Radiation Question: Estimating Ωm & Time to t2×

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In summary, the conversation is about the energy balance of the universe dominated by Λ and how it will change over time. The question asks for an estimate of the value of Ωm at t2×, the time until t2×, and the Hubble distance at t2×. It also asks for an expression of the ratio Ωm/ΩΛ in terms of initial values and a(t). The conversation ends with a request for more details and a suggestion to integrate the Friedmann equation for part b).
  • #1
bolahab
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Hey guys, can someone please help with this question.

We now live in a time when the energy balance of the universe is dominated
by Λ. A long time from now, at t2× the universe will have doubled
in size, i.e.: a(t2×) = 2. At present, radiation is negligible: Ωr,0 ~ 0,
and will remain so, while Ωm,0 = 0.3 and ΩΛ,0 = 0.7 now. Note that
since ΩΛ,0 + m,0 = 1 now, their sum will remain the same.
a) Estimate the value of Ωm at t2×. Consider how the ratio Ωm/ΩΛ
changes with time, and use the flatness constraint mentioned above.
b) Estimate the time from now until t2×.
c) What will the Hubble distance be at t2×?
 
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  • #2
Can you express

[tex]\frac{\Omega_m \left( t \right)}{\Omega_\Lambda \left( t \right)}[/tex]

in terms of

[tex]\frac{\Omega_{m,0}}{\Omega_{\Lambda,0}}[/tex]

and [itex]a \left( t \right)[/itex]?
 
  • #3
Yeah it can be expressed like that
 
  • #4
bolahab said:
Yeah it can be expressed like that

This with [itex]a \left( t \right) = 2[/itex] and [itex]\Omega_\Lambda \left( t \right) + \Omega_m \left( t \right) = 1[/itex] give two equations with two unknowns.

For part b), integrate the Friedmann equation.
 
  • #5
Thnx George that really helped, but can you please give more details ?
 

1. What is radiation?

Radiation is a form of energy that is transmitted through space or materials in the form of waves or particles. It can come from various sources such as the sun, nuclear reactions, and electronic devices.

2. How is radiation measured?

Radiation is typically measured in units of radiation dose or exposure, which are defined as the amount of energy deposited in a given material by radiation. Common units of measurement include the gray (Gy) and the sievert (Sv).

3. How is Ωm estimated in radiation studies?

Ωm, also known as the matter density parameter, is a measure of the amount of matter in the universe. It is estimated in radiation studies by measuring the cosmic microwave background radiation, which is the leftover radiation from the Big Bang.

4. What is t2× in relation to radiation?

t2×, also known as the doubling time, is the amount of time it takes for the radiation dose to double. It is a measure of the rate at which a population is being exposed to radiation and can be used to estimate the potential health effects of radiation exposure.

5. How is the time to t2× calculated?

The time to t2× can be calculated by dividing the doubling dose by the annual radiation dose. The doubling dose is the amount of radiation that would cause a population to double its baseline cancer rate, and the annual radiation dose is the average amount of radiation a population is exposed to per year.

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