ConceptChecks
ConceptCheck 25-1: Bright. Even though more distant stars would individually appear dimmer, that loss of intensity is made up for by there being a greater number of distant stars in any given patch of the sky. Taken together, these two effects would tend to make the universe appear bright, instead of dark as it actually does. This is Olber’s paradox.
ConceptCheck 25-2: The spectral shift toward the shorter blue wavelengths means that the Andromeda Galaxy is moving toward our Milky Way Galaxy.
ConceptCheck 25-3: The cosmological principle applies over very large regions of outer space; it does not apply to the distribution of stars in objects as small as a galaxy.
ConceptCheck 25-4: Older. A smaller Hubble constant corresponds to slower expansion. That means it would have taken longer for galaxies to reach their present separation distances.
ConceptCheck 25-5: The receding star appears dimmer. As its light travels through expanding space, the wavelength of its light is stretched. This lowers the light’s energy and the star appears dimmer.
ConceptCheck 25-6: The observable universe becomes larger as more light from never-before-seen distant galaxies has sufficient time to reach us.
ConceptCheck 25-7: The expansion of the universe over the past 13.7 billion years has stretched and redshifted these photons to such a great degree that they are now low-energy, long-wavelength microwave photons.
ConceptCheck 25-8: Earth formed about 4.5 billion years ago, when the universe was about 9 billion years old, and the universe has been dominated by matter for most of its history.
ConceptCheck 25-9: The universe had to be sufficiently cool for atoms to form, so if the early universe was hotter for longer, the first atoms would have appeared more slowly.
ConceptCheck 25-10: Cooler blue regions correspond to denser concentrations of mass in the early universe. These are often the seeds of structures that form later in that same region. A visible-light telescope would probably find a supercluster of galaxies in that same region.
ConceptCheck 25-11: Yes, as in Figure 25-14a. In a universe with the geometry of spherical space, parallel light beams will eventually cross. In this case, the universe is considered a closed space and has positive curvature.
ConceptCheck 25-12: It would appear larger in size. As illustrated in Figure 25-15a, since the light rays are bent inward as they travel from the object toward an observer on Earth, the light rays appear to be coming from ends of the stick that are farther apart than as would be observed in a flat universe (Figure 25-15b). This makes the stick appear larger in the closed universe.
ConceptCheck 25-13: The total energy density of the universe determines whether the universe is open, closed, or flat. The cosmic microwave background reveals that the universe is nearly flat with Ω0 close to 1.0. Since matter can only account for about 0.24 of this energy density (and radiation is negligible), the remaining dark energy density is around 0.76.
ConceptCheck 25-14: Astronomers must make the assumption that all Type Ia supernovae have identical luminosities, regardless of the galaxy in which they are found.
ConceptCheck 25-15: The comparison in the middle, corresponding to size scales of around 1 degree, shows the greatest difference between the actual fluctuations (which include sound waves) and the variations that would be observed without sound waves. This is consistent with the peak in the lower part of the figure, showing that the effects of sound waves are strongest on scales of 1 degree.
CalculationChecks
CalculationCheck 25-1: Because z = the change in wavelength (λ − λ0) divided by the original λ0, z = (725.6nm − 656.3nm) ÷ 656.3 nm = 0.11.
CalculationCheck 25-2: Hubble’s Law, v = H0d can be rearranged as d = v ÷ H0. Using H0 = 73 km/s/Mpc, d = v ÷ H0 = 10,000 km/s ÷ 73 km/s/Mpc = 134 Mpc (million parsecs).
CalculationCheck 25-3: In a flat universe, Ω0 is equal to 1. That means ρ0 = (the combined average mass density) equals ρc = (the critical density). Therefore, ρ0 = 1.0 × 10−26 kg/m3.
CalculationCheck 25-4: The combined total density parameter for both mass and energy has a value of nearly Ω0 = 1. The density parameter for ordinary matter is Ωb = 0.04, so ordinary matter contributes only 4% to the total energy content of the universe. For dark energy, ΩΛ = 0.76, so dark energy makes up about 76% of the universe’s energy content.