# Cosmological Models of the Universe

## Is The Universe Flat?

An important question in cosmology is, is space flat? Cosmology is the study of the history and future of the universe. One branch of cosmology, physical cosmology, studies the origin, structure, and fate of the universe. This study draws on work from many areas of both theoretical and experimental physics.

In cosmology, when people refer to the shape of the universe, they are generally referring to the curvature. Specifically, is the universe flat or curved? If the universe is curved, is it open or closed? There are three main cosmological models that have been described for the shape of the universe. These are:

- A
**flat**universe with zero curvature. - An
**open**universe with a curvature that does not curve back on itself. - A
**closed**universe with a curvature that folds back on itself like a saddle.

According to the Theory of General Relatively developed by German-born theoretical physicist Albert Einstein, the overall shape of the universe depends on the average density of matter and energy in the universe. The universe can only be flat if the density of the matter and energy precisely equals a value known as the **critical density**. A density parameter is also defined as the ratio between the actual density of the universe and the critical density. The parameter is represented by {eq}\Omega {/eq}.

- For a flat universe: {eq}\Omega = 1 {/eq}.

- For a closed universe: {eq}\Omega > 1 {/eq}

- For an open universe:{eq}\Omega < 1 {/eq}.

The density parameter has been calculated experimentally in a number of ways. These experiments then provide evidence for theories regarding the shape of the universe.

## Flat Universe

The exact shape is still up for debate; however, experimental data from many independent sources indicate that the universe is most likely flat. The **flat universe** model can be visualized as a sheet of paper, with no curvature. In this model, the universe is infinite and will continue to expand forever.

The density parameter has been determined experimentally in several ways. One method is to sum all the mass energy in the universe and find the average density. This has been done using data from the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck spacecraft which performed measurements of the Cosmic Microwave Background radiation. Another method is to measure the angle across the observable universe, which is also done using the CMB. This method was used in the BOOMERanG experiment using high-altitude balloons. These measurements have all returned values of the density parameter that correspond to a flat universe within experimental error.

Why is the universe flat? This is believed to be a consequence of inflation. In cosmology, inflation describes the theory that the universe underwent an exponential expansion of space the instant after the Big Bang. The expansion only lasted for {eq}10^{-36} {/eq} seconds after the Big Bang before the expansion slowed significantly. Experimental evidence from as early as the 1960s began to indicate that the density of the universe was very close to the critical density, or the density necessary for a flat universe. Inflation can explain why the overall shape of the universe is flat or very close to flat. Consider a point on a balloon as it is inflated, the surface around a single point flattens as the balloon inflates. The flattening of space is thought to have occurred in the same way and would have been so enormous that any curvature that the universe had previously would only be noticeable on scales much larger than the observable universe.

## Closed Universe

Another theory about the structure of the universe is the closed universe theory. So, what is the meaning of a closed universe? A **closed universe** describes one with non-zero curvature which curves back on itself. This can be thought of as a sphere, as shown in the diagram. A closed universe is said to have positive curvature.

A closed universe is one in which the average density is greater than the critical density, meaning the density parameter, {eq}\Omega {/eq}, is greater than 1. This causes the space to fold back onto itself. This type of universe is finite but has no center and no edge. To understand this, it may help to imagine a two-dimensional being moving on the surface of a three-dimensional sphere. The being can move in every direction on the surface of the sphere, but can't move up or down. The space on the surface of the sphere is finite but there is no edge and no center.

This model of the universe predicts an event named the Big Crunch. The density of a closed universe is sufficient to not only stop the expansion of the universe but to cause it to reverse and begin to contract. Eventually, the universe will contract to a single point, in a reverse of the Big Bang.

## Open Universe

If the density of the universe is less than the critical density, it is an open universe. The **open universe** theory describes a universe that has a non-zero curvature that does not curve back on itself. The structure of an open universe is openly called a saddle shape. The structure is shown in the diagram. This universe is infinite and said to have negative curvature.

In an open universe, there is insufficient matter to cause the universe to curve back on itself. A consequence of this is that there is an insufficient gravitational pull to stop the universe from expanding. As a result, the universe will continue to expand forever and not experience a Big Crunch event.

Consider a final example to explain the difference between flat, open, and closed universes. Two rockets are flying next to each other through space. In a flat universe, these two rockets will always remain parallel as they travel through space. If the two rockets are traveling through a closed universe, their paths will diverge, but eventually, they will meet again where they started due to the curvature of space. Conversely, in an open universe, the paths of the two rockets will diverge and they will never meet again.

## Lesson Summary

The shape of the universe refers to the geometry of the universe, specifically the curvature. There are three major cosmological models that describe the curvature of the universe. These models are:

- The
**flat universe**, which is infinite and has zero curvature. - The
**open universe**, which is infinite and has non-zero curvature that does not curve back on itself, or negative curvature. This universe has a saddle shape. - The
**closed universe**, which is finite and has non-zero curvature that curves back on itself, a positive curvature, but has no center and no edge. This universe has a sphere shape.

The overall shape of the universe depends on the density of matter and energy. The **critical density** is defined as the density required for a flat universe. Current experimental data indicates that the average density in the universe is very close to the critical density. This means that the universe is most likely flat.

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#### What happens in a closed universe?

For a closed universe, the expansion will eventually be stopped by the force of gravity. After this, the universe will begin to collapse to a single point.

#### What is an open universe?

An open universe is one that is curved by does not fold back onto itself. This type of universe will expand forever because there is not enough mass for gravity to stop it.

#### Is the universe geometrically flat?

The exact shape of the universe is still up for debate. But the best current theories suggest that the universe is geometrically flat.

#### What happens if the universe is closed?

In a closed universe, gravity will eventually stop the universe from expanding. After this, it will begin to contract to a single point called the Big Crunch.

#### Is the universe closed, open, or flat?

There is not a general consensus on the shape or structure of the universe. Several theories exist which each agrees with some available evidence. The best current theories predict the universe is likely flat.

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