Friedmann Equation and the age of empty universe

In summary, the conversation was about using the Friedmann equation to show the age of an empty universe with an average density of 0 is equal to 1 divided by Hubble's Constant. The person got stuck because the equation required k to be an imaginary number, but they were unsure if this was correct and questioned if the spatial curvature had to be positive. Another person clarified that k can be negative and it means the universe is open.
  • #1
darkar
187
0
Got stuck in this question, the question asked to use friedmann equation to show that the age of an empty universe (average density = 0) is

τ=1/H₀

where H₀ is the present day value of Hubble's Constant.

Well, i got the friedmann equation by put the value ρ(average)=0 but the trouble is that u have H₀^2 = - kc^2/R^2. which mean k has to be an imaginary number. But i am kind of not accepting it. Did i miss out something?
 
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  • #2
Does spatial curavture have to be positive?

Regards,
George
 
  • #3
Ummm, rite. Just recheck, K can be negative and it mean the universe is open.

Btw, still i will get some constand infront 1/H₀
 

Related to Friedmann Equation and the age of empty universe

1. What is the Friedmann Equation and how does it relate to the age of an empty universe?

The Friedmann Equation is a mathematical expression used in cosmology to describe the expansion of the universe. It relates the rate of expansion of the universe to the matter and energy content of the universe. In an empty universe, the equation predicts a constant rate of expansion, which can be used to estimate the age of the universe.

2. How is the age of an empty universe calculated using the Friedmann Equation?

The age of an empty universe can be calculated by using the Friedmann Equation in reverse. By measuring the current rate of expansion of the universe and knowing the matter and energy content, we can calculate how long it would take for the universe to expand from a single point to its current size.

3. What is the current estimated age of an empty universe based on the Friedmann Equation?

The current estimated age of an empty universe based on the Friedmann Equation is approximately 9.2 billion years. This calculation assumes a flat universe and a matter content consisting of only non-relativistic particles, such as cold dark matter.

4. Does the Friedmann Equation account for the effects of dark energy on the age of the universe?

No, the Friedmann Equation does not directly account for the effects of dark energy on the age of the universe. However, it does take into account the total energy density of the universe, which includes the effects of dark energy. The presence of dark energy is one of the reasons why the age of the universe is currently estimated to be around 13.8 billion years, as opposed to the 9.2 billion years estimated for an empty universe.

5. How do observations of the cosmic microwave background (CMB) radiation support the predictions of the Friedmann Equation?

The cosmic microwave background (CMB) radiation is the remnant heat signature of the Big Bang and is considered one of the strongest pieces of evidence for the expansion of the universe. The predictions of the Friedmann Equation regarding the rate of expansion and the age of the universe are supported by observations of the CMB. The CMB also confirms the presence of dark energy, which is a key factor in the predictions of the Friedmann Equation.

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