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Mapping the redshift drift at various redshifts through cosmography

Anna Chiara Alfano, Orlando Luongo

Abstract

The redshift drift provides a kinematic test of the cosmic expansion history through the slow time variation of the redshift of comoving sources. Motivated by the expected Sandage-Loeb measurements from future facilities, we investigate the drift within a cosmographic framework, modeling the Hubble rate through both a second-order Taylor expansion and a $(2,1)$ Padé approximant. We constrain the cosmographic parameters $(H_0,q_0,j_0)$ by combining Pantheon+ and SH0ES type Ia supernovae with gamma-ray bursts and then examine the impact of adding baryon acoustic oscillation measurements from the second DESI data release. The resulting constraints are used to construct a mock Sandage-Loeb catalog, after which the analyses are repeated including the simulated drift data. In this way, we assess the internal consistency of the reconstructed background rather than perform an independent forecast. Accordingly, we find that, for the SNeIa+GRB analysis, the Taylor reconstruction is compatible at the $1σ$ level with the $ω_0ω_1$CDM scenario, whereas the Padé parameterization improves the agreement of $q_0$ with the $Λ$CDM paradigm. Once DESI BAO data are included, the agreement with the reference background models weakens to the $2σ$ level. The addition of the mock Sandage-Loeb sample mainly tightens the bounds on $q_0$ and $j_0$, with moderate shifts in the central values. We finally compare the reconstructed redshift drift with the corresponding behavior predicted by the $Λ$CDM and $ω_0ω_1$CDM scenarios.

Mapping the redshift drift at various redshifts through cosmography

Abstract

The redshift drift provides a kinematic test of the cosmic expansion history through the slow time variation of the redshift of comoving sources. Motivated by the expected Sandage-Loeb measurements from future facilities, we investigate the drift within a cosmographic framework, modeling the Hubble rate through both a second-order Taylor expansion and a Padé approximant. We constrain the cosmographic parameters by combining Pantheon+ and SH0ES type Ia supernovae with gamma-ray bursts and then examine the impact of adding baryon acoustic oscillation measurements from the second DESI data release. The resulting constraints are used to construct a mock Sandage-Loeb catalog, after which the analyses are repeated including the simulated drift data. In this way, we assess the internal consistency of the reconstructed background rather than perform an independent forecast. Accordingly, we find that, for the SNeIa+GRB analysis, the Taylor reconstruction is compatible at the level with the CDM scenario, whereas the Padé parameterization improves the agreement of with the CDM paradigm. Once DESI BAO data are included, the agreement with the reference background models weakens to the level. The addition of the mock Sandage-Loeb sample mainly tightens the bounds on and , with moderate shifts in the central values. We finally compare the reconstructed redshift drift with the corresponding behavior predicted by the CDM and CDM scenarios.

Paper Structure

This paper contains 12 sections, 22 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The cosmographic approach
  3. The redshift drift
  4. Cosmic probes
  5. Problems with baryonic acoustic oscillation data
  6. Preliminary numerical outcomes
  7. Analysis 1 results
  8. Analysis 2 results
  9. Constraints with the Sandage-Loeb test
  10. Conclusions
  11. Calibration of the Amati correlation
  12. Preliminary contour plots

Figures (4)

  • Figure 1: Behavior of the redshift drift $\Dot{z}$ in units of $\text{yrs}^{-1}$ for the flat $\Lambda$CDM and $\omega_0\omega_1$CDM models compared with $\Dot{z}$ written adopting the cosmographic approach in both cases of Taylor (upper plot) and Padé (lower plot). The values of $H_0$, $q_0$ and $j_0$ are taken from Tab. \ref{['tab:bfsl']} for Analysis 1SL-2SL. For the $\Lambda$CDM and $\omega_0\omega_1$CDM models we consider $H_0$, $\Omega_m$, $\omega_0$ and $\omega_1$ from the Planck Collaboration 2020AA...641A...6P. In both figures on the bottom left a zoom plot in the interval $z\in [1,\ 2]$.
  • Figure 2: Confidence contours representation comparing Analyses 1-2 with Analyses 1SL-2SL for the $q_0-j_0$ plane. Upper panel shows the contours when the Taylor series is adopted with (upper right) and without (upper left) DESI-BAO while lower panel shows them when the $(2,1)$ Padé approximation is used with (lower right) and without (lower left) DESI-BAO.
  • Figure 3: Contour plot of the Bézier coefficients. Darker (lighter) blue areas depict the $1$-$\sigma$($2$-$\sigma$) confidence level.
  • Figure 4: Contour plots for the preliminary MCMC outcomes for the GRB and cosmographic parameters in both the case of the Taylor or Padé series for Analysis 1-Analysis 2. Right panel shows the contour plot when Taylor is used while the left panel shows the contour plot when using Padé.