Podcast
Questions and Answers
What is the significance of the temperature T ~ 10^10 T GUT in the context of energy density of the Universe?
What is the significance of the temperature T ~ 10^10 T GUT in the context of energy density of the Universe?
Which of the following conditions leads to a decrease in the difference between 1 and Ω over time?
Which of the following conditions leads to a decrease in the difference between 1 and Ω over time?
What does the equation (90) suggest about the relationship between Ω and time during the Inflationary era?
What does the equation (90) suggest about the relationship between Ω and time during the Inflationary era?
What is the current probability of finding a single magnetic monopole within the surface of last scattering?
What is the current probability of finding a single magnetic monopole within the surface of last scattering?
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What implication does the scale factor a(t) growing from ~2×10^-27 to a0 = 1 have on monopole density?
What implication does the scale factor a(t) growing from ~2×10^-27 to a0 = 1 have on monopole density?
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What is suggested as the main reason for the almost zero probability of finding a magnetic monopole today?
What is suggested as the main reason for the almost zero probability of finding a magnetic monopole today?
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In the Inflationary Scenario, how does the behavior of the left side of equation (86) change over time?
In the Inflationary Scenario, how does the behavior of the left side of equation (86) change over time?
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What condition must be satisfied for ω to ensure that the left side of equation (86) decreases over time?
What condition must be satisfied for ω to ensure that the left side of equation (86) decreases over time?
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What mathematical expression describes the scale factor as it relates to the time variable in a non-flat universe?
What mathematical expression describes the scale factor as it relates to the time variable in a non-flat universe?
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What does the density of monopoles after the Universe's expansion indicate about their presence today?
What does the density of monopoles after the Universe's expansion indicate about their presence today?
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Study Notes
Energy Density of the Universe
- The universe's energy density, when the scale factor grew by ~1010, corresponded with temperatures falling to T ~ 1010 TGUT ~ 1018 K and an age of t ~ 10-16 seconds.
Monopole Problem
- Today, the universe is not dominated by magnetic monopoles.
- This raises the "monopole problem": Where did all the monopoles go?
Inflationary Scenario - Flatness Problem
- Equation (86) describes the relationship between the Hubble parameter (H), time (t), and density parameter (Ω) in a universe not perfectly flat, dominated by a component with ω ≠ -1.
- The scale factor (a) and Hubble parameter (H) depend on time as a(t) ∝ t3(1+ω)/2 and H(t) = 2/3(1+ω)/t.
- If ω < -1/3 (but ω > -1), the difference between 1 and Ω decreases with time.
- During inflation, the difference between 1 and Ω decreases exponentially with time, as shown in equations (90) and (91).
- The equations demonstrate how in the inflationary era, the difference between 1 and Ω decreases exponentially with time.
Monopole Density Today
- The number density of monopoles today, after expansion from a(tf) ~ 2 × 10-27 to a0 = 1, is approximately 10-61 Mpc-3.
- Thus, the probability of finding even a single monopole within the surface of last scattering is virtually zero.
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Description
Explore the key topics of energy density in the universe, the monopole problem, and the inflationary scenario including the flatness problem. This quiz covers the relationships between critical parameters like the Hubble parameter, time, and density parameters. Test your understanding of these fundamental cosmological concepts.
