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COSMOLOGICAL REDSHIFT

The discovery of the expanding Universe from redshift, which we discussed above, is clearly one of the biggest breakthroughs in astronomy. Now we will discuss how astronomers determine the largest distances in space, how that relates to cosmological redshift, and importantly, what the meaning is of "distance" in an expanding Universe.


Cosmological redshift is measured from the spectra of distance objects just like optical redshift, but it is not a Doppler effect. Due to the expansion of space photons are "stretched" while they are travelling towards us. This "stretching" is a bit of an odd metaphoric concept, but what happens is that the wavelength of the light increases because the photons lose a small amount of energy during the long time they are traveling through expanding space.

photon energy

 

Photon energy E is a linear function of frequency f (h is Planck’s constant) and inversely related to wavelength λ (for more see our lecture The Nature of Light in the course Leaving the Solar System; soon possibly also available as an EBook). Therefore, lower energy means lower frequency and longer wavelength. The longer the photons have been travelling through expanding space, the more energy they lost and the larger the cosmological redshift we observe. Therefore, cosmological redshift in principle is a measure for how long ago the light left the source.



cosmologicalredshift500
In this animation, the galaxy on the left was formed a long time ago, while the galaxy on the right was formed more recently. Although each galaxy emits the same wavelength of light, the light from the left hand galaxy has spent longer travelling through the expanding Universe, and has therefore experienced a greater ‘stretching’ (redshift). Thus the more redshift is measured the longer these photons have been travelling.
Source: Cosmos, Swinburne Astronomy Online



We need a Cosmological Model
Very large distances in the Universe can be determined from cosmological redshift. But the relationship between cosmological redshift and distance is quite complicated. This relationship depends on the geometry of space-time and the expansion history of the Universe. The big advantage of cosmological redshift is that it is directly observable from spectra. It is successfully used as a measure for distance in the deep Universe, but that derived distance is always dependent on the cosmological model used.

The cosmological model that describes the geometry and history of space-time contains a number of critical parameters, one of which is the Hubble parameter. So all the research that is being done to find the most reliable value of the Hubble parameter is also very important for measuring extreme distances, but only in the context of the complete cosmological model. Further down in this EBook we will give some examples of calculating distance from cosmological redshift. But first we must discuss what we actually mean with the concept of “distance” in an expanding Universe.










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