- 3992 - DARK ENERGY - expanding the Universe? Most astronomical data we have today confirms the 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”
--------------- 3992 - DARK ENERGY - expanding the Universe?
- 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”
-
- 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 = 0
-
---------------- 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.
-
-
- 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.
-
- 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.
-
------------------ Universe Mass in terms of galaxies = 4.2
*10^105 . That is how many Milky Way
size galaxies would be in the Universe.
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.
-
- 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.
-
May 9, 2023 DARK
ENERGY - expanding the Universe? 1290 3992
----------------------------------------------------------------------------------------
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whomever is interested. ---
--- Some
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--- to:
------
jamesdetrick@comcast.net
------ “Jim Detrick” -----------
--------------------- --- Tuesday, May 9, 2023
---------------------------------
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