  Gamma-ray bursts (GRBs) are cosmological explosions which carry valuable
information from the distant past of the expanding universe. One of the
greatest discoveries in modern cosmology is the finding of the accelerated
expansion of the universe using Type Ia supernovae (SN Ia) as standard candles.
However, due to the interstellar extinction SN Ia can be seen only up to a
redshift $z\sim 1.5$. GRBs are considered as the potential alternative to push
this limit to as high as $z\sim 10$, a redshift regime corresponding to an
epoch when the universe just started to form the first structures. There exist
several correlations between the energy and an observable of a GRB which can be
used to derive luminosity distance. In recent works, we have studied spectral
evolution within the individual pulses and obtained such correlations within
the pulses. Here we summarize our results of the pulse-wise GRB correlation
study. It is worth mentioning that all GRB correlations are still empirical,
and we cannot use them in cosmology unless we understand the basic physics of
GRBs. To this end, we need to investigate the prompt emission spectrum which is
so far generally described by the empirical Band function. We shall discuss our
current understanding of the radiation process particularly the finding of two
blackbodies and a powerlaw (the 2BBPL model) as the generic spectral model and
its implication. This is a work in progress and we expect to obtain the most
fundamental GRB correlation based on our improved spectral model.
