Scale factor (cosmology)

The universe is growing.

We use a special number to show this growth. This number is called a scale factor.

Long ago, the universe was very small. The scale factor was less than one. At this time, light was the main thing.

Then, things changed. Matter became more important. The universe grew even more.

Now, a dark energy helps it grow. This energy makes the growth speed up. This has happened for billions of years.

Today, the scale factor is one. It helps us see how far things move. It is a way to track space.

The universe is growing. We use a special number to track this. This number is called the scale factor.

It tells us how much space has grown. Today, the scale factor is exactly 1.0. In the past, the scale factor was less than one. This number helps us find the distance between objects. For example, it helps us find the distance between galaxies.

The universe has gone through three big stages. First, there was a radiation era. In this stage, radiation was the main thing. This lasted until the universe was 47,000 years old. Next came the matter era. During this time, matter was the most important part. This stage lasted for a very long time.

About 4 billion years ago, things changed again. We entered the dark energy era. Dark energy is a force that fills empty space. This energy makes the universe grow faster and faster. This is called acceleration. Because of this, galaxies move away from us at higher speeds. This growth happens in every direction. It does not matter where you look in space.

The universe is constantly growing and changing shape. Scientists use a special number to track this growth called the scale factor.

This number is a way to measure how much space has stretched over time. We set the scale factor to exactly 1.0 for right now. In the past, this number was much smaller than 1.0. This number helps us understand the distance between things like galaxy clusters. It works the same way no matter which direction you look in space.

To understand how the scale factor works, think about the distance between two objects. The scale factor links the distance we see now to the distance in the past. This is called the proper distance.

If the scale factor is 0.5, the distance between objects was half of what it is today. The way the scale factor changes depends on what fills the universe. This change is part of a set of rules called the Friedmann equations. These equations tell us how the expansion moves step by step. The scale factor changes based on the energy and matter present.

History shows the universe has moved through three main stages. The first was the radiation-dominated era. During this time, energy from light and particles like neutrinos drove the expansion. This stage lasted until the universe was about 47,000 years old.

After that, the universe entered a matter-dominated era. This lasted for a very long time, until about 9.8 billion years after the Big Bang. During this era, the density of matter was the most important part of the universe.

We are now in a third stage called the dark-energy–dominated era. This stage began about 4 billion years ago. Dark energy acts like a mass within empty space.

Because dark energy stays constant as space grows, it eventually becomes the strongest force. Recent studies of distant supernovae show that the expansion is actually speeding up. This is called acceleration. This means the scale factor is increasing faster and faster as time goes on. It is a very big change for the history of the universe.

We can use the scale factor to connect the distant past to our world today. For example, we can use it to find the redshift of light. Redshift is a way to see how much light has stretched as it travels.

If we see a certain redshift, we can calculate the scale factor at the moment that light was first sent. This helps us map out the 13.8 billion year history of our cosmos. The scale factor is a key tool for seeing how everything fits together. It turns the history of space into a measurable path.

In cosmology, the scale factor is a dimensionless number used to track the expansion of the universe. It is also known as the cosmic scale factor or the Robertson–Walker scale factor. This value is a vital part of the Friedmann equations, which describe how the universe evolves. By using this factor, scientists can characterize how the universe stretches over time. It is a geometrical scaling factor that is conventionally set to 1.0 at the present time. At any time in the past, the scale factor was less than 1.0.

The scale factor helps us understand the distance between objects in an expanding universe. We distinguish between the comoving distance and the proper distance. The comoving distance is a fixed value set to the distance we see today. The proper distance is the actual distance between two objects, such as galaxy clusters, at a specific time. The scale factor acts as the link between these two measurements. If the scale factor is 0.5, the proper distance between objects is half of their current distance. This mathematical relationship allows researchers to map the history of space.

The way the scale factor changes over time is a dynamical process. This movement is determined by the equations of general relativity. In a universe that is locally isotropic and homogeneous, these are called the Friedmann equations. The rate of expansion is also described by the Hubble parameter. This parameter is the time derivative of the scale factor. The Hubble constant is the specific value of this parameter at our current time. While the Hubble parameter changes over time, it does not change based on location in space.

History shows that the universe has moved through three distinct eras. The first was the radiation-dominated era. This began after inflation and lasted until the universe was about 47,000 years old. During this stage, radiation like photons and neutrinos was the dominant influence on expansion. The energy density of radiation scaled in a specific way during this period. This led to a very rapid early expansion. As the universe expanded and cooled, the roles of matter and radiation began to shift.

The second stage is the matter-dominated era. This era began when the universe was roughly 47,000 years old. At this point, the mass-energy density surpassed the radiation energy. This era lasted for a very long time, until the universe was about 9.8 billion years old. During this period, the energy density of matter was the most important factor in the expansion. It was not until about 378,000 years after the Big Bang that the universe became transparent to radiation. This event is known as recombination.

We have now entered the third phase, known as the dark-energy–dominated era. This era began when the universe was approximately 9.8 billion years old. This means we have been in this phase for about 4 billion years. Dark energy is often linked to the cosmological constant, represented by the symbol Λ. This constant can be viewed as a mass of empty space. Unlike matter or radiation, the density of dark energy does not drop as the universe grows. Because this density remains constant, it eventually becomes the most powerful influence on the universe.

Recent evidence suggests that the expansion of the universe is actually accelerating. This means the second derivative of the scale factor is positive. Observations of distant supernovae have supported this finding. Because of this acceleration, any given galaxy recedes from us at an increasing speed over time. However, the Hubble parameter itself appears to be decreasing over time. This means that later galaxies passing a fixed distance will move at a smaller velocity than earlier ones. This complex behavior shows how the scale factor evolves in a changing cosmos.

The scale factor also provides a way to connect light to the history of the universe. Scientists use a concept called redshift, or z, to measure this connection. If we receive light from a distant object with a certain redshift, we can calculate the scale factor at the moment that light was emitted. The formula for this relationship is 1/(1+z). This allows us to look back at the state of the universe billions of years ago. By studying these connections, we can better understand the 13.8 billion-year history of our universe.