# 29.2 A model of the universe  (Page 5/10)

 Page 5 / 10

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 ):

${\rho }_{\text{crit}}=\frac{3{H}^{2}}{8\text{π}G}$

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

## Solution

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,

${\rho }_{\text{crit}}=\frac{3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}5.36\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{–36}}{8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}3.14\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}6.67\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{–11}}=9.6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{–27}\phantom{\rule{0.2em}{0ex}}{\text{kg/m}}^{3}$

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 ).

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

$V=\frac{{E}_{\text{grain}}}{{\rho }_{\text{crit}}}=\frac{1.1\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{–13}\phantom{\rule{0.2em}{0ex}}\text{kg}}{9.6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{–26}\phantom{\rule{0.2em}{0ex}}{\text{kg/m}}^{3}}=1.15\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{12}\phantom{\rule{0.2em}{0ex}}{\text{m}}^{3}={\left(10,500\phantom{\rule{0.2em}{0ex}}\text{m}\right)}^{3}\cong {\left(10.5\phantom{\rule{0.2em}{0ex}}\text{km}\right)}^{3}$

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 ${\rho }_{\text{crit}}=4\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}9.6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{–27}\phantom{\rule{0.2em}{0ex}}{\text{kg/m}}^{3}=3.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{–26}\phantom{\rule{0.2em}{0ex}}{\text{kg/m}}^{3}.$

