# Proportions and other Stuff about Expansion

• ComaBerenices
In summary, the conversation discusses the expansion of the universe and its effects on gravitational potential energy and the motion of galaxies. It also touches on the idea of communication between distant objects and the role of gravity in conservation of energy. There is a mention of the Hubble radius, but it is clarified that this does not determine the gravitational binding of massive systems. The concept of gravitational potential energy is also questioned in an expanding, homogeneous universe.
ComaBerenices
I'm not too well read in cosmology, but I know the universe is presumed to be homogeneous in space but not in time, therefore the curvature of the universe can essentially be calculated under one mean.
I just have a few questions about how the universe expands and whether some proportions are legit.
Firstly, say you have two gravitationally attracted points in space that are expanding away from each other:
http://geometry.freehomeworkmathhelp.com/Geometry_Main_0/geometry_homework_help_line_segment.GIF
Because I have heard that DE does not affect the actual motion of galaxies in space, but simply expands the space between them, would these objects continually accelerate 'towards' each other until they reach the distance where a signal cannot be communicated between them due to the increasing expansion between them? If so, if the two objects were within the range where gravitation and expansion balance out, would the two objects soon come together due to acceleration of velocity because of gravity?

Secondly, in an expanding, homogeneous universe, as distances grow, so does gravitational potential energy, as the curvature of space becomes less steep, the gravitational potential energy grows more slowly. This has seemed to correlate with a decreasing Hubble rate of expansion over time, however it is currently decreasing at a decelerated rate. I find this proportion curious so I was wondering whether any cosmologist has looked into this.

Regards,

ComaBerenices said:
Because I have heard that DE does not affect the actual motion of galaxies in space, but simply expands the space between them, would these objects continually accelerate 'towards' each other until they reach the distance where a signal cannot be communicated between them due to the increasing expansion between them? If so, if the two objects were within the range where gravitation and expansion balance out, would the two objects soon come together due to acceleration of velocity because of gravity?
Yes, that's why overdense regions in the early universe collapsed to form gravitationally bound objects, like galaxies and groups of galaxies, and why the expansion is visible only on the large scales (e.g. the solar system doesn't expand).
You don't have to separate the two 'kinds' of velocities here, though - you might just as well treat the recession due to expansion as escape velocity w/r to the mass of the overdense region.

Also, this has got nothing to do with the ability to 'communicate signals' - the scale where groups of galaxies are too far away from each other to be gravitationally bound is much less than the distance at which recession exceeds the speed of light. In the same way, when you shoot a probe out of the Solar system with escape velocity, it is going to be continuously affected by the gravity of the Sun, even as you can be sure it'll never return.I'm not too comfortable with the second question, so I'll let somebody else take it (or get back to you later if nobody does).

Okay thanks, I would think there'd still be a gravitational effect creating acceleration, can gravity effect things that recede beyond the Hubble radius?
Apologies if the second bit sounds a bit weird, I read a bit of an arvix preprint that stated that expansion doesn't violate conservation of energy if you take into account gravity as a decreasing negative factor, so I was curious.

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I'm saying Hubble radius has got nothing to do with massive systems being gravitationally bound or not. The recession velocities are high enough to exceed escape velocity of a typical overdense region (group of galaxies) on the scale as small as a few megaparsecs.

sorry, misinterpreted! C:

ComaBerenices said:
in an expanding, homogeneous universe, as distances grow, so does gravitational potential energy

Not really. The concept of "gravitational potential energy" isn't well-defined in a spacetime that is not static. The expanding universe is not static.

## 1. What is the definition of proportion?

A proportion is a statement that two ratios are equal. It is a way of comparing two quantities and expressing their relationship to each other.

## 2. How do you solve a proportion?

To solve a proportion, you can use cross-multiplication, where you multiply the numerator of one ratio by the denominator of the other ratio and set the two products equal to each other. Then, you can solve for the unknown variable.

## 3. How are proportions used in real life?

Proportions are used in many different fields, such as cooking, finance, and science. For example, in cooking, recipes are often written in proportions, where the ingredients are listed in ratios. In finance, proportions are used to calculate interest rates and determine loan payments. In science, proportions are used to analyze data and make predictions based on patterns.

## 4. What is the difference between direct and inverse proportions?

In a direct proportion, as one quantity increases, the other quantity also increases at the same rate. In an inverse proportion, as one quantity increases, the other quantity decreases at the same rate. For example, the more hours you work, the more money you earn (direct proportion), but the more people you invite to a party, the less food each person gets (inverse proportion).

## 5. How does expansion relate to proportions?

Expansion is the increase in size or amount of something. Proportions can be used to understand and predict how expansion will affect different quantities. For example, if a balloon is inflated, its volume will increase, and this expansion can be described using proportions. Similarly, in chemistry, proportions can be used to determine the amount of a substance that will be produced in a reaction based on the amount of reactants.

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