# The True Model and Ultimate Fate of the Universe

FROM THE LECTURE SERIES: INTRODUCTION TO ASTROPHYSICS

## In the mid-1990s, astronomers started getting good at discovering Type Ia supernovae in distant galaxies of the universe. They act like standard candles. You can determine the distance based on the flux-luminosity relationship. And you can measure the redshift of the galaxy where the supernova took place. So, each new supernova adds a new data point to the Hubble diagram and astronomers were adding them at ever greater distances and higher redshifts.

### The Most Probable Model of the Universe

The distance, divided by c, tells us how much time has elapsed since the supernova went off. And the redshift, z, tells us the value of the cosmological scale factor at that time: it’s one over a equals one plus z. So, we can convert the redshift distance data into a chart of a versus time.

If gravity were irrelevant, and the universe were just coasting along, we would see a is proportional to t. That would be a straight line through a equals one, with the same slope as the other curve. And if the density were higher than the critical density, the universe would re-collapse; the model curve goes up, and then down. said that a should be growing like t to the 2/3. We can plot that curve. We need to make sure a is equal to one at the present day, and the slope is equal to the Hubble constant. That curve hits a equals zero at a time 9.3 billion years in the past.

We can also plot some other cases. If gravity were irrelevant, and the universe were just coasting along, we would see a is proportional to t. That would be a straight line through a equals one, with the same slope as the other curve. And if the density were higher than the critical density, the universe would re-collapse; the model curve goes up, and then down.

So, now, let’s look at the supernova data: Which of these models turned out to be closest to the truth? The answer is none of them! The data points are higher than any of the curves. What does that mean?

Well, if we want connect the data points to the present day, when a equals one and the slope is H-naught, we need to draw a curve that bends upwards. The scale factor is not just increasing; the rate of increase has grown with time. The expansion of the universe is not decelerating, and it’s not coasting, it’s accelerating.

Now, that seems absurd. It’s easy to understand why the expansion rate might be slowing down, from the attraction of gravity. But what would speed it up? For that you’d need some kind of anti-gravity! It doesn’t make a whole lot of sense, but that’s where the data have led us.

This article comes directly from content in the video series Introduction to AstrophysicsWatch it now, on Wondrium.

### An Unsolved Problem

We have reached the number one unsolved problem in astrophysics. Cosmologists, astronomers, and particle physicists have united in the effort to understand what’s going on. The phenomenon itself—the force, or substance, that propels the expansion of the universe with ever increasing speed—has become known as dark energy, in analogy with dark matter. But it’s just a label. We’re completely in the dark as to its true nature. There must be something called dark energy to explain the expansion of the universe. (Image: NASA/Public domain)

But, you know what might have something to do with it? Good old Lambda! That integration constant that we so casually discarded a few minutes ago, on the advice of Albert Einstein. Lambda might have a physical meaning, after all. Let’s go back to the Friedmann equation, but this time we’ll retain the Lambda, and see what happens.

In an expanding universe, as time goes on, rho goes down, matter and radiation get diluted. But Lambda, being a constant, persists. So, eventually we must reach a point at which we can neglect the rho term altogether.

That implies one over ada/dt is a constant, an equation for which the solution is exponential growth. So, that could be what we’re observing today. A transition in the history of the universe, when the gravitational attraction of ordinary matter has been overcome by a universal repulsive force, represented by the cosmological constant.

### The Cosmological Constant Is the Key

Fitting the supernova data to an upwardly bending line also has the effect of increasing the calculated age of the universe. The curve doesn’t cross a equals zero until all the way back to 14 billion years ago.

So, the cosmological constant solves the problem of the stars that appeared to be older than the universe. It also explains how the universe can be flat, even though the density of matter is less than the critical density.

In the Friedmann equation, Lambda over 8pi G acts like a density that gets added to rho. According to the data, the actual rho is 30% of the critical density, and that Lambda-term makes up the other 70%. So, even though we don’t understand dark energy, once we invoke it, everything fits together.

### What Will Happen in the Future?

Let me sum up the current situation by taking you through the history of the universe as we know it, with a logarithmic chart of a versus t. This is what you get when you solve the Friedmann equation, including the effects of matter, radiation, and dark energy, all at the numerical levels consistent with data from Type Ia supernovas, the cosmic microwave background, and numerous other sources.

The model predicts that in the future, the scale factor will continue rising exponentially. The ultimate fate of the universe is to dilute itself to near nothingness. Nobody will be able to see anything outside their own galaxy. It’ll be a lonelier universe.

### Common Questions about the True Model and Ultimate Fate of the Universe

Q: What would accelerate the speed of the universe’s expansion?

Astronomers suspect that something known as dark energy is responsible for the universe’s expansion at an accelerated speed. However, the true nature of dark energy is still unknown.

Q: Why did none of the suggested models turn out to be closest to reality?

Because if we want to connect the data points up to the current day, when a equals one and the slope is H-naught, we need to draw a curve that bends upwards. This indicates that the scale factor is not only increasing but also has grown with time. So, the expansion of the universe is neither decelerating nor coasting, it’s accelerating.

Q: What is the ultimate fate of our universe?

Based on what we know so far, the scale factor will continue rising exponentially. Therefore, the universe will expand forever, to the point that nobody will be able to see anything outside their own galaxy.