--------- #1290 - Why is Dark Energy Expanding the Universe?
- Most astronomical data we have today confirms the fact (theory in fact) that the Universe is still expanding at an ever increasing rate. The cause is suspected to be some type of anti-gravity that is named “ Dark Energy”. We know what gravity is and we expected gravity to eventually stop the expansion and reverse the Universe into a “ Big Crunch”. However, we now think that Dark Energy is the predominate force in the Universe and that it will expand the Universe forever into a “Cold , Rarified Space of almost Nothing”
- Attachment - Big Bang
- The math for this tug of war between gravity and expansion was first invented by Albert Einstein. Einstein put a fudge factor in his equations because he did not know the Universe was expanding. He thought it was static and he needed to add the “ Cosmological Constant” to balance the two forces and make the Universe static. In 1920 Edwin Hubble discovered that indeed the Universe was not static, it was expanding and the galaxies were receding away at enormous speeds. The further their distance the faster their recession.
- In addition to this revelation from Hubble other scientists pointed out that his equations in balance were impossible in reality. It was like balancing a pencil on its point. The slightest imbalance would cause the pencil to collapse to the ground. For the equations to work the Universe had to be either expanding or collapsing. Einstein was humiliated and called the Cosmological Constant the greatest blunder in his life.
- To get a static Universe Einstein had to balance the acceleration of gravity with a negative vacuum pressure. The sum of the two had to be zero.
----------- The Force of gravity = F = G * M * m / R^2
------------ The Force of gravity is equal to the product of the Gravitational Constant, “G”, the two masses, “M*m”, and inversely to the square of the distance, “R^2”.
------------ The Force of gravity = mass * acceleration of gravity
------------- F = m*a
----------- Acceleration of gravity = F / m = G * M / R^2
- Next we introduce the term “ Critical Density” which is the precise amount of mass in the Universe to exactly balance between the re-collapse of gravity and the expansion of Dark Energy. Density is the mass per unit volume.
--------------- Density = mass / volume
------------------ If we assume the volume to be a uniform sphere = 4/3 pi* R^2
---------------- Acceleration of gravity = G* M / R^2
----------------- Acceleration of gravity = G * Density * Volume / R^2
---------------- Acceleration of gravity = G * Density * 4/3pi * R
- Now we need to subtract the negative pressure due to the vacuum energy density of space. In this case we use Einstein’s equation, E = m*c^2
----------------------- E = Density * Volume * c^2
------------------- Vacuum energy = Density * 4/3pi * R^3 * c^2
-------------------- Acceleration of gravity - Vacuum energy = zero
---------------- G * (Matter Density) * 4/3pi * R - (Vacuum Density) * 4/3pi * R^3 * c^2 = 0
- Unfortunately this equation for a static Universe is unstable. It can not stay static. The slightest tilt in favor of gravity or vacuum energy will cause a runaway Universe either collapsing or expanding, but, not static. Einstein called this the greatest blunder of his life.
- But, maybe the Cosmological Constant is not a blunder. In 1998 astronomers discovered that not only was the Universe expanding , it was expanding at an accelerating rate. Some anti-gravity force existed in the vacuum of space to cause this acceleration. The Cosmological Constant may be this Dark Energy that is this anti-gravity force. The Cosmological Constant just needs the right sign and the right value to match what astronomers were seeing.
- Dark Energy was a form of negative pressure counteracting gravity. It was a vacuum energy density that is constant over time and distance. Unlike gravity that is constant over time ( in theory) but decreases at the square of distance of separation.
- To illustrate negative pressure from a vacuum put a piston in a cylinder inside a vacuum. Pull the piston out and it produces another vacuum inside the cylinder. That vacuum must have some energy equal to the force used to pull out the piston. Vacuum energy. If the vacuum is trying to pull the piston back into the cylinder it must have “negative pressure”
- How can we estimate this negative pressure that is the force of Dark Energy? The amount of gravity trying to collapse the Universe depends on the amount of matter that occupies the volume of space. This “critical density” is the average density for the entire Universe that marks the dividing line between a re-collapsing Universe and one that will expand forever.
- What astronomers believe today is that the density is slightly less than the critical density. The force of gravity was dominant the first 7 billion years after the Big Bang. After that Dark Energy took over and has been the dominant force in the Universe for the last 7 billion years. The calculation for the critical density in this scenario is:
------------------------- Critical Density = 10^-26 kilograms / meter^3
- This seems like a very small number. To begin to understand it let’s calculate the average density inside our Solar System:
--------------------------- Density = mass / volume.
- The Sun is 99.85% of the total mass of the Solar System. The Sun’s mass is 2*10^30 kilograms.
--------------------- Solar System mass = 2 * 10^30 kilograms
--------------------- Solar System volume = 10^44 meters^3
-------------------- Solar System average density = 2*10^30 kilogram / 10^44 meter^3
-------------------- Solar System average density = 2*10^-14 kilogram / meter^3
-------------------- The average density of (10^-14 kg/m^3) is much heavier than the Critical Density (10^-27) so our Solar System must be dominated by gravity.
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- What is the average density inside the Milky Way Galaxy?
-------------------- Galaxy mass = 10^12 Solar Mass = 2 * 10^42 kilograms
-------------------- Galaxy radius = 100,000 lightyears = 10^21 meters
------------------- Galaxy area of disk = 10^42 meters ^2
-------------------- Galaxy volume = 6.7 * 10^62 meters^3
------------------- Height of the cylinder of the disk is 0.85 ^10^19 meters, or 900 lightyears.
------------------- Galaxy density = 3 *10^-21 kilograms / meters^3
- The average density inside the Milky Way Galaxy, (10^-21) is more rarified and closer to the Critical Density but still it is dominated by gravity by a factor of 1,000,000 times.
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- What is the average density of the Universe ?
------------------ Universe density = 8 * 10^-27 kilograms / meter^3.
------------------ Dark Energy density = 6 * 10^-27 kilograms / meter^3
------------------ Matter density = 2 * 10^-27 kilograms / meter^3
------------ Dark Energy density / Critical Density + Matter density / Critical Density = Critical Density / Critical Density = 1
------------ 0.75 + 0.25 = 1
- Dark Energy is 75% of the mass/energy of the Universe. And, it is expanding. Matter and Dark Matter are 25% of the mass/energy of the Universe.
-------------- 0,50 + 0.50 = 1 is the relationship for a static Universe which we do not have. Ours is a dynamic Universe unbalanced by the mysterious Dark Energy.
----------------- Universe Radius = 10^58 meters.
----------------- Universe volume = 4.2 *10^174 meters^3
------------------ Universe Mass = 8.4 * 10^147 kilograms
---------------- Universe mass in terms of Solar Mass = 4.2*10^117. That is how many Sun-size stars would be in the Universe if it were all matter.
------------------ Universe Mass in terms of galaxies = 4.2 *10^105 . That is how many Milky Way size galaxies would be in the Universe if it were all matter. The Observable Universe is estimated to have 100 billion galaxies (10^11) each with 100 billion stars (10^11). Therefore the Observable Universe has (10^22) Sun-sized stars (2*10^52 kilograms). That would mean the actual Universe is 10^95 times larger than the Observable Universe. The Observable Universe only has 10^58 atoms. This may be what makes us think that 75% of the Universe is Dark Energy. Energy and matter are two forms of the same thing, E=mc^2
- I have a problem with big numbers. I have to take off my shoes.
CONCLUSION: The conclusion is that the Universe has a positive but small vacuum energy density that is accelerating its expansion.
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(1) #1047 “ Is the universe like Swiss cheese
(2) Dark Energy ( 7 pages)
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