[Paper Review] Power of the redshift drift on cosmological models and expansion history

Shuang‐Nan Zhang, Wenbiao Liu|arXiv (Cornell University)|Nov 27, 2013

Cosmology and Gravitation Theories7 references3 citations

TL;DR

This study quantifies the cosmological constraint power of redshift drift (velocity drift, Δv) using the Fisher information matrix, demonstrating that 10–30 years of Δv observations can significantly improve constraints on cosmological parameters—particularly Ωₘ, w, and the deceleration parameter q(z)—outperforming current OHD and SNIa data. It shows Δv with 12–30 years can match or exceed the precision of existing observations, especially for the equation of state w and transition redshift.

ABSTRACT

We investigate the power of the velocity drift ($Δv$) on cosmological parameters and expansion history with observational Hubble data (OHD), type Ia supernova (SNIa). We estimate the constraints of $Δv$ using the Fisher information matrix based on the model by \citet{pasquini2005codex,whitelock2006scientific}. We find that $Δv$ with 20 years can reduce the uncertainty of $Ω_m$ by more than 42% than available observations. Based on the statistical figures of merit (FoM), we find that in order to match the constraint power of OHD and SNIa, we need 21 and 26 future measurements, respectively. We also quantitatively estimate for the first time the number of years required for the velocity drift to become comparable with current observations on the equation of state $w$. The statistical FoM indicate that we need at least 12 years to cover current observations. Physically, we could monitor 30 quasars for 30 years to obtain the same accuracy of $w$. Considering two parameterized deceleration factor $q(z)$, we find that the available observations give an estimation on current value $-0.9 \lesssim q_0 \lesssim -0.3$. Difference between the two types of $q(z)$ is the precise determination of variation rate $dq/dz$. For the first model with constant $dq/dz$, $Δv$ with only 10 years provides a much better constraint on it, especially when compared with SNIa. However, we need $Δv$ for more years in the variable $dq/dz$ model. We find that $Δv$ with 30 years reduces the uncertainty of transition redshift to approximately three times better than those of OHD and SNIa.

Motivation & Objective

• To quantitatively assess how future velocity drift (Δv) observations can improve constraints on cosmological parameters compared to current data.
• To determine the number of years or data points of Δv required to match the statistical power of existing observational Hubble data (OHD) and type Ia supernovae (SNIa).
• To evaluate the sensitivity of Δv to key cosmological parameters, including Ωₘ, w, and the deceleration parameter q(z), especially in the 'redshift desert' (z ≈ 2–5).
• To investigate the role of Δv in breaking parameter degeneracies, particularly in the q₀–q₁ plane, and improving the precision of the transition redshift zₜ.
• To compare the constraint power of Δv with OHD and SNIa using the figure of merit (FoM) under ΛCDM and XCDM models.

Proposed method

• Employs the Fisher information matrix to estimate parameter uncertainties for cosmological models, assuming a fiducial ΛCDM and XCDM framework.
• Uses the theoretical model of Pasquini et al. (2005, 2006a) to simulate Δv measurements from 30 quasars over varying observation durations (5 to 50 years).
• Calculates the Fisher matrix for Δv based on the time-derivative of the Hubble parameter, derived from the redshift drift equation dΔv/dt ∝ dH/dt.
• Compares the statistical figure of merit (FoM) of Δv with those of OHD and SNIa to assess relative constraint power.
• Analyzes two parameterized models of the deceleration parameter q(z): one with constant dq/dz and one with variable dq/dz, to study sensitivity to q₁.
• Quantifies the improvement in uncertainty reduction for Ωₘ, w, and zₜ by comparing Δv results with those from OHD and SNIa using the same statistical framework.

Experimental results

Research questions

• RQ1 How many years of velocity drift (Δv) observations are needed to match the constraint power of current OHD and SNIa data on cosmological parameters?
• RQ2 To what extent can Δv improve the precision of the dark energy equation of state w, and when does it match or exceed the accuracy of Planck or WMAP9 results?
• RQ3 How does Δv constrain the transition redshift zₜ, and by how much does it reduce uncertainty compared to OHD and SNIa?
• RQ4 What is the relative constraint power of Δv compared to OHD and SNIa in breaking degeneracies in the q₀–q₁ plane?
• RQ5 How does the constraint power of Δv depend on the assumed model of q(z), particularly when dq/dz is constant versus variable?

Key findings

• Δv with 20 years reduces the uncertainty of Ωₘ by more than 42% compared to current observations, indicating strong sensitivity to matter density.
• To match the constraint power of OHD and SNIa, Δv requires 21 and 26 years of observations, respectively, based on the figure of merit (FoM).
• A minimum of 12 years of Δv is required to achieve the same FoM as OHD and SNIa for constraining the equation of state w.
• With 30 years of Δv, the uncertainty in the transition redshift zₜ is reduced to approximately three times better than current OHD and SNIa constraints.
• Δv with 10 years provides significantly better constraints on dq/dz (especially in the constant dq/dz model) than SNIa, and its constraint on q₀–q₁ is nearly orthogonal to OHD, aiding degeneracy breaking.
• A 50-year Δv observation yields Δw ≈ 0.1098, comparable to the Planck result (w = −1.13 ± 0.13), suggesting Δv can match or exceed current CMB-based precision.