15-3 The expanding universe emerged from a cataclysmic event called the Big Bang

The universe has been expanding for billions of years. This means that in the past the matter in the universe must have been closer together and therefore denser than it is today. If we look far enough into the very distant past, there must have been a time when the density of matter was almost inconceivably high. This leads us to conclude that some sort of tremendous event caused ultradense matter to begin the expansion that continues to the present day. This event, which we have named 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 were to 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 would take for the galaxies to collide by using a version of the familiar distance = rate × time equation as:

This 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, ν = H₀d, to replace the velocity ν in this equation, we get an even more powerful and easy-to-use formula:

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

The most recent observations suggest that H₀ = 73 km/s/Mpc to within a few percent, and this is the value we choose as our standard. 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 seconds. Converting units, we get

This calculation shows our universe is nearly 14 billion years old. 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, which may or may not be true. 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 is remarkably close to our simple estimate.

Go to Video 15-2

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. The most recent observations, combined with calculations based on the theory of stellar evolution, indicate that these stars are about 13.6 billion years old (with an uncertainty of about 10%). Encouragingly enough, this is (slightly) less than the calculated age of the universe: The oldest stars in our universe are younger than the universe itself!

Our Observable Universe and the Dark Night Sky

The Big Bang helps to even further resolve Olbers’s paradox posited at the beginning of this chapter. 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 15-7). This is true even if the universe is infinite, with galaxies scattered throughout its limitless expanse.

Our entire observable universe is located inside an imaginary sphere, as depicted in Figure 15-7. We cannot see anything beyond the edge of this imaginary sphere, 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 our observable universe increases. Galaxies are distributed sparsely enough in our observable universe that there are no stars along most of our lines of sight. This helps explain 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—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 edge of our observable universe 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 straightforward, logical consequence of having an expanding 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 infinite. As a result, throughout the universe space and time were completely jumbled up in a condition of infinite curvature similar to that at the singularity found at the center of a black hole. For this reason, a better name for the Big Bang might be the cosmic singularity. Thanks to the infinite curvature, the usual laws of physics do not tell us exactly what happened at the moment of the Big Bang.