[Paper Review] Probing dark energy with gamma-ray bursts

Keitaro Takahashi, Masamune Oguri+2 more|arXiv (Cornell University)|May 15, 2003

Gamma-ray bursts and supernovae3 citations

TL;DR

This paper proposes using gamma-ray bursts (GRBs) as cosmological distance indicators by calibrating luminosity-variability and luminosity-lag relations with low-redshift GRBs whose distances are known from Type Ia supernovae. It demonstrates that combining Swift-era GRB data with current SNIa observations enables precise, independent constraints on the matter density $Ω_m$ and dark energy equation of state $w$, achieving ~20% accuracy in parameter estimation.

ABSTRACT

We propose a new method to use gamma-ray bursts (GRBs) as an alternative probe of the dark energy. By calibrating luminosity-variability and luminosity-lag time relations at low redshift where distance-redshift relations have been already determined from type Ia supernova (SNIa), GRBs at high redshift can be used as a distance indicator. We investigate the potential impact of future GRB data on determining the current matter density $Ω_{m}$ and the dark energy equation of state $w$ which is assumed to be constant. We show that a combined analysis of a data set expected from the {\it Swift} and the current SNIa data results in excellent determination of both $Ω_{m}$ and $w$.

Motivation & Objective

• To develop a method for using GRBs as standard candles to probe dark energy, overcoming limitations in current SNIa-based constraints.
• To calibrate luminosity relations (with variability and spectral lag) at low redshift using SNIa-derived distance measurements.
• To assess the potential of future GRB surveys (e.g., Swift) to independently constrain cosmological parameters $\Omega_m$ and $w$.
• To evaluate the robustness of GRB-based constraints against systematic errors and data volume variations.

Proposed method

• Calibrate the luminosity-variability ($L \propto V^{\alpha_V}$) and luminosity-lag ($L \propto \tau_{\rm lag}^{\alpha_{\rm lag}}$) relations using low-redshift GRBs with known distances from SNIa.
• Use the calibrated relations to estimate absolute luminosities of high-redshift GRBs ($z > 1$) for distance measurement.
• Apply the luminosity distance formula $d_L(z) = \frac{(1+z)c}{H_0} \int_0^z \left[ \Omega_m(1+z')^3 + (1-\Omega_m)(1+z')^{3+3w} \right]^{-1/2} dz'$ to relate magnitude and redshift.
• Perform $\chi^2$ minimization using observed apparent magnitudes, derived absolute magnitudes, and redshifts to constrain $\Omega_m$ and $w$.
• Simulate a GRB data set of 500 bursts with flux limits and redshift distribution matching Swift's expected performance.
• Combine simulated GRB data with current SNIa data (SCP, High-Z, Calán-Tololo) to improve parameter constraints.

Experimental results

Research questions

• RQ1 Can GRBs be reliably used as standard candles via luminosity-variability and luminosity-lag relations?
• RQ2 To what extent can future GRB data from Swift improve constraints on $\Omega_m$ and $w$ when combined with SNIa data?
• RQ3 How robust are the GRB-based constraints to systematic errors such as redshift uncertainty or reduced sample size?
• RQ4 Can GRB-based distance measurements break degeneracies that limit SNIa-only constraints on dark energy?

Key findings

• A combined analysis of simulated Swift GRB data and current SNIa data yields constraints on $\Omega_m$ and $w$ with approximately 20% accuracy.
• The $L/V$ and $L/\tau_{\rm lag}$ relations are successfully recovered from simulated low-redshift GRBs, yielding $L \propto V^{2.13}$ and $L \propto \tau_{\rm lag}^{-0.99}$.
• The GRB data set, with an average redshift of $\sim 3$, provides high leverage on $w$ due to its high-redshift distribution, complementing low-$z$ SNIa data.
• Even under pessimistic assumptions—300 GRBs or 0.2 in logarithmic redshift error—the $1\sigma$ confidence regions for $\Omega_m$ and $w$ remain well-constrained.
• Constraints from GRBs and SNIa are largely insensitive to other cosmological parameters such as $H_0$, spectral index, or mass fluctuation normalization, reducing degeneracy issues.
• The method enables independent, high-precision determination of both $\Omega_m$ and $w$, demonstrating the potential of GRBs as a complementary probe of dark energy.