[Paper Review] Gravitational Lensing and the Extragalactic Distance Scale

R. D. Blandford, Tomislav Kundić|arXiv (Cornell University)|Nov 27, 1996

Geophysics and Gravity Measurements2 references3 citations

TL;DR

This paper evaluates gravitational lensing as a method to measure the Hubble constant independently of the cosmic distance ladder, using time delays between lensed quasar images. It assesses the feasibility of achieving <10% total uncertainty in H₀ by combining accurate time delays with modeling of lens mass distributions and large-scale structure effects.

ABSTRACT

The potential of gravitational lenses for providing direct, physical measurements of the Hubble constant, free from systematic errors associated with the traditional distance ladder, has long been recognized. However, it is only recently that there has been a convincing measurement of a time delay sufficiently accurate to carry out this program. By itself, an accurate time delay measurement does not produce an equivalently definite Hubble constant and the errors associated with models of the primary lens, propagation through the potential fluctuations produced by the large-scale structure and the global geometry of the universe must also be taken into account. The prospects for measuring several more time delays and the feasibility of making the corresponding estimates of the Hubble constant with total error smaller than ten percent are critically assessed.

Motivation & Objective

• To assess the potential of gravitational lensing to provide a direct, physically grounded measurement of the Hubble constant.
• To address systematic errors in lens modeling, large-scale structure effects, and global cosmological geometry that affect H₀ estimates.
• To evaluate whether multiple time-delay measurements can yield a Hubble constant with total uncertainty below 10%.
• To determine the feasibility of achieving robust, independent distance measurements free from the traditional cosmic distance ladder.
• To provide a critical assessment of current and future prospects for time-delay lensing in extragalactic distance scale calibration.

Proposed method

• Utilizes time delays between multiple images of gravitationally lensed quasars as a direct geometric probe of the Hubble constant.
• Applies lens mass modeling to interpret time delays and infer the time-delay distance, which scales inversely with H₀.
• Incorporates corrections for line-of-sight structure and large-scale mass fluctuations to reduce systematic errors.
• Considers the global geometry of the universe (e.g., curvature) as a source of uncertainty in H₀ determination.
• Employs statistical and theoretical frameworks to estimate total error budgets in H₀ measurements from lensing.
• Analyzes the expected performance of upcoming time-delay measurements from improved monitoring of known lens systems.

Experimental results

Research questions

• RQ1 Can time-delay measurements in strong gravitational lenses provide a robust, independent determination of the Hubble constant?
• RQ2 What are the dominant systematic errors in H₀ estimation from time-delay lenses, and can they be reduced below 10%?
• RQ3 How do large-scale structure along the line of sight and lens mass model uncertainties affect H₀ precision?
• RQ4 What is the expected contribution of multiple time-delay lens systems to reducing overall uncertainty in H₀?
• RQ5 Can gravitational lensing achieve a Hubble constant measurement with comparable or better precision than the traditional distance ladder?

Key findings

• Time-delay measurements in gravitational lenses offer a direct, physical method to determine the Hubble constant without relying on the cosmic distance ladder.
• Accurate time delays alone are insufficient; systematic errors from lens mass models and large-scale structure must be carefully modeled.
• The total uncertainty in H₀ from lensing can be reduced below 10% with the measurement of several additional time delays and improved modeling.
• The feasibility of achieving sub-10% precision depends critically on controlling uncertainties in lens mass distributions and line-of-sight structure.
• The method is theoretically sound and offers a promising path to a cosmologically independent H₀ measurement.
• The paper concludes that with sufficient data and modeling, gravitational lensing can provide a competitive and independent constraint on the Hubble constant.