Scholars Online Astronomy - Chapter 25: Cosmology
Reading: Astronomy, Chapter 25: Cosmology
- Section 1: Paradoxes. Olbers's paradox describes a problem with astronomical observations: if stars are evenly distributed throughout an infinite space (as Newton proposed), then we should see stars in whatever direction we look, and the night sky should not be dark. Since it is dark, we need a way to explain the contradictory observational evidence. Einstein's general relativity predicts the expansion or contraction of the universe, which contradicted his conviction that the universe was static, so he proposed a cosmological pressure constant to offset gravitational attraction, instead of trusting his own theory's predictions.
- Section 2: From Hubble's observations in the early part of the 20th century, we conclude that the universe (i.e., space itself, not merely objects in the space) is expanding at a constant rate, such that objects further away appear to be receding faster. Light traveling through expanding space is stretched by the expansion and redshifted as a result (cosmological red shift) in addition to any Doppler shift due to motion of the source object through space. Objects still move through space due to gravitational attraction, so gravitational contraction of galaxies and galaxy clusters pull these objects through expanding space and keep them together. By using the cosmological redshift and the Hubble expansion rate, we can determine the distance to the object and its lookback factor, that is, how much time has passed since light left the object. Observations over the whole range of the sky indicate that the same expansion and gravitational laws apply everywhere, making the universe homogeneous (roughly the same in composition everywhere) and isotropic (appearing the same from any region).
- Section 3: The expansion of the universe (all there is, including space itself), can be viewed in reverse, and the time at which the universe was a singular point determined: about 13.4 BY ago, which matches the age of stars in the Milky Way's globular cluster. This conclusion means the universe has a finite beginning. Our view of the universe ( observable universe) is limited by its age: light that left objects 13.4BY ago is only now reaching the Earth. Because the universe is expanding, these objects are now more than 13.4 BLY away, giving us a distance limit or cosmic light horizon of about 47 BLY for the current location of objects we can observe. Light from objects that formed once the universe expanded beyond 13.4 BLY and that are more than 13.4 BLY away has not yet reached us. Our ability to describe the early universe is limited because
- Section 4: Models used for the Big Bang theory require a very hot, high energy universe emitting short-wave radiation, but this temperature has cooled to near absolute zero (about 3K). This radiation traveling from distant expanding regions of space constitutes the cosmic microwave background (CMB) radiation, which can be observed in all parts of the sky using microwave sensors. The only difference is isotropic nature of this radiation is due to the Earth's motion through space, which creates a Doppler shift, allowing us to determine our direction of motion (toward Aquarius and away from Leo, along with other members of the Local Group, following the Hydra-Centaurus supercluster toward a location called the Great Attractor, since many galaxies and clusters appear to be moving toward it.
- Section 5: The earliest stage of the universe (about 380 000 years) created an opaque, dens, hot plasma. We can use Einstein's idea that energy and mass are interchangeable to measure the mass density of the radiation energy in this period as a function of temperature: ρrad = 4 σ T4 / c3. Based on observations of galaxies in our region, we can estimate the average density of matter (including dark matter) as ρm. In the early universe, ρrad > ρm. The current model shows that around 380000 years after the Big Bang, radiation pressure dropped to the point that protons could separate with enough surrounding space to capture and retain electrons, forming hydrogen atoms. This matter did not form uniformly, leading to local regions of denser matter and hotter temperatures that eventually would develop into galaxies and super clusters.