what is steral evolution (star evolution
hi
Nisha
when a star's mass changes over time
Joe
hi
Joe
hi
Lisette
Hii
Asim
hi
Nisha
what big bang
Nisha
yes joe over time chang star mass
Nisha
star prouduce nucluer fusion first stag ( hydroge fusion helium- carbon-neon-oxygen-silicon- last fusion iron hevy star mass not handle iron blast super nova
Nisha
what is the worm hole theory
it states that you can travel back through time by this. It's like folding a paper into half and making two points, and there states that you can bend spacetime but according to Einstein's equation that it can break easily and only really small particles can pass through it.
Dark
dark dream what is dark matter
Nisha
what is the great filter theory
Nisha
the great filter theory it's just like the literally filtering it says that when once a civilization achieved its highest state or let's say the highest technology for instance their civilization will end.
Dark
Nisha
Nisha
what is the simulatin hypothies
Nisha
smart obsevatin
Nisha
In radio astronomy, a fast radio burst (FRB) is a transient radiopulse of length ranging from a fraction of a millisecond to a few milliseconds, caused by some high-energy astrophysical process not yet identified. We can say that this can be they way to at least know if there's other civilizations~
Dark
~out there
Dark
Simulation hypothesis it proposes that the earth, the universe and the reality you are in is just an artificial simulation or like you are living in a computer simulation.
Dark
sir possible time travel
Nisha
?
Nisha
Yes. Everything is possible.
Dark
replay
Nisha
thanks
Nisha
sir how to make neutron star
Nisha
replay
Nisha
?
Nisha
sir what is the white hole?
Nisha
hi good morning
Nisha
why does the matter of an objects density change the fabric of space time rather than the objects volume..? (hopefully I have expressed that question properly) thanks
because an objects density consists of it's energy & momentum. an objects volume, for example a photon can have no density (hopefully I expressed that answer properly)
Joe
I suppose each Individual has his or hers different laws and assumptions, so it can be difficult to ask and answer physics questions, but discussions are always positive
Joe
how
Melaku
which matter use rocket
Nisha
Does their is any procedure of star making
Hope That Helps.....
how to produce star and how to dead star?
Nisha
waad mahad santnihiin dhamaan waxaan doonayaa inaan wax ka barto astronomyga waa maxay xidigis?
understanding astronomy
yap
Janmarc
what is astronomy?
Janmarc
define..
Janmarc
Currently, I'm studying in 10th grade. What should I do after my 10th so that I can get an astronomy career?
try jee exam and achieve a good score in jee advance to join in IIST(Space research institute)
Sri
okay.. thanks
Chaya
Hey there I want to be an astrophysicist... and I'm grade 9... what should I do to be an astrophysicist
Aymen
Know more about space,watch movies related to space ,and to become an astrophysicist u should be very good in physics,train urself to think everything logically. Start to focus on JEE Exam ,train urself or join any institute which is good in coaching for JEE ,then if u score high ,u can join IIST
Sri
Which is the best university for Astronomy
Asim
Probably Massachusetts Institute Of Technology.....
Math Math Math, Get Familiar With All Types Of Math.....
Which subject is most important for Astronomy
Asim
Geometry, Algebra, Calculus, Trigonometry, Do Alot Of It And Often.....
I Can't Say It Enough, Math Is The Language Of The Cosmos.....
Adam you are in which university?
Asim
I Went To University But Never Finished My Degree..... Had To Work And Couldn't Afford School.....
MaryMount University..... Philosophy Of Science Major.....
It ia a cathloic University. Am i write
Asim
And its main campas is in Arlington country
Asim
No, It's In New York City.....
It's Not A Catholic University.....
Ohh sorry
Asim
Are you interested in Astronomy
Asim
IIT ain't so good for Pure Astronomy. If you want to know how the universe works,go for pure science. If you want to make spacecraft,go for Aerospace Engineering
priyanshu
Your are in which university brother
Asim
I Love Astronomy, I'm An Active Amateur Astronomer.....
I also love Astronomy very much
Asim
And to help me to solve some puzzling questions
Asim
this famous person was the first to recognise earthshine on the moin
Leonardo Da Vinci.....
what is string theory?
A Cosmological Theory Based On The Exsistence Of Cosmic Vibrating Strings.....
Good Morning Asim Ali.....
I Can't Do That, You Can Ask Me What Ever You Want.....
If you don't mind can i ask why?
Asim
Do You Understand The Millions Of People Have Access To This Site, I Wouldn't Put My Information Out There, Knowing What People With Bad Intent Can Do With Personal Information.....
Ohh sorry
Asim
My question is that, there are many collision of stars in a day So that cause black hole. But is there any procedure of star making? Hopefully i ask my question properly.
Asim
No Need To Apologize, I Will Answer Anything You Need Answered And If I Can't Answer It I Will Guide You To The Answer.....
Thier Is Only One Way Stars Are Made, Gravity Makes Matter Come Together, And When The Amount Of Matter Gets Massive Enough Nuclear Fusion Starts Up And A Star Is Born.....
What is white drawft?
Asim
A White Dwarf Is A Low Mass Star That Has Exhausted All It's Central Nuclear Fuel And Lost It's Outer Layers As A Planetary Nebula.....
what is the great filter theory
Nisha
hi adam what is great filter theory
Nisha
Well First It's Not A Theory, It's A Hypothesis, The Great Filter Hypothesis States That What Ever Causes Dead Matter To Under Go Abiogenesis(Start Of Life) Must Be Very Hard And Very Rare In Our Universe, Because So Far We Only See 1 Civilisation That Made Through All The Requirements For.....
Intelligent Life, So Far Only Our Planet Has Intelligent Life, That We Know Of, And Again This Is Only A Hypothesis, No Evidence Exist To Back This Up.....
Nisha
Good Day.....
Good to see you sir
Asim
hi
Nisha
good day
Nisha
hi
Nisha
Same Here.....
What's The Good Word For The Day?
Does MIT have good astrophysics courses ?
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.....
Gospel
How did ASTRONOMY helped you understand yourself ? 🤔
why do you want to study ASTRONOMY?
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)
SuperNova
because everything in the space is just beautiful...interesting and worth studying and exploring...
Memo
I have been studying astrophysics an love it
Carla
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
Carla
How did ASTRONOMY helped you understand yourself ?
Hussain
Because it proves the impossibles and the limitless.
Dark
It helped me realize that there are like countless possibilities in life and get all through it.
Dark
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.
Da
What does ASTRONOMY means?
Hussain
Does anyone know where can I study astronomy in Spain? My budget is too low for traveling out there...
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?
how many galaxies in universe?
10 to the power 11
Wwe
testing
thnx
Shaikh
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...
Gospel
it's ok bro
Wwe
I hope you will become a member of nasa
Wwe
just new in this area, from art background not science
what's ur name wwe
Shaikh
The Observable Universe Contains Between 200 Billion To 2 Trillion Galaxies.....
are u sure?
Caleb
It actually hasn't been proven, people have just made estimations.
Ariana
the thing is u can't count,maybe the our number system will collapse there...who knows?
Abdullah
What's the exact time when the laws of physics became active after the big bang ?
Mostak
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
Ismaee
we didn't actually find the exact number but may be it is around 100 billion
Smridhi
why this universe is expanding?
ATUL
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.
ATUL
Can you tell me the expanding speed of this universe.
ATUL
yes that would be a great question to have answered what is the expanding speed of the universe?
Daijahrel
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.
SuperNova
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.
Gospel
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
Gospel
ok....... that will be nice one
Gospel
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.
SuperNova
Pretty Much.....
there are nearly 200 million I suppose.
Amit