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- · arXiv e-print (arXiv:1401.2939)
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Abstract
We study the dark energy equation of state as a function of
redshift in
a non-parametric way, without imposing any {\it a priori} $w
(z
)$ (ratio
of pressure over energy density) functional form. As a check of the
method, we test our scheme through the use of synthetic data sets
produced from different input cosmological models which have the same
relative errors and
redshift distribution as the real data. Using the
luminosity-time $L_
{X
}-T_
{a
}$ correlation for GRB X-ray afterglows (the
Dainotti et al.
correlation), we are able to utilize GRB sample from the
{\it Swift} satellite as probes of the expansion history of the Universe
out to $z \approx 10$. Within the assumption of a flat FLRW universe and
combining SNeIa data with BAO constraints, the resulting maximum
likelihood solutions are close to a constant $w=-1$. If one imposes the
restriction of a constant $w$, we obtain $w=-0.99 \pm 0.06$ (consistent
with a cosmological constant) with the present day Hubble constant as
$H_
{0
}=70
.0 \pm 0.6$ ${\rm km} \, {\rm s
}^
{-1} {\rm Mpc
}^
{-1
}$ and
density parameter as $\Omega_{\Lambda 0
}=0
.723 \pm 0.025$, while
non-parametric $w
(z
)$ solutions give us a probability map which is
centred at $H_
{0
}=70
.04 \pm 1$ ${\rm km} \, {\rm s
}^
{-1} {\rm Mpc
}^
{-1
}$
and $\Omega_{\Lambda 0
}=0
.724 \pm 0.03$. Our chosen GRB data sample with
full correlation matrix allows us to estimate the amount, as well as
quality (errors) of data, needed to constrain $w
(z
)$ in the
redshift
range extending an order of magnitude in beyond the farthest SNeIa
measured.
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