Age of Universe @ 1 MeV, 1 GeV & 1014 GeV: Calculation

In summary, we are assuming a Robertson-Walker universe with matter, radiation, and curvature. The present mass density is given by ρm = 3Ω0H20/(8πG), where H0 = 100 h km s-1 Mpc-1 and Ω0(1+ρr,0/ρm;0) ≤ 1 (i.e., k ≤ 0). The present radiation temperature is T0 = 2.725 K. We are also assuming that only photons, with a present temperature of T0 = 2.725K, contribute to the radiation and we are ignoring neutrinos in this problem. To determine the age of the universe when the radiation temperature was
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Ailar
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Assume that we live in a Robertson-Walker universe with matter, radiation and curvature. The present mass density is ρm = 3Ω0H20/(8πG), where H0 = 100 h km s-1 Mpc-1 and Ω0(1+ρr,0/ρm;0) ≤ 1 (i.e., k ≤ 0). The present radiation temperature is T0 = 2.725 K.
Assume that only photons, with present temperature T0 = 2.725K contribute to the radiation; ignore neutrinos in this problem.
How old was the universe when the radiation temperature was 1 MeV? 1GeV?
1014 GeV? (Hint: you need g*, the effective number of relativistic spin states contributing to the energy density. At 1 GeV g* = 61.75 and at 1014 GeV, g* = 106.75 without supersymmetry or double this with SUSY.)
Thanks so much!
 
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This looks like a homework question, as such I am moving to the relevant homework forum. What attempts have you made the answer the question?
 

1. What is the age of the universe at 1 MeV?

The age of the universe at 1 MeV is approximately 13.8 billion years. This is calculated using the current rate of expansion of the universe, known as the Hubble constant, and taking into account the effects of dark energy and matter on the expansion.

2. How does the age of the universe change at higher energy scales, such as 1 GeV?

As the energy scale increases, the age of the universe decreases. This is because at higher energy scales, the universe was much hotter and denser, and therefore expanded at a faster rate. At 1 GeV, the age of the universe is approximately 3.7 billion years.

3. What is the significance of calculating the age of the universe at 1 MeV, 1 GeV, and 1014 GeV?

These are important energy scales in the history of the universe. At 1 MeV, the universe had cooled enough for protons and neutrons to form, marking the beginning of the era of nucleosynthesis. At 1 GeV, the universe was still very hot and dense, but had expanded enough for quarks to form into hadrons. At 1014 GeV, the universe was in its earliest stages, undergoing rapid expansion known as inflation.

4. How accurate are these calculations of the age of the universe at different energy scales?

The calculations of the age of the universe at different energy scales are based on our current understanding of the universe and its expansion. While they are considered accurate within a certain margin of error, it is possible that future discoveries or advancements in our understanding could lead to revisions of these calculations.

5. What other factors are considered when calculating the age of the universe at different energy scales?

In addition to the Hubble constant and the effects of dark energy and matter, other factors such as the density of matter and radiation in the universe, the composition of the universe, and the rate of expansion in the early universe are also taken into account when calculating the age of the universe at different energy scales.

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