One of the biggest obstacles to measuring the curvature or deceleration of the universe is the fact that objects in the universe evolve, or change their properties, with time. Cosmological tests require observations over a large span of red shift. But when we look out in red shift, we also look back in time. So when we compare nearby objects with distant objects, we are comparing old objects with younger objects. This is an unavoidable aspect of observational cosmology.
The way that angular diameter varies with red shift can be used to measure the curvature of space. A practical problem is the fact that galaxies do not have sharp edges. It is very difficult to accurately measure the size of a faint fuzzy thing in the distant universe. However, a more fundamental problem is cosmic evolution. Galaxies at high red shift are seen when they were young. A high red shift corresponds to a large look-back time, and cosmic evolution means that we must always view younger objects at larger distances. If galaxies are built up from smaller pieces, then they might well have been intrinsically smaller when they were young. The comparison of nearby and distant objects is a comparison of apples and oranges.
One important cosmological test involves the way that the apparent brightness of objects changes with red shift. First, note that the distance to an object depends on the cosmological model. Distance relates to red shift by the approximation d = cz/H0. However, the effects of space curvature begin to be seen at red shifts of a few tenths, from z = 0.2 to 0.3. By red shifts of one or two (z = 1 to 2), the differences between cosmological models are substantial. A flat universe with zero curvature is smaller than an open universe with negative curvature. Therefore, any particular red shift in a flat universe corresponds to a smaller distance than the same red shift in an open universe. Now imagine that we find an object of known luminosity far off in the distant universe. If the universe is flat, that object will be closer and appear brighter than if the universe is open. The application of the test requires that we find a particular type of object that can be found over a wide range of red shifts. By seeing how the apparent brightness changes with red shift, we can distinguish between different values of the density parameter, or space curvature.
The Hubble Deep Field. Click here for original source URL.
Observations of distant galaxies sound straightforward, but a serious complication arises due to cosmic evolution. When the apparent brightness test is applied to elliptical galaxies, models show that at a red shift of one, an elliptical galaxy would be a factor of two brighter in a flat universe than in an open, low-density universe. The problem is that a high-red shift galaxy is a very distant galaxy. A very distant galaxy is a young galaxy since its light has taken billions of years to reach us. Look-back time has the unavoidable consequence of forcing us to compare nearby objects with distant ones that are younger. In other words, astronomers cannot make a test of the cosmological model without first making a model of the evolution of galaxy light. The test is not as direct as we would like.
Astronomers try to choose the simplest stellar systems for cosmological tests. Elliptical galaxies are luminous — enabling them to be seen out to large red shifts — and they usually have old stellar populations. Assuming that most of its stars formed at the same time, an elliptical galaxy will fade and become redder. The galaxy fades quickly at first because the first light is dominated by luminous and short-lived blue stars. The galaxy then fades more slowly, as lower- and lower-mass stars move off the main sequence. A simple evolutionary model of a galaxy has a single burst of star formation. The change in energy distribution, particularly the loss of blue and ultraviolet light, is dramatic in the first billion years. The change in the amount of radiation strongly depends on wavelength. The red and infrared radiation declines by a factor of 100 after the initial burst of star formation, while the ultraviolet radiation declines by a factor of 100,000.
The Hubble Ultra Deep Field. Click here for original source URL.
The evolution of stellar populations complicates cosmological tests for two reasons. First, more distant galaxies are likely to be brighter and bluer, simply because they are younger. Second, galaxies are measured over a fixed range of optical wavelengths, usually defined by a filter. Distant galaxies are red shifted, so we observe successively bluer parts of the energy distributions of more distant galaxies. For example, suppose that we measure galaxies at a wavelength of 500 nm. However, a galaxy at z = 2 has had its ultraviolet light stretched out into visible light over time and space. The wavelength of the radiation we observe in this distant galaxy is 500/(1+z) = 170 nm. A youthful 107-year-old galaxy is putting out far more energy at this ultraviolet wavelength. By contrast, an old 109-year-old galaxy is putting out far less energy at this ultraviolet wavelength. (We cannot apply this reasoning to a 1010-year-old galaxy because the universe at z = 2 is barely old enough to contain a ten billion year old stellar population.) The simple truth is that we do not understand galaxy evolution well enough to apply it in cosmological tests with any confidence.