Red Shift and the Expansion of the Universe

The original clue that we live in an expanding universe was from the red shift of light from distant galaxies. We have explained this red shift as being caused by the Doppler effect. The distant galaxies are moving away from us, and it is the recessional motion that stretches the wavelengths of the radiated waves, as seen in the ripple tank photograph back in Figure (1) reproduced here.

Figure 1: The doppler effect.

There is another way to view the red shift that gives the same results but provides a more comprehensive picture of the evolution of the universe. Consider a galaxy that is, for example, receding from us at 10% the speed of light. According to the Doppler effect, the wavelength of the light from that galaxy will be lengthened by a factor of 10%.
Where is that galaxy now? If the galaxy were moving away from us at 10% the speed of light, it has traveled away from us 1/10th as far as the light has traveled in reaching us. In other words the galaxy is 10% farther away now than when it emitted the light. If the recessional motion of the galaxy is due to the expansion of the universe, then the universe is now 10% bigger than it was when the galaxy emitted the light.
In this example, the universe is now 10% bigger and the wavelength of the emitted light is 10% longer. We can take the point of view that the wavelength of the light was stretched 10% by the expansion of the universe. In other words it makes no difference whether we say that the red shift was caused by the 10% recessional velocity of the galaxy, or the 10% expansion of the universe. Both arguments give the same answer.
When we are studying the evolution of the universe, it is easier to use the idea that the universe's expansion stretches the photon wavelengths. This is especially true for discussions of the early universe where recessional velocities are close to the speed of light and relativistic Doppler calculations would be required.