Relationship between Dark Energy and Dark Matter

I have encountered two seemingly contradictory theories on this(I don't know which one of them is correct, or where I am wrong):-

1. From Wikipedia:

Measurements of cosmic microwave background (CMB) anisotropies indicate that the universe is close to flat. For the shape of the universe to be flat, the mass/energy density of the universe must be equal to the critical density. The total amount of matter in the universe (including baryons and dark matter), as measured from the CMB spectrum, accounts for only about 30% of the critical density. This implies the existence of an additional form of energy to account for the remaining 70%."

The above statement, if correct, I suppose indicates that there is a critical density for which mass/energy has to account for. This means that if suppose there was no Dark Matter, our calculations/assumptions regarding the amount of Dark Energy would have been much higher(because then Dark Energy would have to account for a greater share of critical density).

2. The universe is accelerating in expanding. Dark Energy is supposed to cause this acceleration in expansion. While ordinary matter plus Dark Matter, is supposed to reduce this acceleration/expansion through gravity. So, according to this theory, if there would have been no Dark Matter, then there would be less Dark Energy required to account for the observed acceleration in expansion, so our calculations/assumptions regarding the amount of Dark Energy would have been lower.

First of all, if there were no dark matter (DM), you wouldn't ask this question, since structures — including galaxies, stars, planets, and you — wouldn't have had the time to form in the early Universe before it had expanded too much for gravitational collapse to occur. But let's use magic and make the galaxies anyway:

1. The CMB (specifically the power spectrum of the CMB) shows that the total density $\rho_\mathrm{tot}$ of mass/energy in the Universe is extremely close to the critical density $\rho_\mathrm{c}$. That is, $$\frac{\rho_\mathrm{tot}}{\rho_\mathrm{c}} \equiv \Omega_\mathrm{tot} \simeq 1.$$ The "$\Omega$" is a common way to express densities; as a ratio to the critical density. The CMB also gives some constraints on the total amount of mass (DM + "normal" matter, i.e. baryons), but it is better at constraining the ratio of baryons-to-DM. Together with the matter density $\Omega_\mathrm{M}=\Omega_\mathrm{b}+\Omega_\mathrm{DM}$ obtained from observations of supernovae and, in particular, baryonic acoustic oscillations, we then obtain the amount of DM. This fraction is roughly $\Omega_\mathrm{DM}=0.26$ (Planck Collaboration et al. 2016). If there were no DM, then $\Omega_\mathrm{tot}$ just wouldn't be $1$, but rather $\Omega_\mathrm{tot} - \Omega_\mathrm{DM} \simeq 0.74$.

2. Similarly, if there were no DM, there would be less matter to counteract the expansion of the Universe. That means that we wouldn't observe the same relation between the brightness and the distance of supernovae, from which we infer the presence of dark energy (DE). Instead, the brightnesses would be somewhat lower, because the supernovae would be farther away due to the faster expansion.

In other words, you are right that if there were no DM, and if we observed the same thing as we do, then there would be a contradiction. But if there were no DM, we wouldn't see what we see. Therein lies the resolution.

• I am unable to fully understand your explanation. I am not a pro in this subject. Can you please try to explain in more lucid terms. One thing specifically I didn't got, was the mathematical sign with subscripts 'tot' and 'DM'. What does it represent? – amsquareb Jun 27 '17 at 8:27
• @amsquareb: Sorry, I was being a bit too fast. Generally, the $\Omega$'s are used as the ratio between some component of the Universe (e.g. dark matter (DM), baryons (b), dark energy ($\Lambda$), radiation (rad), …) and the critical density. Specifically, $\{\Omega_\mathrm{DM}, \Omega_\mathrm{b}, \Omega_\Lambda, \Omega_\mathrm{rad}\} \simeq \{0.263, 0.045, 0.692, 10^{-5}\}$. I tried to explain better. Let me know if something's still unclear. – pela Jun 27 '17 at 12:08
• @amsquareb I think the real point to stress is the last two sentences. The contradictions pointed out don't really exist because the universe wouldn't be the same if you made the changes you proposed. You artificially caused the contradiction by saying, let's assume some parts of the universe are different but other parts aren't. – zephyr Jun 27 '17 at 15:24
• @pela Thanks a lot, I really appreciate. However, by the below statement:- "If there were no DM, then Ωtot just wouldn't be 1, but rather Ωtot−ΩDM≃0.74." - Do you mean that Ωtot would be .74 if there were no DM? – amsquareb Jun 27 '17 at 18:06
• @pela Also, it seems from your answer that DM and DE are completely independent of each other. Is that really the case? Suppose we lower or increase one entity, will there be no effect on the total amount of the other? – amsquareb Jun 27 '17 at 18:15

refers to “Retarded Gravitation Theory"

C. K. Raju “ The abstract says

Retarded gravitation theory C. K. Raju School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia Current address: Albukhary International University, 05200 Alor Setar, Malaysia ckr@ckraju.net

"Abstract. We propose a Lorentz-covariant theory of gravity, and explain its theoretical origins in the problem of time in Newtonian physics. In this retarded gravitation theory (RGT), the gravi- tational force depends upon both retarded position and velocity, and the equations of motion are time-asymmetric retarded functional differential equations. We explicitly solve these equations, un- der simplifying assumptions, for various NASA spacecraft. This shows that the differences from Newtonian gravity, though tiny within the solar system, are just appropriate to explain the flyby anomaly as a v effect due to earth’s rotation. The differences can, however, be large in the case of c a spiral galaxy, and we show that the combined velocity drag from a large number of co-rotating stars enormously speeds up a test particle. Thus, the non-Newtonian behaviour of rotation curves in a spiral galaxy may be explained as being due to velocity drag rather than dark matter. RGT can also be tested in the laboratory. It necessitates a reappraisal of current laboratory methods of deter- mining the Newtonian gravitational constant G. Since RGT makes no speculative assumptions, its refutation would have serious implications across physics."

Dark matter is an artifact introduced to get over the use of Newtonian mechanics without accounting for propagation of gravity over long distances (like light) knowing well that gravity has the same speed of propagation."

C.K. Raju thinks it is a major error.

• The question asked for clarification of dark matter theory, not for alternatives in case it's wrong. – Mike G May 3 at 17:26
• This is about dark matter. If it does not exist, it is important to know! Anyhow it is science where questions are welcome even if it is not exactly on the point. – Partha Shakkottai May 3 at 17:51
• There are alternatives to Dark Matter, yes, but there are very many other points that Dark Matter solves, that other DM alternatives do not. Scientists use the working hypothesis which explains the most data points and that's DM at the moment. OP asked about DM and not about alternatives. Particularly, this is not a place to promote this work. Scientific conferences would be. – AtmosphericPrisonEscape May 3 at 19:40