25-3 The expanding universe emerged from a cataclysmic event called the Big Bang

The Hubble flow shows that the universe has been expanding for billions of years. Therefore, we can conclude that in the past the matter in the universe must have been closer together and therefore denser than it is today. Indeed, as we look farther into the past, we clearly see the density of the universe increasing. There is even strong evidence of increasing density back to the first moments of time. Therefore, some sort of tremendous event caused high-density matter to begin the expansion that continues to the present day. This event, called the Big Bang, marks the creation of the universe.

Estimating the Age of the Universe

How long ago did the Big Bang take place? To estimate an answer, imagine two galaxies that today are separated by a distance d and receding from each other with a velocity v. A movie of these galaxies would show them flying apart. If you run the movie backward, you would see the two galaxies approaching each other as time runs in reverse. We can calculate the time T₀ it will take for the reverse-run galaxies to collide by using the equation

This expression says that the time to travel a distance d at velocity v is equal to the ratio d/v. (As an example, to travel a distance of 360 km at a velocity of 90 km/h takes (360 km)/(90 km/h) = 4 hours.) If we use the Hubble law, v = H₀d, to replace the velocity v in this equation, we get

Note that the distance of separation, d, has canceled out and does not appear in the final expression. Distance not appearing in the expression means that T₀ is the same for all galaxies. This period is the time in the past when all the matter in galaxies was crushed together, the time back to the Big Bang. In other words, the reciprocal (or inverse) of the Hubble constant H₀ gives us an estimate of the age of the universe called the Hubble time this is one reason why H₀ is such an important quantity in cosmology.

Observations suggest that H₀ = 73 km/s/Mpc to within a few percent, and this is the value we choose as our standard (see Section 23-5). Using this value, our estimate for the age of the universe is

To convert this into units of time, we simply need to remember that 1 Mpc equals 3.09 × 10¹⁹ km and 1 year equals 3.156 × 10⁷ s. Using the technique we discussed in Box 1-3 for converting units, we get

By comparison, the age of our solar system is only 4.56 billion years, or about one-third the age of the universe. Thus, the formation of our home planet is a relatively recent event in the history of the cosmos.

The value of H₀ has an uncertainty of about 5%, so our simple estimate of the age of the universe is likewise uncertain by at least 5%. Furthermore, the formula T₀ = 1/H₀ is at best an approximation, because in deriving it we assumed that the universe expands at a constant rate. In Section 25-8 we will discuss how the expansion rate of the universe has changed over its history. When these factors are taken into consideration, we find that the age of the universe is 13.7 billion years, with an uncertainty of about 0.2 billion years. This time period is remarkably close to our simple estimate.

Whatever the true age of the universe, it must be at least as old as the oldest stars. The oldest stars that we can observe readily lie in the Milky Way’s globular clusters (see Section 19-4 and Section 22-1). The most recent observations, combined with calculations based on the theory of stellar evolution, indicate that these stars are about 13.4 billion years old (time period with an uncertainty of about 6%). This time period is less than the calculated age of the universe: As required, the oldest stars in our universe are younger than the universe itself.

What was our universe like 15 billion years ago? The passage of time (as we understand time) in the only universe we know of did not exist prior to the Big Bang. Nor did space (as we understand space) exist in the universe until expansion from the Big Bang. Time began to pass and space began to exist at the Big Bang. Since the universe, as we understand it, is only 13.7 billion years old, there does not appear to be physical meaning to the question of what things were like in the universe 15 billion years ago.

Our Observable Universe and the Dark Night Sky

The Big Bang helps resolve Olbers’s paradox, which we discussed in Section 25-1. We know that the universe had a definite beginning, and thus its age is finite (as opposed to infinite). If the universe is 13.7 billion years old, then the most distant objects that we can see are those whose light has traveled 13.7 billion years to reach us. (Due to the expansion of the universe, these objects are now more than 13.7 billion light-years away.) As a result, we can only see objects that lie within an immense sphere centered on Earth (Figure 25-5). This is true even if the universe is infinite, with galaxies scattered throughout its limitless expanse.

Figure 25-5: R I V U X G
Our Observable Universe The part of the universe that we can observe lies within our cosmic light horizon. The galaxies that we can just barely make out with our most powerful telescopes lie inside our cosmic light horizon; we see them as they were less than a billion years after the Big Bang. We cannot see objects beyond our cosmic light horizon, because in the 13.7 billion years since the Big Bang their light has not had enough time to reach us.

(Inset: Robert Williams and the Hubble Deep Field Team, STScI; NASA)

The surface of the sphere depicted in Figure 25-5 is called our cosmic light horizon. Our entire observable universe is located inside this sphere. We cannot see anything beyond our cosmic light horizon, because the time required for light to reach us from these incredibly remote distances is greater than the present age of the universe. As time goes by, light from more distant parts of the universe reaches us for the first time, and the size of the cosmic light horizon—the size of our observable universe—increases. The finite size of the observable universe, with a finite number of stars and galaxies, also helps to resolve Olber’s paradox: Galaxies are distributed sparsely enough in our observable universe that there are no stars along most of our lines of sight. This sparse distribution of visible stars is one reason why the night sky is dark.

Besides the finite age of the universe, a second effect also contributes significantly to the darkness of the night sky—the redshift. According to the Hubble law, the greater the distance to a galaxy, the greater the redshift. When a photon is redshifted, its wavelength becomes longer, and its energy—which is inversely proportional to its wavelength (see Section 5-5)—decreases. Consequently, even though there are many galaxies far from Earth, they have large redshifts and their light does not carry much energy. A galaxy nearly at the cosmic light horizon has a nearly infinite redshift, meaning that the light we receive from that galaxy carries practically no energy at all. This decrease in photon energy because of the expansion of the universe decreases the brilliance of remote galaxies, helping to make the night sky dark.

The concept of a Big Bang origin for the universe is a straight-forward, logical consequence of an expanding universe. In Section 25-4, we will see direct evidence of the primordial fireball associated with the Big Bang and other confirmations of the Big Bang back to the first few moments. But how far back in time can our laws describe the universe? If you can just imagine far enough back into the past, you can arrive at a time 13.7 billion years ago, when the density throughout the universe was nearly infinite. As a result, throughout the universe space and time were jumbled up with nearly infinite curvature. A full description of this earliest instant requires (as do aspects of black holes) a valid mathematical theory of quantum gravity, which is a work in progress. But when in the past did the known laws of physics begin to apply?

A very short time after the Big Bang, space and time began to behave in the way we think of them today. This short time interval, called the Planck time (t_P), is given by the following expression:

The Planck time

• t_P = Planck time
• G = universal constant of gravitation
• h = Planck’s constant
• c = speed of light

We do not yet understand how space, time, and matter behaved in that brief but important interval from the beginning of the Big Bang to the Planck time, about 10⁻⁴³ seconds later. (Indeed, the laws of physics suggest that it might be impossible ever to know what happened during this extremely short time interval.) Hence, the Planck time represents a limit to our knowledge of conditions at the very beginning of the universe.