Abstract
Gamma-ray bursts (GRBs) are brief, intense flashes of gamma rays, representing
the most energetic explosions in the universe. GRBs are hundreds of times more
luminous than supernovae and can last from a few milliseconds to several minutes,
originating in distant galaxies. Their enormous energy output, reaching up to 1055 erg
in isotropic-equivalent energy, combined with their detectability at high redshifts (up
to z = 9.4), positions them as promising candidates for use as cosmological standard
candles. In contrast, Type Ia supernovae (SNe Ia) are limited to redshifts of (z ∼ 2.6
and 2.9). This exceptional reach has motivated increasing interest in utilizing GRBs as
cosmic probes to measure distances, investigate the large-scale structure of the universe,
and study its evolution and dynamics.
Many GRB-based cosmological studies rely on spectral analyses of observable
data to infer redshifts and constrain cosmological parameters through spectral indices.
Accurate redshift determination is crucial for establishing correlations between GRB
energetics and cosmological distances, a foundational step toward validating GRBs as
reliable standard candles. In recent years, machine learning (ML) techniques have been
increasingly applied to estimate redshifts, particularly for GRBs lacking spectroscopic
measurements. These approaches offer innovative solutions to overcome observational
limitations and enhance the utility of GRBs in cosmological research.
This thesis investigates two complementary approaches: (1) employing machine
learning techniques to estimate GRB redshifts, and (2) conducting joint spectral analyses
to examine empirical correlations, such as the Amati and Yonetoku relations. These correlations
require redshift measurements to connect GRB energetics with phenomenological
trends.
The Amati relation links the intrinsic peak energy (Ei,peak) of a GRB’s spectrum to its
isotropic-equivalent energy (Eiso) over the burst duration (T90). This correlation provides
insight into the energy distribution of GRBs and their potential as standard candles. The
Yonetoku relation, in contrast, connects Ei,peak to the isotropic luminosity (Liso), further
strengthening the case for using GRBs in cosmological applications, particularly for
highly energetic GRBs observed by modern space telescopes.
The study begins with an analysis of GRBs with known redshifts, focusing on those
observed by the Fermi Gamma-ray Burst Monitor (GBM) 126 GRBs and Konus-Wind
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(KW) 338 GRBs between 2005 and 2018. To overcome the limited availability of
spectroscopic redshifts, various machine learning models, including deep learning and
random forest algorithms, are employed to estimate pseudo-redshifts for additional
Fermi-GBM GRBs. These models, referred to collectively as the “Ensemble Model,“ are
designed to mitigate overfitting, improve redshift estimation, and significantly expand
the usable dataset. Using spectral data from the Fermi-GBM and KW catalogs, with
fits based on the Band and Comptonized (Comp) models for both fluence and flux, a
Kolmogorov–Smirnov test reveals the best agreement between true and pseudo-redshifts
using the Comp-flux model (p-value = 0.863), suggesting the two samples are statistically
consistent.
With the enlarged sample of 1708 GRBs, the Amati and Yonetoku relations are further
investigated. The Yonetoku relation is applied using the best-performing ensemble model
trained on Comptonized spectral fits, allowing a more robust evaluation of whether the
increased data volume improves constraints on the empirical correlations.
This analysis improves cosmological constraints by incorporating external datasets,
including the U2.1 supernova compilation and data from the Dark Energy Survey. A
joint analysis of these with the GRB dataset yields updated cosmological parameters.
Using both the pseudo-redshift and true-redshift GRB samples, the results are H0 =
69.88 ± 0.44 and ΩΛ = 0.72 ± 0.02. These values are derived using the Yonetoku
correlation.
Building upon prior studies, a joint spectral analysis is also performed for 42 GRBs
observed between 2008 and 2024 using data from the Fermi GBM, Large Area Telescope
(LAT), and LAT Low Energy (LLE) instruments. The main objective is to reduce
uncertainties in key spectral parameters, especially the spectral indices and intrinsic peak
energy (Ei, peak). Each GRB is analyzed over two time intervals: (1) the time-integrated
(T90) and (2) the peak-flux interval. Separate spectral fits are conducted using joint
GBM–LAT–LLE data and GBM-only data. This comparison assesses improvements in
parameter precision and their implications for the Amati and Yonetoku correlations.
Results from 37 Fermi GRBs with known redshifts indicate that joint spectral
fits provide more precise measurements and consistently shift Epeak to higher values
compared to GBM-only fits. Furthermore, lower Bayesian Information Criterion (BIC)
values in joint fits suggest improved statistical validity. These enhancements lead to
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reduced uncertainties in the Amati and Yonetoku correlations, reinforcing their reliability
for cosmological applications.
Finally, cosmological parameters are estimated using the distance modulus derived
from GRBs with spectroscopic redshifts, combined with GRBs from previous studies.
The joint analysis yields H0 = 69.63 ± 0.23 and ΩΛ = 0.57 ± 0.02 from the Amati
correlation, and H0 = 69.68±0.43 and ΩΛ = 0.70±0.02 from the Yonetoku correlation.