar compilation Hubble diagram and the one obtained by assuming a flat CDM model [57]. The difference between the 2015 and 2020 quasar compilation may due to the fact that the tension with the CDM model is not observed in the 2015 quasar compilation, which also seems to show a much higher dispersion in the Hubble diagram compared to the 2020 quasar compilation.…”