The Big-Bang theory
Luis Anchordoqui
AST-101, Ast-117, AST-602
1Thursday, November 21, 19
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Understanding the Universe: Geometry, Density, and Dark Matter, Slides of Earth, Atmospheric, and Planetary Sciences
The geometry and density of the universe, including the concept of critical density and the implications for the fate of the universe. It also covers the discovery of dark matter through observations of galaxy rotation curves and the current understanding of its role in the universe. The document also touches upon the cosmological parameters and the theory of inflation as an explanation for the horizon problem.
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The Big-Bang theory
Luis Anchordoqui
AST-101, Ast-117, AST-
17.1 The Expanding Universe! Last class....
The redshift of a Galaxy is: A. The rate at which a Galaxy is expanding in size B. How much reader the galaxy appears when observed at large distances C. the speed at which a galaxy is orbiting around the Milky Way D. the relative speed of the redder stars in the galaxy with respect to the blues stars E. The recessional velocity of a galaxy, expressed as a fraction of the speed of light
The redshift of a Galaxy is: A. The rate at which a Galaxy is expanding in size B. How much reader the galaxy appears when observed at large distances C. the speed at which a galaxy is orbiting around the Milky Way D. the relative speed of the redder stars in the galaxy with respect to the blues stars E. The recessional velocity of a galaxy, expressed as a fraction of the speed of light
To a first approximation, a rough maximum age of the Universe can be estimated using which of the following? A. the age of the oldest open clusters B. 1/H 0 the Hubble time C. the age of the Sun D. the age of the Galaxy E. there is no simple estimate
17.2 Cosmological Models!
The Friedmann and Lemaitre Models!
! Alexander Friedmann!
In 1922 developed the GR-based, expanding
universe model. It was not taken very
seriously at the time, since the expansion of
the universe has not yet been established.!
Georges Lemaitre !
In 1927 independently developed cosmological
models like Friedmanns. In 1933, he ran the
film backwards to a hot, dense, early state of the
universe he called the cosmic egg. This early
prediction of the Big Bang was largely ignored.!
They used the homogeneity and isotropy to reduce the full set of
16 Einstein equations of GR to one: the Friedmann-Lemaitre eqn.!
Kinematics of the Universe!
We introduce a scale factor ,
commonly denoted as R(t) or a(t):
a spatial distance between any two
unaccelerated frames which move
with their comoving coordinates!
This fully describes the evolution of
a homogeneous, isotropic universe!
R(t)! t!
Computing R(t) and various derived quantities defines the
cosmological models. This is accomplished by solving the
Friedmann (or Friedmann-Lemaitre) Equation!
The equation is parametrized (and thus the models defined) by
a set of cosmological parameters!
Mass-energy determines geometry Geometry determines where mass- energy can go
Cosmological Parameters!
Hubble Constant Defines the Scale of the Universe!
R 0!
0!^ t 0!
H 0 = slope at t 0!
1 / H 0 = Hubble time!
c / H 0 = Hubble length!
Critical Mass Density for the Universe I We can get an estimate of how much mass is needed to “close” the universe. More accurately, we calculate the mean density needed to close the universe. We balance gravitational potential energy and kinetic energy using simple Newtonian mechanics. V m M R Potential energy of mass m in gravitational field of M Kinetic energy of mass m
PE =
GM m
R
KE = 1 2 mV 2
Total energy: E = KE + PE =
mV
2
GM m
R
E = 0 corresponds to mass m having escape velocity from M
Vesc =
2 GM
R
Example: Earth R ~ 6371 km M = 5.97 x 10^24 kg G = Gravitational constant G = 6.67 x 10-8^ cm^3 g-1s-2^ or G = 6.67 x 10-11^ m^3 kg-1^ s- Vesc ~ 11.2 km/s
If the density of the Universe is less than critical, then the Universe: A. will ultimately collapse back in on itself B. will expand forever C. must be spherical D. will have a temperature of 2.73K forever E. must be static, with an unknown cause for the redshifts
If the density of the Universe is less than critical, then the Universe: A. will ultimately collapse back in on itself B. will expand forever C. must be spherical D. will have a temperature of 2.73K forever E. must be static, with an unknown cause for the redshifts