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Dark Energy's Number | Cosmological Constant: Explained! - Duration: 8:56.

These are the Einstein equations. They belong to general relativity our current

theory of the behavior of macroscopic objects as well as gravity. But they didn't

always look like this. The Einstein equations were originally going to look

like this. But for a very specific reason this term was added. Spoiler alert!!

It was the acceleration of the expansion of the universe.

Let me explain. While Einstein was developing general relativity he was

asking astronomers at the time many questions, and something all astronomers

agreed on was that the universe were static and unchanging.

There was no start to the universe and there will be no ending this is how the

universe has always been and how it's always gonna be. There is no global

motion this is where the astronomical objects have always been. There may be

local motion, the earth is going around the Sun, but in the grand scheme of

things the universe is static. But this was bothering Einstein a lot. You see if

there was really no start to the universe, then his theory predicted that

gravity would eventually pull all matter into an infinitesimal point. So he

thought: But if every astronomer tells me the universe static it's more probable

that my theory is wrong instead of every astronomer in the world to be

wrong. So in order to fix his theory he had this term to his equations. Lambda

times G mu nu. This lambda is called the cosmological constant. Its purpose back

then was to counter the gravitational collapse. That way his theory would be

consistent with the astronomical observations. But in 1930 thinks changed.

Edwin hubble using the most powerful telescope at the time, made a

revolutionary discovery. He found that the universe wasn't static. It was

expanding. The further away he pointed his telescope the faster the galaxies

were moving away from us. So Einstein thought lambda wasn't needed anymore and

he removed it from his equations. But now lambda is back. Why? To explain dark

energy. We now know that the universe is not only expanding, but it does owe at an

ever-increasing rate. And the reason behind the acceleration of the expansion

is dark energy. Mathematically dark energy is expressed using lambda, the

cosmological constant. A positive value of lambda suggests an exponential

expansion of the universe. The current data that we have supports the idea of

a constant positive cosmological constant across the whole universe. Such

a thing would counter all the mass and pressure from the matter which would

gravitationally slow down the expansion. According to the second Freedman

equation with just Einstein's equations solved for the whole universe.

because of the cosmological constant we have a positive acceleration of the

scale factor, a double dot. Which means that the universe's expansion rate is

increasing. Without lambda the a double dot term would be negative, because the

density Rho and the pressure P of the universe both slow down the expansion.

But overall lambda wins and we have an accelerated expansion of the universe.

It's easy to underestimate the significance of the cosmological

constant and hard to overestimate it. Since lambda is dark energy's number and

dark energy is 68.3% of the universe. The reason why the

universe is how it is is mostly due to the cosmological constant. Lambda is the

reason the universe is flat. We derive that from the first Freedman equation.

The first Freedman equation is also a byproduct of the einstein's equations

solved for the whole universe and if you don't take into account lambda then the

first Freedman equation predicts that the universe has a negatively curved

hyperbolic spatial curvature. Because there is not enough matter, or I should

say density Rho, to stop the current acceleration of the universe that we

measure. Even without dark energy. If you include dark energy particles though you

find that there is enough stuff to flatten the universe. By including lambda

into Einstein's equations and as a consequence into the first Freedman

equation we get zero in both sides of the equation. Because cosmological

constant exactly cancels the right side from being negative. And that is

consistent with what we observe a flat universe, an Omega, the number which

describes the special shape of the universe, equal to one or more accurately

something between one point zero 28 and 0.9 72. So dark energy has two roles that

work against each other. First it introduces an anti-gravity effect which

fights and wins gravity from all the matter and results in an accelerated

expansion. But second it increases the density of the universe which helps

matter pull gravitationally the universe together by adding more stuff to the

universe. The former role is the reason why the expansion accelerates because

otherwise it will slowly decelerate but never reach zero. And the lateral role is the

reason the density of the universe is high enough to reach the critical

density and result in a flat geometry. So what is the value of the cosmological

constant? haha good question! Experimentally by measuring the

expansion rate of the universe and by analyzing the CMB, we have found that in

SI units lambda is 1.5 times 10 to the minus nine joules of energy per cubic

meter the average of one point 52 times ten to the minus nine and one point

forty eight times ten to the minus nine. This is the amount of dark energy a

cubic meter of vacuum has. So we know what lambda does we know what's the

value of lambda but what is lamda? What is vacuum energy? Well the leading

interpretation of dark energy suggests that this energy comes from quantum

fluctuations described by quantum field theory. But if you apply the quantum

field theory prediction of how much energy a cubic meter of vaccum contains

just from quantum fluctuations you conclude that lambda is 10 to the power

of 113 joules per cubic meter. See the problem? Experimentally we know

that lambda is 1.5 times 10 to the minus 9 but QFT predicts a vacuum energy of 10

to the power of 113. This is one of the biggest mysteries of physics. It is

called the cosmological constant problem. When we say that we don't fully

understand dark energy that's what we mean. And the worst part is we have no

explanation. But it may lead us the way to another revolution in physics.