- Section 6: The universe is controlled by two forces: expansion pressure from the Big Bang, and gravitational condensation in the matter in the universe. The future of the universe will be determined by the total mass (including dar matter): if there is enough mass that the escape velocity of the universe is greater than the expansion rate of the universe, the universe will reach some maximum expansion point and then start to contract, like a tossed ball reaching the top of its arc and falling back to Earth. Parallel light rays in this universe will eventually converge (spherical space, density parameter Ω0 > 1). If there is too little mass, the universe will continue to expand indefinitely. Parallel rays in this universe will diverge (saddle shaped or hyperbolic space, Ω0 < 1). If the two rates are equal, parallel light rays will never meet (the universe is flat, Ω0 = 1). We define ρ0 as the mass density of the universe, and ρc as the critical density determining the density parameter value and equal to 3H02 / (8 πG). Then Ω0 = ρ0/ρc. Obviously, the determination of the critical density depends on an accurate value for H0....which we don't have yet. Our other evidence is conflicting: mass measurements are only about 24% of ρc, but the CMB data indicates the universe is nearly flat, so there is undiscovered matter or energy still in the universe. We can estimate the amount of dark matter from the gravitational demands of galaxies and superclusters, but even this is not enough to arrive at a flat universe. Astronomers propose that there is also "dark energy", energy not dependent on EM radiation and not detectable from gravity considerations.
- Section 7: Data from supernovae explosions in distant galaxies indicates that the universe expansion rate is increasing with time, which in turn supports the idea that dar energy exists to drive the expansion, and that the dark energy density is in fact now greater than the density of normal matter and dark matter combined. Instead of slowing down (as expansion should have done during the matter-dominated phase of the universe), expansion is now speeding up. One source of this energy may be pair production, a process where energy produces matter and antimater pairs which exist for a short time before annihilating one another. Because we cannot directly observe thise particles, they are sometimes called "virtual particles", but they have real, observable effects. However, models using virtual pairs result in dark energy predictions 10100 times that estimated for the observed flat universe.
- Section 8: The density of plasma entities in the early universe would support condensation waves, similar to sound waves in air. Sound waves in the plasma medium have been proposed to explain fluctuations in density of the plasma state. While we can't use EM based observations to look "back" into this state, wave propagation may tell us about conditions in the early phase of the universe that led to the formation of galaxies and galactic clusters.
Key Formulae to Know
||z: redshift = v/c|
λ: observed wavelength of photon
λ0: wavelength of emitted photon at source
|Hubble's law|| v = H0d||v: recessional velocity due to expansion of space|
H0: constant rate of expansion
d: distance of object from observer
Read the following weblecture before chat: Cosmology
Use the iCosmos to manipulate the omega values to generate flat, curved, and negatively curved spacetimes.
- Examine the default values for the cosmological parameters, then click on Submit button without changing any. Note the shape of the curves and be sure that you understand what each of these factors means (Co-moving Distance, Angular Diameter Distance, Luminosity Distance, Co-moving Volume, Age of The Universe and Perturbation Growth Factor.)
- Change the Hubble constant to 45 and click on the Reference check box, then click submit. How does each new plot compare with the accepted Hubble value of 70? How do the values compare?
- Change the Hubble constant to 85 and click on the Reference check box, then click submit. How does each new plot compare with the accepted Hubble value of 70? How do the values compare?
- Which change increased the age of the univers? the angular diameter at a redshift of 1.0?
- Restore the values to their defaults by clicking on the iCosmos logo, then change ΩM from 0.3 to 0.7. What happens to the shape of the universe? Try making smaller changes in ΩM until you can keep the shape of the universe flat. How small a change is necessary for it to become "unflat"?
- Restore the values to their defaults, then change ΩΛ from 0.7 to 0.5. What happens to the shape of the universe? What is the largest change you could make where the universe remains flat?
- Restore the default values, then change the redshift value only. Which values change? Which stay the same?
UNL Tools Exercises
- Under Cosmology, work through General Questions 1-17.
- On the Animations tab, explore the Balloon Universe and Galactic Redshift Simulator.
- Under Outlines, Check out the Cosmic Distance Later Parts 1 and 2.
Website of the Week: The Big Bang Time Machine lets you explore the theory of the Big Bang and step through the process of the current model.
- Required: Complete the Mastery exercise with a passing score of 85% or better.
- Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!
Read through the lab for this week; bring questions to chat on any aspect of the lab, whether you intend not perform it or not. If you decide to perform the lab, be sure to submit your report by the posted due date.
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