Are we accelerating in the universe?

In summary: But in the simplest cases the two criteria agree.In summary, the conversation discusses the concept of the universe's accelerating expansion in the context of cosmology. It is clarified that this acceleration is not the same as ordinary acceleration in motion, but rather a change in the rate of change in the distances between stationary observers. The concept of comoving observers is introduced as those who are at rest relative to the cosmic microwave background (CMB). It is also noted that the FRW coordinate time is not the same as the proper time of all observers, but is the same as the proper time of comoving observers. The criteria for determining if an observer is comoving or not is also discussed.
  • #1
instanton
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OK, I'm not an expert in cosmology but I'm quite curious about it. Current observations tells us that the universe is accelerating (in what sense I don't quite understand). On the other hand, the Friedman equation says that the scale factor a(t) has a positive second time derivative provided the equation of state of the whole universe obays some condition (e.g. \rho+3 p < 0 if the whole matter content in the universe is an ideal fluid). What bothers me is that the time t in Friedman equation is only the FRW coordinate time, not the proper time. So a(t) has a possitive second time derivative does not gurantee that the universe is accelerating irrespective of observers. In particular, in FRW coordinates, observers sitting at the origin of FRW coordinates should not be accelerating in t, because the actual radial coordinate should be a(t) times r, rather than just a(t). on the other hand, we can easily infer that other (comoving) observers sitting at other places of the universe should percieve us as being accelerating in their owh FRW coordinate (with the origin located at their own place). If the other observers are not comoving, they might found the evolotion of the universe very different from what we observe. So, what it really means by the statement that the universe is under acceletating expansion? Are we accelerating ourselves in the universe?
 
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  • #2
instanton said:
...tells us that the universe is accelerating (in what sense I don't quite understand)... So, what it really means by the statement that the universe is under acceletating expansion? ...

It doesn't mean ordinary acceleration of ordinary motion. It simply means that the second time deriv. a"(t) of the scalefactor a(t) is positive.

The scalefactor is most simply understood if you think of a network of observers who are all stationary relative to the CMB and have a common idea of time that goes with being at "CMB rest". That means the present moment in time (tpresent) has a definite meaning and we can normalize the scalefactor by setting a(tpresent) = 1.

The distances that are increasing are distances between stationary observers---observers who are at rest with respect to the CMB. The simple fact that a"(t) > 0 merely means that distances between stationary observers are growing at an increasing rate.

Ordinary acceleration has a definite direction, but the mere fact that a"(t) > 0 is not associated with any direction. The familiar idea of motion is normally associated with some destination that you are getting closer to, but a galaxy participating in the cosmic expansion of distances is not approaching any destination. It is not getting closer to anything, just farther apart from everything. It is a change in geometry (not motion within a fixed geometry.)

Since the "acceleration" has no preferred direction it should not be thought of as acceleration of ordinary motion. But that is OK. We often speak of changes that don't involve directed motion as speeding up or slowing down--- in technology, economics, global climate change, or changes in human and other species populations. Just a change in the rate of change.
 
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  • #3
Hi, instanton,

Welcome to PF!

The FRW t coordinate is not the same as the proper time of every possible observer, but it *is* the same as the proper time of a comoving observer.

FRW models are homogeneous, so there is nothing special about the coordinate origin.

The equivalence principle says that any observer can be considered as either accelerating or nonaccelerating, and this is perceived the same as a gravitational field. Comoving observers are special because they perceive zero gravitational field.

Here is a coordinate-independent way of stating the fact about acceleration. Let L be the distance measured between comoving galaxies A and B by laying a chain of comoving rulers between them, and let t be the time on a comoving clock. Then d^2L/dt^2>0.

-Ben
 
  • #4
Yes, a network of "comoving" observers is for practical purposes another way of talking about observers who are at CMB rest.

Maybe we should say what the practical criterion for telling if you are comoving or not would be. The observer looks around and measures the temperature of the CMB in all directions. If there is an obvious Doppler hotspot then he is moving relative CMB.

A moving observer sees a Doppler dipole in the radiation map, significantly hotter (bluer) ahead of him and colder (redder) behind.

It's an approximate notion, since there is some noise or random fluctuation in the temperature map. And there is another criterion involving galaxy redshifts that doesn't depend on the CMB.
 
  • #5


First of all, let me clarify that the statement "the universe is accelerating" refers to the expansion of the universe, not the motion of individual objects within it. The expansion of the universe is described by the scale factor a(t) in the Friedman equation, which represents the changing size of the universe over time.

The observations that suggest the universe is accelerating come from the study of distant supernovae, which show that the expansion of the universe is actually accelerating rather than slowing down as we would expect based on the matter and energy content of the universe. This is known as the "cosmological constant problem" and is still an active area of research in cosmology.

Now, to address your concern about the use of FRW coordinates in the Friedman equation, it is important to remember that these coordinates are simply a mathematical tool to describe the universe and are not tied to any particular observer. So, while an observer at the origin of FRW coordinates may not perceive themselves as accelerating, this does not mean that the expansion of the universe is not accelerating for all observers.

In fact, according to the theory of general relativity, the expansion of the universe is not tied to any particular reference frame or observer. It is a fundamental property of the universe that can be observed and measured by any observer, regardless of their location or motion.

In conclusion, the statement that the universe is accelerating refers to the expansion of the universe itself, not the motion of individual objects within it. The use of FRW coordinates in the Friedman equation does not affect this conclusion, as the expansion of the universe is a fundamental property that can be observed and measured by any observer.
 

FAQ: Are we accelerating in the universe?

1. What is acceleration in the context of the universe?

Acceleration in the context of the universe refers to the expansion of the universe, which is the increase in distance between galaxies and other celestial bodies. This expansion is thought to be caused by a mysterious force called dark energy.

2. How do we know that the universe is accelerating?

We know that the universe is accelerating because of observations of distant supernovae, which are exploding stars that can be used as "standard candles" to measure distances in the universe. These observations have shown that galaxies are moving away from each other at an increasing rate, indicating acceleration.

3. Is the acceleration of the universe constant?

No, the acceleration of the universe is not constant. It is thought to be increasing over time, meaning that the expansion of the universe is accelerating at a faster and faster rate.

4. What is causing the acceleration of the universe?

The exact cause of the acceleration of the universe is still unknown, but it is thought to be caused by a repulsive force called dark energy. This force is believed to make up about 70% of the total energy in the universe, but its exact nature is still a subject of ongoing research and debate.

5. What are the implications of the accelerating universe?

The accelerating universe has significant implications for our understanding of the universe and its future. It suggests that the expansion of the universe will continue to accelerate, eventually leading to the "heat death" of the universe, where all matter and energy are evenly distributed and the universe reaches a state of maximum entropy.

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