- 4053 - DARK ENERGY - Why is it 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”.
---------- 4053 - DARK ENERGY - Why is it expanding the Universe?
- 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.
-
-
June 13, 2023 DARK ENERGY
- Why is it expanding the
Universe? 4053
------------------------------------------------------------------------------------------
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------ “Jim Detrick” -----------
--------------------- ---
Tuesday, June 13, 2023 ---------------------------------
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