WMAP determined that the universe is flat, from which it follows that the mean energy density in the universe is equal to the critical density (within a 0.5% margin of error). This is equivalent to a mass density of 9.9 x 10-30 g/cm3, which is equivalent to only 5.9 protons per cubic meter.
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There seem to be two parts to your question
- Why is the universe flat?
and
- Why is the energy density of the dark energy component so similar to the matter density?
The theory of inflation was proposed to explain 1) as well as the 'horizon problem'. For 2) there doesn't seem to be a generally accepted and convincing answer at the moment.
Supporters of the mainstream 'Concordance Cosmology' believe that answers to your questions have been found (for 1) or will be found for 2).
Others believe that a more radical approach is needed.
answered Dec 6, 2021 at 12:57
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$\begingroup$ @ Kapish Lakhotia for an alternative non mainstream proposal vixra.org/pdf/2006.0209v2.pdf $\endgroup$ Commented Dec 6, 2021 at 13:02
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$\begingroup$ please give some images for explanation and explain it with your mathematical derivations. $\endgroup$– user318515Commented Dec 7, 2021 at 5:03
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1$\begingroup$ It can't be done quickly, but the main idea is that the Hubble parameter is half the mainstream value, but $v=2Hd$, since the redshift-scale factor relation is changed. That causes $\Omega_m$ to be $1.0$ from measurements of $\Omega_mh^2$ and $\Omega_{\Lambda}$ to be zero, then there is no longer a coincidence problem, for more details please see the link. $\endgroup$ Commented Dec 7, 2021 at 9:17
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$\begingroup$ How can v=2Hd, it is described by the equation v = H0D, with H0 the constant of proportionality—Hubble constant—between the "proper distance" D to a galaxy, which can change over time, unlike the comoving distance, and its speed of separation v, i.e. the derivative of proper distance with respect to cosmological time coordinate. $\endgroup$– user318515Commented Dec 7, 2021 at 9:34
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1$\begingroup$ It's because$ H=\frac{H_0}{2}$ due to an alternative redshift scale factor relation $\endgroup$ Commented Dec 7, 2021 at 9:37