Search
- 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/1.10%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/1.09%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/1.05%3A_Euclidean_GeometryThis optional 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 t...This optional 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/1.37%3A_RedshiftsWe begin to work out observational consequences of living in an expanding spatially homogeneous and isotropic universe. In this and the next two chapters we derive Hubble's Law, v=H0d, and a m...We begin to work out observational consequences of living in an expanding spatially homogeneous and isotropic universe. In this and the next two chapters we derive Hubble's Law, v=H0d, and a more general version of it valid for arbitrarily large distances.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.20%3A_Equilibrium_Particle_AbundancesAt sufficiently high temperatures and densities, reactions that create and destroy particles can become sufficiently rapid that an equilibrium abundance is achieved. In this chapter we assume that suc...At sufficiently high temperatures and densities, reactions that create and destroy particles can become sufficiently rapid that an equilibrium abundance is achieved. In this chapter we assume that such reaction rates are sufficiently high and work out the resulting abundances as a function of the key controlling parameter. We will thus see how equilibrium abundances change as the universe expands and cools.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.19%3A_Equilibrium_Statistical_MechanicsOut of the early Universe we get the light elements, a lot of photons and, as it turns out, a bunch of neutrinos and other relics of our hot past as well. To understand the production of these particl...Out of the early Universe we get the light elements, a lot of photons and, as it turns out, a bunch of neutrinos and other relics of our hot past as well. To understand the production of these particles we now turn to the subject of equilibrium statistical mechanics.
