# The Mystery of Equation (3.1.3) and the Origin of the Universe

• bobsan
In summary, the conversation discusses the attempt to determine the initial mass of the universe by setting the Universal time T = Tp as the first instance of the universe. However, the equation (3.1.3) does not directly imply that the initial mass M0 is equal to half of the Planck mass Mp. The suggested method is to consider the initial volume of the universe as a sphere with diameter equal to the Planck length, and then multiply it by the density as given in equation 3.1.4. This may provide an expression for the initial mass that can be compared to the standard formula for the Planck mass.
bobsan
Homework Statement
How can we know that the initial mass of the universe was half of the Planck mass from the formula mass density of the Universe as a function of universal time?
Relevant Equations
(ρ reduced)(Tp)^2 = ρT^2
ρ reduced = 3c^5/(4hG^2)

I tried setting the Universal time T = Tp as when T = 0 there was no universe and thought Tp would be the first instance of the universe, but I still can't figure out how equation (3.1.3) implies that M0 = Mp/2

Last edited by a moderator:
bobsan said:
Homework Statement:: How can we know that the initial mass of the universe was half of the Planck mass from the formula mass density of the Universe as a function of universal time?
Relevant Equations:: (ρ reduced)(Tp)^2 = ρT^2
ρ reduced = 3c^5/(4hG^2)

View attachment 301814
I tried setting the Universal time T = Tp as when T = 0 there was no universe and thought Tp would be the first instance of the universe, but I still can't figure out how equation (3.1.3) implies that M0 = Mp/2
Hi @bobsan. Welcome to PF.

The reasoning in the attachment isn’t clear (well, it's missing actually). Not a familiar area for me but you could try this...

Consider the initial volume to be a sphere with diameter (or possibly radius) equal to the Planck length. Express this volume in terms of ℏ, G and c.

Multiply this by the density as given in equation 3.1.4. This gives you an expression for the initial mass. Compare this expression to the standard formula (expressed in in terms of ℏ, G and c)for the Planck mass.

If you’re lucky, you may find your expression for mass is half the Planck mass. No idea if that’s what’s intended though.

bobsan
Where are you getting this from?

vanhees71

## 1. What is Equation (3.1.3) and how does it relate to the origin of the universe?

Equation (3.1.3) is a mathematical formula that is used to describe the expansion of the universe. It is also known as the Friedmann equation and is a key component of the Big Bang theory, which is currently the most widely accepted explanation for the origin of the universe.

## 2. How was Equation (3.1.3) discovered?

Equation (3.1.3) was first derived by Russian physicist Alexander Friedmann in the 1920s. He used Einstein's theory of general relativity to develop a mathematical model of the universe and found that it could be described by a single equation. This equation was later refined by other scientists and is now a fundamental part of our understanding of the universe.

## 3. What does Equation (3.1.3) tell us about the early universe?

Equation (3.1.3) tells us that the universe was once much smaller and denser than it is now. It also suggests that the universe is expanding, with the rate of expansion increasing over time. This expansion is thought to have started with the Big Bang and has been ongoing for approximately 13.8 billion years.

## 4. Can Equation (3.1.3) be used to predict the future of the universe?

Yes, Equation (3.1.3) can be used to make predictions about the future of the universe. By plugging in different values for certain variables, such as the density of matter and energy in the universe, scientists can estimate how the expansion of the universe will continue in the future. However, these predictions are subject to change as our understanding of the universe evolves.

## 5. How does Equation (3.1.3) fit into the larger picture of understanding the universe?

Equation (3.1.3) is just one piece of the puzzle in understanding the origin and evolution of the universe. It is a key part of the Big Bang theory, which is supported by a wealth of observational evidence. However, there are still many unanswered questions about the universe, and scientists continue to study and refine our understanding of Equation (3.1.3) and other theories in order to gain a deeper understanding of the universe as a whole.

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