The universe consists of all matter, energy, and space-time that we can ever detect or that will ever be able to affect us. (We use this definition because there may be matter and energy in other dimensions or matter and energy that are moving away from us so quickly that their influence will never reach us.) So far in this text, we have explored matter on size scales from atoms to superclusters of galaxies. We also learned in Section 13-17 that the superclusters are all moving away from one another, implying that the universe is expanding. In this chapter we take the observational evidence from the rest of the book and use it to explore the Big Bang theory of cosmology. Cosmology is the study of the large-scale structure and evolution of the universe.

Modern cosmology almost began in 1915 when Einstein published his theory of general relativity. To his surprise and dismay, the relativity equations predicted that the universe is not static: They indicated that it should be either expanding (which it is) or contracting. But Einstein was not ready for what the equations were telling him.

At the time that Einstein published the theory of general relativity, the existence of galaxies and clusters and superclusters of galaxies had not yet been established and the 1925 discovery of the Hubble flow (Section 13-17) was a decade away. The prediction of a changing universe flew in the face of the then widely accepted belief in an infinite, static universe, a concept promoted by Isaac Newton more than two centuries earlier. Newton believed that each star is fixed in place and held under the influence of a uniform gravitational pull from every part of the cosmos. If the stars were not uniformly distributed, he argued, one region would have more mass than another. The denser region’s gravity would then attract other stars, causing them to further clump together. Because he did not observe this clumping, Newton concluded that the stars in the universe must be distributed uniformly over an infinite space.

The apparently static universe and the prevailing philosophy that the universe had existed forever made Einstein doubt the implications of his own theory, so he missed the opportunity to propose that we live in a changing universe. Instead, he adjusted his elegant equations to yield a static, finite cosmos. He did this by adding a repulsive (outward-pushing) term, called the cosmological constant, to his equations so that gravity’s normal attractive force would be counterbalanced and the universe would be static. After observations revealed that the universe is expanding, Einstein said that adding the cosmological constant was the biggest blunder of his career.

Although the value of the cosmological constant that Einstein inserted was wrong, the concept of such a constant may be correct. Observations since 1997 indicate that the universe is not just expanding but actually accelerating outward. This acceleration means that there must be an outward pressure that more than counteracts the effects of normal gravitation, which is trying to slow the universe’s expansion. One of the two current theories that can explain this acceleration is the presence of a cosmological constant that creates the outward pressure. We discuss these two theories further in Section 14-15.

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Edwin Hubble is credited with discovering that we live in an expanding universe (see Section 13-17). The redshifts of clusters and superclusters of galaxies that Hubble found moving away from us appear to be produced by the Doppler effect, but they actually are not. Recall that the normal Doppler shift is caused by an object moving toward or away from us through fixed spacetime (see Sections 3-2 and 3-18). However, using Einstein’s theory of general relativity, we find that spacetime, the fabric of the universe, is not fixed but is actually expanding. This expansion is what is carrying the superclusters away from each other and, in many cases, carrying clusters in a given supercluster away from one another. (The gravitational force that holds objects like planets and stars and entire galaxies together is so strong that these bodies and systems are not being pulled apart. The expansion of space just acts to increase the separation between superclusters of galaxies and between clusters of galaxies in the same supercluster that are not gravitationally bound to each other.)

The redshift that Hubble observed, caused by the expansion of the universe, is properly called the cosmological redshift. In other words, the photons that we observe from galaxies in other superclusters are all red-shifted because space is expanding. To understand why, consider a wave drawn on a rubber band (Figure 14-1). The wave has an unstretched wavelength (see Section 3-1) of λ₀. As the rubber band stretches, the wavelength increases (λ > λ₀). Now imagine a photon coming toward us from a distant galaxy. As the photon travels through space, space is expanding, and, like stretching the rubber band, this expansion stretches the photon’s wavelength. When the photon reaches our eyes, we see a drawn-out wavelength—the photon is redshifted. The longer the photon’s journey, the more its wavelength is stretched by the expansion of the universe. Therefore, astronomers observe larger redshifts in photons from relatively distant galaxies than in photons from relatively nearby galaxies.

As we saw in Section 13-16, Hubble discovered the linear relationship between the distances to galaxies in other superclusters and the redshifts of those galaxies’ spectral lines. For example, a galaxy twice as far from Earth as another galaxy has twice the cosmological red-shift of the closer one. The normal Doppler shift has the same relationship. As a result of the two effects being described by the same equations, the normal Doppler shift and the cosmological redshift predict the same relationship between redshift and motion—except for the most distant galaxies and quasars, where effects of relativity must be taken into account. Working with relatively nearby galaxies, Hubble was fully justified in using the “normal” Doppler equation to calculate the recession of galaxies.

Hubble’s law gives us a way to estimate the age of the universe. Imagine watching a movie of two superclusters receding from each other. If we then run the film backward, time runs in reverse, and we observe all the superclusters coming together. The time it would take for them all to collide is the time since they were last combined as a single clump of matter. Assuming that the universe began expanding when it came into existence and that it has always expanded at a constant rate, we can use a simple equation to estimate the age of the universe:

Recall that Hubble found the relationship

Recessional velocity = H₀ × separation distance

which we can rewrite as

Comparing the first and last equations here, we see that Hubble’s constant is the reciprocal of the time since the universe began. Using a Hubble constant of 69 km/s/Mpc, we find:

1/H₀ ≈ 1/69 km/s/Mpc ≈ 13.8 billion years

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As of 2014, the most accurate measurement is 13.798 ±0.037 billion years. In what follows, we will simply use an age of 13.8 billion years.