# Can FLRW metric be taken to describe stretching in time rather than space?

• themos
In summary, the conversation discusses the concept of conformal time and its relation to scaling both time and space. The advantages and disadvantages of abandoning the notion of "expansion" of space in favor of "speeding up" or "slowing down" time are also considered, with the potential impact on our understanding of atoms being a major consideration.
themos
I hope the title makes sense. I see a factor a(t)^2 in from of the space part of the metric. Is it equivalent to scaling the time part? If so, is there an advantage in abandoning notion of "expansion" of space in favour of time "speeding up" or "slowing down"?

themos said:
I hope the title makes sense. I see a factor a(t)^2 in from of the space part of the metric. Is it equivalent to scaling the time part? If so, is there an advantage in abandoning notion of "expansion" of space in favour of time "speeding up" or "slowing down"?

Welcome to Physics Forums!

Conformal time is related to this, but I don't think this is what you mean. When conformal time is used, "time" and space are scaled by the same factor. Take a flat universe with

$$ds^2 = dt^2 - a \left(t\right)^2 \left( dx^2 + dy^2 + dz^2 \right)$$

and define conformal time $\eta$ by

$$dt = a \left(t\right) d \eta .$$

Then,

$$ds^2 = a \left(t\right)^2 \left( d\eta^2 - dx^2 + dy^2 + dz^2 \right).$$

On spacetime diagrams that use conformal time, light rays are straight lines just like in special relativity, which is often useful. For light

$$ds^2 = 0$$

gives

$$d \eta = \pm \sqrt{dx^2 + dy^2 + dz^2}$$

or, for example,

$$\eta = x + const$$

for light in the x-direction.

themos said:
I hope the title makes sense. I see a factor a(t)^2 in from of the space part of the metric. Is it equivalent to scaling the time part? If so, is there an advantage in abandoning notion of "expansion" of space in favour of time "speeding up" or "slowing down"?
The reason why we usually take space as expanding and not time is that we consider atoms to be stable.

If we were to instead take space as static, then yes, we would have to scale the time coordinate. But then we would find that atoms change in size with time. That's not to say that this is wrong, but it is contrary to our usual conception of atoms, and would require some serious rewriting of the laws of physics to get everything to work out properly. So I'm not entirely sure that this would be useful.

## 1. What is the FLRW metric?

The FLRW metric, also known as the Friedmann-Lemaître-Robertson-Walker metric, is a mathematical model used in cosmology to describe the large-scale structure of the universe. It is based on Einstein's theory of general relativity and is used to study the expansion of the universe over time.

## 2. Can the FLRW metric be used to describe stretching in time?

Yes, the FLRW metric can be used to describe the expansion of the universe over time. It is often used to study the relationship between the rate of expansion and the age of the universe.

## 3. Is the FLRW metric only used to describe stretching in space?

No, the FLRW metric can be used to describe both stretching in space and time. It is commonly used to describe the expansion of the universe, which involves both the stretching of space and the passage of time.

## 4. What is the difference between stretching in space and stretching in time?

Stretching in space refers to the expansion of the distances between objects in the universe, while stretching in time refers to the passage of time as the universe continues to expand. Both of these processes are described by the FLRW metric.

## 5. How does the FLRW metric account for the expansion of the universe?

The FLRW metric includes a scale factor, which represents the relative size of the universe at a given point in time. This scale factor changes over time, reflecting the expansion of the universe. The metric also incorporates the effects of gravity, which can affect the rate of expansion over time.

• Special and General Relativity
Replies
3
Views
1K
• Cosmology
Replies
25
Views
2K
• Cosmology
Replies
27
Views
3K
• Cosmology
Replies
1
Views
955
• Cosmology
Replies
4
Views
1K
• Cosmology
Replies
4
Views
2K
• Cosmology
Replies
28
Views
3K
• Special and General Relativity
Replies
52
Views
4K
• Cosmology
Replies
7
Views
2K
• Special and General Relativity
Replies
38
Views
3K