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# Cosmological Principle

Up until the 16th Century, it was widely assumed that the Earth held a special place at the center of the universe, before the likes of Copernicus, Galileo and Newton showed otherwise. In 1637, Isaac Newton published his master work Principia, which set out the idea Earth not at the center of the universe.

Newton argued, moreover, that the universe had no center, and is basically the same no matter where you went. In other words, the universe is homogeneous. Furthermore, he postulated the universe is isotropic, i.e. the same no matter which direction you look. These two postulates became known together as the cosmological principle.

## Cosmological Principle

### Cosmology

# Cosmological Principle

Imagine a universe that is similar to our own, except it is bathed in a faint red light, all coming from the same direction so that one half of every planet is lit by it, while the other is in shadow.

How would a cosmologist describe this universe?

## Cosmological Principle

### Cosmology

# Cosmological Principle

The idea of the universe being homogeneous might seem strange at first. Clearly on a small scale not every bit of the universe is the same. The bit of universe under your feet is not the same as the bit above your head, as one is solid ground while the other is gas. A good way to think about the meaning of homogeneity is to think of a fruitcake. A small piece of the fruitcake could contain a raisin, or something else, but one large piece will look much like another.

What do you think is the smallest scale at which the universe could be considered homogeneous?

## Cosmological Principle

### Cosmology

# Cosmological Principle

Clearly, planets, stars and galaxies all have structure and are not homogeneous. The evidence that the universe is homogeneous at large enough scales comes from the Cosmic Microwave Background. This is radiation that originated in the early universe, and appears to come almost evenly from every direction once you get up to length scales of hundreds of megaparsecs (about $$3000$$ times the diameter of the Milky Way). We will introduce it thoroughly in a subsequent quiz.

Image Credit: NASA/WMAP

Until the mid-20th century, many cosmologists went further and postulated that the universe is homogeneous in time as well as space. This would mean the universe has no beginning or end. The universe would have looked broadly the same $$20$$ billion years ago as it does now. This idea, however, has not held up to scrutiny.

## Cosmological Principle

### Cosmology

# Cosmological Principle

In the next few questions we will be conducting a thought experiment, considering a universe that is homogeneous in both space and time.

To start with, imagine you are looking out into space at a single star. What equation gives the intensity of radiation you are receiving from that star?

Details

• $$L$$ is the luminosity of the star.
• $$r$$ is the distance from you to the star.

## Cosmological Principle

### Cosmology

# Cosmological Principle

In cosmology we are interested in large regions of space which can be considered homogeneous—we do not care about the effects of individual stars on their own.

If $$L$$ is the mean luminosity of stars and $$n_\text{stars}$$ is the mean number density of stars in the universe (i.e., stars per unit volume) find an expression that equal to the intensity of the light you will receive from that region of space with volume $$V.$$

Details

• The volume $$V$$ is very large, so it contains hundreds of stars (or more).
• It is at a distance $$r$$ from you, which is large compared to the diameter of the volume. (The image here is not drawn to scale.)

## Cosmological Principle

### Cosmology

# Cosmological Principle

Now consider a volume of space which forms a spherical shell of thickness $$a$$ at distance $$r$$ from the Earth. What expression gives the intensity of light received on Earth from that shell?

Details & Assumptions

• All the light emitted from the stars in the shell can get to you; none of the light is blocked by Earth or anything else.
• The thickness of the shell, $$a$$, is small in comparison to the radius $$r.$$

## Cosmological Principle

### Cosmology

# Cosmological Principle

Using your answer to the previous question, what would happen to the amount of light you would receive from a spherical shell of space of equal thickness but at a much greater distance $$r$$ from Earth?

## Cosmological Principle

### Cosmology

# Cosmological Principle

Using your answers so far, and assuming that we have a finite density of stars in the universe, what would we expect the night sky to look like if the universe is homogeneous in both space and time (implying also that it is infinitely large and old)?

## Cosmological Principle

### Cosmology

# Cosmological Principle

The idea you have just explored is known as Olber's Paradox. A universe that is infinitely old and homogeneous would have a completely bright night sky. Luckily for us, that is clearly not the case. We now believe the universe to have a finite age, which solves this problem even if the universe is infinitely large, as the light from more distant regions of space simply will not have had time to reach us since the beginning of time.

Cosmology is concerned with these big questions about the universe as a whole—its shape, beginning and ultimate fate. We have just argued that the universe must have had a beginning. In the next quiz we will consider whether it will have an ending, and what that could look like.

## Cosmological Principle

### Cosmology

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