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I have read that Dark energy composes roughly 68% of the Universe and that Dark matter composes about27% and everything else is less than 5%.

Where and how did they come up with these figures?

Big Ed
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There is a model called Lambda-CDM, which stands for Cosmological Constant-Cold Dark Matter. It basically models the universe as a general relativistic fluid made up of ordinary (baryonic) matter, cold dark matter and a cosmological energy density. Baryonic matter and dark matter have gravitational attraction, the cosmological constant produces a repelling term. With this model one can calculate what the universe should look like, for instance it can predict how fast the galaxies should be retreating from us and what the structure of the cosmic microwave background should look like. We then compare the output of this model with the astronomical data that we have and tweak its parameters (the total amount of baryonic matter, cold dark matter and the value of the cosmological constant) until we get the best fit.

CuriousOne
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