Cosmography by orthogonalized logarithmic polynomials

¹ Scuola Superiore Meridionale, Largo S. Marcellino 10, 80138 Napoli, Italy
e-mail: giada.bargiacchi@unina.it
² Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy
³ Istituto Nazionale di Astrofisica (INAF) – Osservatorio Astrofisico di Arcetri, 50125 Florence, Italy
⁴ Dipartimento di Fisica “E. Pancini”, Università degli Studi di Napoli Federico II, Complesso Univ. Monte S. Angelo, Via Cinthia 9, 80126 Napoli, Italy
⁵ Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Complesso Univ. Monte S. Angelo, Via Cinthia 9, 80126 Napoli, Italy
⁶ Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050 Tomsk, Russia

Received: 20 January 2021
Accepted: 15 February 2021

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.