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- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.10%3A_The_Friedmann_EquationSticking with our Newtonian expanding universe, we will now derive the Friedmann equation that relates how the scale factor changes in time to the mass/energy density. We will proceed by using the Ne...Sticking with our Newtonian expanding universe, we will now derive the Friedmann equation that relates how the scale factor changes in time to the mass/energy density. We will proceed by using the Newtonian concept of energy conservation. (You may be surprised to hear me call this a Newtonian concept, but the fact is that energy conservation does not fully survive the transition from Newton to Einstein).
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.15%3A_Distance_and_MagnitudeThere are a bewildering array of different kinds of distances in cosmology. We catalog them here as a resource for you as needed. We also introduce and define other related astronomical technical term...There are a bewildering array of different kinds of distances in cosmology. We catalog them here as a resource for you as needed. We also introduce and define other related astronomical technical terms: apparent and absolute magnitudes.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.04%3A_Spatially_Homogeneous_and_Isotropic_SpacetimesWe introduce the cosmological principle and the geometry of homogeneous and isotropic spacetimes with three spatial dimensions. This will allow us to go on to calculate distance-related observables, a...We introduce the cosmological principle and the geometry of homogeneous and isotropic spacetimes with three spatial dimensions. This will allow us to go on to calculate distance-related observables, an important step toward predicting observable consequences of the expansion.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.14%3A_Pressure_and_Energy_Density_EvolutionWe apply local conservation of energy, valid in general relativity, to infer how density changes in response to scale factor changes, a response that depends on the relationship between pressure and d...We apply local conservation of energy, valid in general relativity, to infer how density changes in response to scale factor changes, a response that depends on the relationship between pressure and density.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.32%3A_Euclidean_GeometryThis chapter is entirely focused on the Euclidean geometry that is familiar to you, but reviewed in a language that may be unfamiliar. The new language will help us journey into the foreign territory ...This chapter is entirely focused on the Euclidean geometry that is familiar to you, but reviewed in a language that may be unfamiliar. The new language will help us journey into the foreign territory of Riemannian geometry. Our exploration of that territory will then help you to drop your pre-conceived notions about space and to begin to understand the broader possibilities -- possibilities that are not only mathematically beautiful, but that appear to be realized in nature.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.02%3A__Spacetime_GeometryWe begin our exploration of physics in an expanding spacetime with a spacetime with just one spatial dimension that is not expanding: a 1+1-dimensional Minkowski spacetime. We then generalize it sligh...We begin our exploration of physics in an expanding spacetime with a spacetime with just one spatial dimension that is not expanding: a 1+1-dimensional Minkowski spacetime. We then generalize it slightly so that the spatial dimension is expanding. After introduction of notions of age and "past horizon," we go on to calculate these quantities for some special cases.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.12%3A_The_Evolution_of_Mass-Energy_Density_and_a_First_Glance_at_the_Contents_of_the_CosmosWe have seen that the rate of change of the scale factor depends on the mass density \( \rho \). In order to determine how the scale factor evolves with time, we thus need to know how the density evol...We have seen that the rate of change of the scale factor depends on the mass density \( \rho \). In order to determine how the scale factor evolves with time, we thus need to know how the density evolves as the scale factor changes, a subject we investigate here.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Cosmology_(Knox)Contemporary knowledge regarding the origin of the universe, including the Big Bang and nucleosynthesis, microwave background radiation, formation of cosmic structure, cosmic inflation, cosmic acceler...Contemporary knowledge regarding the origin of the universe, including the Big Bang and nucleosynthesis, microwave background radiation, formation of cosmic structure, cosmic inflation, cosmic acceleration and dark energy.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.09%3A_A_Newtonian_Homogeneous_Expanding_UniverseRetreating to the use of Newtonian concepts, we show that for a universe to be filled with an expanding fluid that remains homogeneous over time, the flow must be what we call a Hubble flow, with rela...Retreating to the use of Newtonian concepts, we show that for a universe to be filled with an expanding fluid that remains homogeneous over time, the flow must be what we call a Hubble flow, with relative velocities proportional to distance. Thus we derive Hubble's law using Newtonian concepts, setting ourselves up for the next chapter in which we use Newtonian dynamics to relate the expansion rate to the contents of the cosmos.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.13%3A_Energy_and_Momentum_ConservationThe lack of energy conservation in an expanding universe is quite surprising to people with any training in physics and therefore merits some discussion, which we present here in this chapter. The stu...The lack of energy conservation in an expanding universe is quite surprising to people with any training in physics and therefore merits some discussion, which we present here in this chapter. The student could skip this chapter and proceed to 15 without serious harm. If, subsequently, the lack of energy conservation becomes too troubling, know that this chapter is here for you.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.19%3A_Equilibrium_Statistical_Mechanics/1.19.01%3A_Chapter_19_footnotesThere is not agreement between predictions and observations of Lithium abundance, something known as the "Lithium problem." This may look strange, but it's generally true. Remember that in the non-rel...There is not agreement between predictions and observations of Lithium abundance, something known as the "Lithium problem." This may look strange, but it's generally true. Remember that in the non-relativistic limit \(E = mc^2 + p^2/2m \simeq mc^2\).
