Constrained the transparency of the universe & cosmological parameters of interest using the Chi-squared minimization routine.
Is the Universe Transparent?
Please find attached the 'Report' file containing the work.
Abstract: Assuming flat $\Lambda$CDM cosmology, supernovae and $H(z)$ (expansion rate of the universe) data are analyzed to find out ‘How transparent is the cosmos?’. By considering how distances are affected in a non-transparent universe,
and combining analysis of supernovae with analysis of cosmic expansion rate measurements, the parameter $\epsilon$ is constrained. This parameter encodes departures from a transparent universe. It is found that $\epsilon \thicksim -0.02$,
or more coarsely, lies in the range $-0.06 \lessapprox \epsilon \lessapprox 0.04$ ($3\sigma$). These findings support a transparent universe (negligible opacity). The amount of matter (ordinary & dark) and dark energy in the current epoch
are also determined. This is done by constraining the mass density parameter $\Omega_m$ using supernovae data. The following results are obtained: $\Omega_m$ = $0.276_{-0.050}^{+0.061}$ (99.73% confidence), or equivalently
$\Omega_{\Lambda}$ = 0.724. These results imply the universe today is dominated by dark energy ($72\%$) whereas matter makes up the remaining $28\%$.
In this Project:
Constrained cosmological parameters of interest using the $\chi^2$-minimization routine.
Constrained the transparency of the Universe using the $\chi^2$-minimization routine.
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