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In an empty universe (the dashed line [link] and the coasting universe in [link] ), neither gravity nor dark energy is important enough to affect the expansion rate, which is therefore constant throughout all time.

In a universe with dark energy, the rate of the expansion will increase with time, and the expansion will continue at an ever-faster rate. Curve 4 in [link] , which represents this universe, has a complicated shape. In the beginning, when the matter is all very close together, the rate of expansion is most influenced by gravity. Dark energy appears to act only over large scales and thus becomes more important as the universe grows larger and the matter begins to thin out. In this model, at first the universe slows down, but as space stretches, the acceleration plays a greater role and the expansion speeds up.

The cosmic tug of war

We might summarize our discussion so far by saying that a “tug of war” is going on in the universe between the forces that push everything apart and the gravitational attraction of matter, which pulls everything together. If we can determine who will win this tug of war, we will learn the ultimate fate of the universe.

The first thing we need to know is the density of the universe. Is it greater than, less than, or equal to the critical density? The critical density today depends on the value of the expansion rate today, H 0 . If the Hubble constant    is around 20 kilometers/second per million light-years, the critical density is about 10 –26 kg/m 3 . Let’s see how this value compares with the actual density of the universe.

Critical density of the universe

As we discussed, the critical density is that combination of matter and energy that brings the universe coasting to a stop at time infinity. Einstein’s equations lead to the following expression for the critical density ( ρ crit ):

ρ crit = 3 H 2 8 π G

where H is the Hubble constant and G is the universal constant of gravity (6.67 × 10 –11 Nm 2 /kg 2 ).


Let’s substitute our values and see what we get. Take an H = 22 km/s per million light-years. We need to convert both km and light-years into meters for consistency. A million light-years = 10 6 × 9.5 × 10 15 m = 9.5 × 10 21 m. And 22 km/s = 2.2 × 10 4 m/s. That makes H = 2.3 ×10 –18 /s and H 2 = 5.36 × 10 –36 /s 2 . So,

ρ crit = 3 × 5.36 × 10 –36 8 × 3.14 × 6.67 × 10 –11 = 9.6 × 10 –27 kg/m 3

which we can round off to the 10 –26 kg/m 3 . (To make the units work out, you have to know that N , the unit of force, is the same as kg × m/s 2 .)

Now we can compare densities we measure in the universe to this critical value. Note that density is mass per unit volume, but energy has an equivalent mass of m = E / c 2 (from Einstein’s equation E = mc 2 ).

Check your learning

  1. A single grain of dust has a mass of about 1.1 × 10 –13 kg. If the average mass-energy density of space is equal to the critical density on average, how much space would be required to produce a total mass-energy equal to a dust grain?
  2. If the Hubble constant were twice what it actually is, how much would the critical density be?


a. In this case, the average mass-energy in a volume V of space is E = ρ crit V . Thus, for space with critical density, we require that

V = E grain ρ crit = 1.1 × 10 –13 kg 9.6 × 10 –26 kg/m 3 = 1.15 × 10 12 m 3 = ( 10,500 m ) 3 ( 10.5 km ) 3

Thus, the sides of a cube of space with mass-energy density averaging that of the critical density would need to be slightly greater than 10 km to contain the total energy equal to a single grain of dust!

b. Since the critical density goes as the square of the Hubble constant, by doubling the Hubble parameter, the critical density would increase by a factor a four. So if the Hubble constant was 44 km/s per million light-years instead of 22 km/s per million light-years, the critical density would be ρ crit = 4 × 9.6 × 10 –27 kg/m 3 = 3.8 × 10 –26 kg/m 3 .

