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A pie chart shows 26.8 percent dark matter, 4.9 percent atoms and 68.3 percent dark energy.
Estimated distribution of matter and energy in the universe. (credit: NASA/WMAP Science Team)

Summary

  • The early universe was hot and dense.
  • The universe is isotropic and expanding.
  • Cosmic background radiation is evidence for the Big Bang.
  • The vast portion of the mass and energy of the universe is not well understood.

Key equations

Momentum of a charged particle in a cyclotron p = 0.3 B r
Center-of-mass energy of a colliding beam machine W 2 = 2 [ E 1 E 2 + ( p 1 c ) ( p 2 c ) ] + ( m 1 c 2 ) 2 + ( m 2 c 2 ) 2
Approximate time for exchange of a virtual particle between two other particles Δ t = h E
Hubble’s law v = H 0 d
Cosmological space-time metric d s 2 = c 2 d t 2 a ( t ) 2 d Σ 2

Conceptual questions

What is meant by a “cosmological model of the early universe?” Briefly describe this model in terms of the four fundamental forces.

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Describe two pieces of evidence that support the Big Bang model.

The observed expansion of the universe and the cosmic background radiation spectrum.

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In what sense are we, as Newton once said, “a boy playing on the sea-shore”? Express your answer in terms of the concepts of dark matter and dark energy.

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If some unknown cause of redshift—such as light becoming “tired” from traveling long distances through empty space—is discovered, what effect would that have on cosmology?

If light slow down, it takes long to reach Earth than expected. We conclude that the object is much closer than it really is. Thus, for every recessional velocity (based on the frequency of light, which we assume is not disturbed by the slowing), the distance is smaller than the “true” value, Hubble’s constant is larger than the “true” value, and the age of the universe is smaller than the “true” value.

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In the past, many scientists believed the universe to be infinite. However, if the universe is infinite, then any line of sight should eventually fall on a star’s surface and the night sky should be very bright. How is this paradox resolved in modern cosmology?

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Additional problems

Experimental results suggest that a muon decays to an electron and photon. How is this possible?

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Each of the following reactions is missing a single particle. Identify the missing particle for each reaction.

(a) p + p n + ? (b) p + p p + Λ 0 + ? (c) π + p Σ + ? (d) K + n Λ 0 + ? (e) τ + e + + υ e + ? (f) υ e + p n + ?

a. n ; b. K + ; c. K + ; d. π ; e. ν τ ; f. e +

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Because of energy loss due to synchrotron radiation in the LHC at CERN, only 5.00 MeV is added to the energy of each proton during each revolution around the main ring. How many revolutions are needed to produce 7.00-TeV (7000 GeV) protons, if they are injected with an initial energy of 8.00 GeV?

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A proton and an antiproton collide head-on, with each having a kinetic energy of 7.00 TeV (such as in the LHC at CERN). How much collision energy is available, taking into account the annihilation of the two masses? (Note that this is not significantly greater than the extremely relativistic kinetic energy.)

14.002 TeV 14.0 TeV

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When an electron and positron collide at the SLAC facility, they each have 50.0-GeV kinetic energies. What is the total collision energy available, taking into account the annihilation energy? Note that the annihilation energy is insignificant, because the electrons are highly relativistic.

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Questions & Answers

what is energy
Isiguzo Reply
friction ka direction Kaise pata karte hai
Rahul Reply
A twin paradox in the special theory of relativity arises due to.....? a) asymmetric of time only b) symmetric of time only c) only time
Varia Reply
fundamental note of a vibrating string
fasoyin Reply
every matter made up of particles and particles are also subdivided which are themselves subdivided and so on ,and the basic and smallest smallest smallest division is energy which vibrates to become particles and thats why particles have wave nature
Alvin
what are matter waves? Give some examples
mallam Reply
according to de Broglie any matter particles by attaining the higher velocity as compared to light'ill show the wave nature and equation of wave will applicable on it but in practical life people see it is impossible however it is practicaly true and possible while looking at the earth matter at far
Manikant
Mathematical expression of principle of relativity
Nasir Reply
given that the velocity v of wave depends on the tension f in the spring, it's length 'I' and it's mass 'm'. derive using dimension the equation of the wave
obia Reply
What is the importance of de-broglie's wavelength?
Mukulika Reply
he related wave to matter
Zahid
at subatomic level wave and matter are associated. this refering to mass energy equivalence
Zahid
it is key of quantum
Manikant
how those weight effect a stable motion at equilibrium
Nonso Reply
how do I differentiate this equation- A sinwt with respect to t
Evans Reply
just use the chain rule : let u =wt , the dy/dt = dy/du × du/dt : wA × cos(wt)
Jerry
I see my message got garbled , anyway use the chain rule with u= wt , etc...
Jerry
de broglie wave equation
LoNE Reply
vy beautiful equation
chandrasekhar
what is electro statics
fitsum Reply
when you consider systems consisting of fixed charges
Sherly
Diagram of the derive rotational analog equation of v= u+at
Nnamnso Reply
what is carat
Arnulfo Reply
a unit of weight for precious stones and pearls, now equivalent to 200 milligrams.
LoNE
a science that deals with the composition, structure, and properties of substances and with the transformations that they undergo.
LoNE
what is chemistry
Mrs Reply
what chemistry ?
Abakar
Practice Key Terms 4

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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