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Scientists often explain the Big Bang expansion using an inflated-balloon model ( [link] ). Dots marked on the surface of the balloon represent galaxies, and the balloon skin represents four-dimensional space-time ( Relativity ). As the balloon is inflated, every dot “sees” the other dots moving away. This model yields two insights. First, the expansion is observed by all observers in the universe, no matter where they are located. The “center of expansion” does not exist, so Earth does not reside at the “privileged” center of the expansion (see [link] ).

Figure a shows a balloon connected to a cylinder for inflation. The balloon is marked with a grid, and a few dots on the grid are highlighted. Figure b shows the same balloon, now inflated. The highlighted dots are further apart from each other.
An analogy to the expanding universe: The dots move away from each other as the balloon expands; compare (a) to (b) after expansion.

Second, as mentioned already, the Big Bang expansion is due to the expansion of space, not the increased separation of galaxies in ordinary (static) three-dimensional space. This cosmological expansion affects all things: dust, stars, planets, and even light. Thus, the wavelength of light ( λ ) emitted by distant galaxies is “stretched” out. This makes the light appear “redder” (lower energy) to the observer—a phenomenon called cosmological redshift    . Cosmological redshift is measurable only for galaxies farther away than 50 million light-years.

Calculating speeds and galactic distances

A galaxy is observed to have a redshift:

z = λ obs λ emit λ emit = 4.5 .

This value indicates a galaxy moving close to the speed of light. Using the relativistic redshift formula (given in Relativity ), determine (a) How fast is the galaxy receding with respect to Earth? (b) How far away is the galaxy?

Strategy

We need to use the relativistic Doppler formula to determine speed from redshift and then use Hubble’s law to find the distance from the speed.

Solution

  1. According to the relativistic redshift formula:
    z = 1 + β 1 β −1 ,

    where β = v / c . Substituting the value for z and solving for β , we get β = 0.93 . This value implies that the speed of the galaxy is 2.8 × 10 8 m/s .
  2. Using Hubble’s law, we can find the distance to the galaxy if we know its
    recession velocity:
    d = v H 0 = 2.8 × 10 8 m / s 73.8 × 10 3 m / s per Mpc = 3.8 × 10 3 Mpc .

Significance

Distant galaxies appear to move very rapidly away from Earth. The redshift of starlight from these galaxies can be used to determine the precise speed of recession, over 90 % of the speed of light in this case. This motion is not due to the motion of galaxy through space but by the expansion of space itself.

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Check Your Understanding The light of a galaxy that moves away from us is “redshifted.” What occurs to the light of a galaxy that moves toward us?

blueshifted

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View this video to learn more about the cosmological expansion.

Structure and dynamics of the universe

At large scales, the universe is believed to be both isotropic and homogeneous. The universe is believed to isotropic because it appears to be the same in all directions, and homogeneous because it appears to be the same in all places. A universe that is isotropic and homogeneous is said to be smooth. The assumption of a smooth universe is supported by the Automated Plate Measurement Galaxy Survey conducted in the 1980s and 1900s ( [link] ). However, even before these data were collected, the assumption of a smooth universe was used by theorists to simplify models of the expansion of the universe. This assumption of a smooth universe is sometimes called the cosmological principle .

Practice Key Terms 5

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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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