Questions & Answers

understanding astronomy
ricardo Reply
What About Understanding Astronomy?
what is astronomy?
Currently, I'm studying in 10th grade. What should I do after my 10th so that I can get an astronomy career?
Chaya Reply
try jee exam and achieve a good score in jee advance to join in IIST(Space research institute)
okay.. thanks
this famous person was the first to recognise earthshine on the moin
Rajan Reply
Leonardo Da Vinci.....
what is string theory?
sakshi Reply
A Cosmological Theory Based On The Exsistence Of Cosmic Vibrating Strings.....
Does MIT have good astrophysics courses ?
priyanshu Reply
Probably The Best In The United States.....
But Don't Get Caught Up On Who's The Best, You Can Be The Next Noble Winning Astrophysicist.....
hmmm..........that's nice one....Adam had said.....
How did ASTRONOMY helped you understand yourself ? 🤔
Hussain Reply
why do you want to study ASTRONOMY?
Hussain Reply
It is one of the natural sciences and therefore worth exploring. You are a part of the universe and it is a part of you. The sky is my classroom. (student of cosmology, Oxford Uni)
because everything in the space is just beautiful...interesting and worth studying and exploring...
I have been studying astrophysics an love it
I love to learn what makes up our lives an heavens an how it works there us so much more out there than books an our veiw of thw heavens can reveal
How did ASTRONOMY helped you understand yourself ?
Because it proves the impossibles and the limitless.
It helped me realize that there are like countless possibilities in life and get all through it.
It honestly showed me to view the world in a balanced way. Because space beautiful and calm yet violent, and so is the world, and we should still help, but there will always be violent people much like violent astrophysical jets.
What does ASTRONOMY means?
Does anyone know where can I study astronomy in Spain? My budget is too low for traveling out there...
Valerian Reply
How long the duration was when the laws of physics became active after the big bang?And why the time is called plank's time?
Mostak Reply
how many galaxies in universe?
Shaikh Reply
10 to the power 11
if u can count all the sands on the beaches and on the deserts then u will know how much it will be.......some said more than 1,000,000,000 galaxies are there in our universe...
it's ok bro
I hope you will become a member of nasa
just new in this area, from art background not science
what's ur name wwe
The Observable Universe Contains Between 200 Billion To 2 Trillion Galaxies.....
are u sure?
It actually hasn't been proven, people have just made estimations.
the thing is u can't count,maybe the our number system will collapse there...who knows?
What's the exact time when the laws of physics became active after the big bang ?
Actually we still don't know the exact number of galaxies in the universe, since the universe is bigger than we can imagine and it is still expanding even bigger today than yesterday
we didn't actually find the exact number but may be it is around 100 billion
why this universe is expanding?
Science Does Not Concern It Self With Why Questions, Science Is Geared For How And What Questions.....
Why Questions Form And Endless Loop.....
According to the universal law of cause and effect .any phenomenon that occur in this universe should have any reason , nothing happen without any reason.
Can you tell me the expanding speed of this universe.
yes that would be a great question to have answered what is the expanding speed of the universe?
Remember that most of what you can see is light years away. We're looking back in time, we can never know the current nature of our observations, only glimpse the galaxies and stars as they once were. Strange but true, and a little sad.
Correct, That's Why Telescopes Are Like Time Machines, You See The Past.....
really telescope can see the past?....i meant everything is in its place, though it rotates or revolve or whatever it is.......but how can this telescope can see the past.....can we see how our Universe was created,how it formed out of it? thats my question to all of you guys can you plz tell me.
Because We Dont See Any Object In Space As It Is, We See It As It Was..... Hope This Clears That Up For You.....
And One Day We Might Have A Telescope That Will Show Us The Big Bang.....
ok....... that will be nice one
ok....... that will be nice one
Travel at light speed in a spaceship at 186,000 miles every SECOND. At this speed it will take you 100,000 years just to cross our Milky Way galaxy, which is just a dot in the sky. Next stop, the Andromeda galaxy, after 2.5 million years, still in the Local Group, Virgo Supercluster, still a dot.
Pretty Much.....
there are nearly 200 million I suppose.
hi i need a telescope would you help mee
Nauman Reply
i can only advice you to go to some museum
wher is it?
but before that.......... i wanna know where are you from and from which state...and if you are nearer to that of the museum or will be able to go then.,.. i donot have any more words.
What Do Plan To Observe?
sorry . i am from asia
Check on amazon.Celeston telescopes are good for beginners.
can yoy introduce your self
can you
Asia...? from which country you belong into ...,,is it India or where?
Do You Want A Telescope With ALot Of Maintenance Or Zero Maintenance?
with alot offf
Any second hand online stores in your area? great for unused Christmas gifts etc..
So You Want A Newtonian Reflector?
hey guys I wanna ask you all that will it be safe or helpful to communicate with an intelligent civilization like are we safe ?
Is the Orion Sky Quest XT6 a good Dobsonian?
Look for a Sky Watcher 130BKS, it has an upgraded dual speed 2" focuser. You can use 1.25" or 2" eyepieces with it and it is quite easy to pollinate using a simple visual collimating eyepiece. This scope is great and ready for prime focus astrophotography if you choose to go that route.
Sorry, spell check error. Pollinate should be collimate. lol
Dobsonians Require A Lot Of Maintenance, If You Don't Mind Cleaning And Collimating On A Regular Basis, Then Go Ahead A Dobsonian Puts Up Excellent Views Especially For Deep Space Objects..... Now If You Don't Want Constant Maintenance Then A Schmidt Cassegrain Might Be A Better Fit For You.....
So what i would put for that answer ?
Abdulla Reply
The largest observatory complex in the world is on Mauna Kea, the tallest mountain on Earth. Whatare some factors astronomers consider when selecting an observatory site? Don’t forget practical ones.Should astronomers, for example, consider building an observatory on Denali (Mount McKinley) or MountEverest?
Abdulla Reply
i need help on the the second part
Should astronomers for example considered building an observatory on Denali (Mount Mckinley) or MountEverest ?
I would take into consideration. climate weather pattern.
also, could an establishment be built and be able to sustain years of being beaten by the weather?
so far Mount Everest to my understanding is a difficult mountain
it is because of light pollution in the cities that the observatories are situated in extremely remote areas.
Everest ist the tallest mountain
how far us milky way galaxy?
ShowsSpy Reply
oh man
We are part of the Milky Way Galaxy. We are within it, so it's not really away from us. Our galaxy is 100,000 light years in diameter. The nearest big galaxy is Andromeda, around 2 million lightyears away.
its 200,000 light years
Where is Rice University located?
Amanda Reply
it is in your vagina
that couldn't be any more wrong 😂😂
what even is this conversation😂😂!?
Show Some Class.....
Houston, Texas.....
Practice Key Terms 3

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Source:  OpenStax, Astronomy. OpenStax CNX. Apr 12, 2017 Download for free at http://cnx.org/content/col11992/1.13
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