# How can we measure the amount of Dark Matter in the universe to the level of a percent?

Through phenomena that scientists have observed we know that dark matter is a big player in maintaining a constant speed of objects in a galaxy which means that dark matter is an active participant. Now many scientists have concluded that dark matter makes up 85% of all the matter in the universe and what I wonder is that how can we approximate that value with only observations of the universe? If possible I would like to know about the idea in depth. Thank you.

• By "integer", I guess you must really mean number. Certainly "integer" is not the right word unless you're looking for an answer about rounding or choosing units of measure. Otherwise, the whole "to an integer" bit is actually redundant. Sep 22 at 4:13
• @JohnBollinger you are right but I used the word integer to put emphasize on the accuracy of the number. Though you are right. I will fix it immediately. Sep 22 at 7:39
• You seem to have missed my point. If you don't specify a unit of measure then saying "whole number" is no better than saying "integer". Any measurement can be made as a whole number by choosing a suitable unit -- defining one if necessary. Sep 22 at 15:40
• So you mean to say that we haven't chosen a unit in this case right? Do you mean it for the percentage or as a quantity? @JohnBollinger Sep 23 at 0:29
• I assumed you meant "to an integer number of percentage points" and changed the title accordingly
– Sten
Sep 23 at 2:22

The most precise figures for the amount of dark matter in the universe arise from measurements of the cosmic microwave background and are supported by estimates of the primordial abundances of helium and deuterium formed in the Big-Bang. There is then supporting evidence from the dynamics of stars and galaxies and from gravitational lensing. I will give an overview of this - you asked for answers "in depth" - Astronomy SE is not the forum for that, you need to ask specific questions.

(i) The cosmic microwave background.

The cosmic microwave background is formed when hydrogen ions (protons) combine with electrons as the temperature of the universe falls below about 3000 K, which happens about 380,000 years after the Big-Bang. The photons that are present in the universe at that time have a blackbody spectrum appropriate for a temperature of 3000 K. When the electrons and protons combine to form hydrogen atoms, the universe essentially becomes transparent to these photons. Then, as the universe expands, this radiation cools and so today is is at a temperature of 2.7 K and the spectrum peaks in the microwave region of the electromagnetic spectrum.

If that's all there were to it, then we would just see a uniform blackbody spectrum of microwaves in all directions as viewed from Earth, but there are small (about 1 part in 100,000) ripples and fluctuations in the temperature of the radiation depending on in which direction we look. These fluctuations arise from small compressions and rarefactions of the primordial plasma at the epoch when the radiation was released. The exact angular spectrum of these fluctuations (by that, I mean the amplitude of the temperature fluctuations and their angular size scale in degrees on the sky) is sensitive to how much normal matter (normal matter will interact with radiation in the early universe and behave like a normal gas when compressed) and dark matter (which does not interact with radiation or itself) there is in the universe. By analysing the fluctuations, both the total amount of matter in the universe and the ratio of dark/normal matter can be estimated. That is basically where your 85% dark matter figure comes from.

(ii) Primordial nucleosynthesis

In the first few seconds after the Big-Bang, the normal matter in the universe consists mainly of neutrons, protons and electrons. Once the temperature falls below about $$10^{10}$$ K, then as the universe expands then the neutrons and protons can start to comine to form deuterium nuclei. Further nuclear reactions are then able to form helium. Big-Bang nucleosynthesis then stops after about 10 minutes because the temperatures become too low to initiate nuclear reactions and any free neutrons decay to protons and electrons. The net result is a primordial abundance of deuterium and helium.

The amount of deuterium and helium (as a ratio to hydrogen) is sensitive to the amount of normal matter that is present in the universe (compared to the number of photons) at the epoch when the nuclear reactions were taking place. By measuring the abundance of deuterium and helium in the the oldest stars; in very metal-poor galaxies and in what is assumed to be pristine gas from the Big-Bang, one is able to estimate what these primordial abundances actually are. Comparing these with a theoretical model of Big-Bang nucleosynthesis, and getting the numbers of photons from the cosmic mirowave background, one obtains an estimate for the amount of normal matter in the universe.

If you then combine this estimate for the amount of normal matter in the universe with the fact that the overall matter density appears to be around 30% of the so-called critical density (which is established precisely from the cosmic microwave background measurements) then again you get an estimate for the ratio of dark/normal matter.

(iii) Supporting evidence

Further supporting evidence (though less precise) for the ratio of dark/normal matter comes from measurig the dynamics of stars and gas in galaxies, from measurements of the motions of galaxies in galaxy clusters and from the effects of gravitational lensing of background objects by foreground galaxies and galaxy clusters. All of these measurements tell us that there appears to be far more gravitating matter than can be accounted for by summing up what can be seen. Again, this "dark matter" appears to be about 85% (on average) of the total gravitating matter.

• Thank you @ProfRob this was exactly what I needed! Sep 21 at 13:27