The Fabric of the Cosmos: Space, Time, and the Texture of Reality (31 page)

We can now illustrate cosmic history by combining the concept of expanding space with the loaf-of-bread description of spacetime from Chapter 3. Remember, in the loaf-of-bread portrayal, each slice—even though two-dimensional—represents all of three-dimensional space at a single moment of time from the perspective of one particular observer. Different observers slice up the loaf at different angles, depending on details of their relative motion. In the examples encountered previously, we did not take account of expanding space and, instead, imagined that the fabric of the cosmos was fixed and unchanging over time. We can now refine those examples by including cosmological evolution.

To do so, we will take the perspective of observers who are at rest with respect to space—that is, observers whose only motion arises from cosmic expansion, just like the Lincolns glued to the balloon. Again, even though they are moving relative to one another, there is symmetry among all such observers—their watches all agree—and so they slice up the spacetime loaf in exactly the same way. Only relative motion in excess of that coming from spatial expansion, only relative motion
through
space as opposed to motion
from
swelling space, would result in their watches falling out of synch and their slices of the spacetime loaf being at different angles. We also need to specify the shape of space, and for purposes of comparison we will consider some of the possibilities discussed above.

The easiest example to draw is the flat and finite shape, the video game shape. In Figure 8.7a, we show one slice in such a universe, a schematic image you should think of as representing all of space right
now.
For simplicity, imagine that our galaxy, the Milky Way, is in the middle of the figure, but bear in mind that no location is in any way special compared with any other. Even the edges are illusory. The top side is not a place where space ends, since you can pass through and reappear at the bottom; similarly, the left side is not a place where space ends, since you can pass through and reappear on the right side. To accommodate astronomical observations, each side should extend at least 14 billion light-years (about 85 billion trillion miles) from its midpoint, but each could be much longer.

Note that right now we can't literally see the stars and galaxies as drawn on this
now
slice since, as we discussed in Chapter 5, it takes time for the light emitted by any object right now to reach us. Instead, the light we see when we look up on a clear, dark night was emitted long ago—millions and even billions of years ago—and only now has completed the long journey to earth, entered our telescopes, and allowed us to marvel at the wonders of deep space. Since space is expanding, eons ago, when this light was emitted, the universe was a lot smaller. We illustrate this in Figure 8.7b in which we have put our current
now
slice on the right-hand side of the loaf and included a sequence of slices to the left that depict our universe at ever earlier moments of time. As you can see, the overall size of space and the separations between individual galaxies both decrease as we look at the universe at ever earlier moments.

Figure 8.7
(
a
)
A schematic image depicting all of space right now, assuming space is flat and finite in extent, i.e. shaped like a video game screen. Note that the galaxy on the upper right wraps around on the left.
(
b
)
A schematic image depicting all of space as it evolves through time, with a few time slices emphasized for clarity. Note that the overall size of space and the separation between galaxies decrease as we look farther back in time.

In Figure 8.8, you can also see the history of light, emitted by a distant galaxy perhaps a billion years ago, as it has traveled toward us here in the Milky Way. On the initial slice in Figure 8.8a, the light is first emitted, and on subsequent slices you can see the light getting closer and closer even as the universe gets larger and larger, and finally you can see it reaching us on the rightmost time slice. In Figure 8.8b, by connecting the locations on each slice that the light's leading edge passed through during its journey, we show the light's path through spacetime. Since we receive light from many directions, Figure 8.8c shows a sample of trajectories through space and time that various light beams take to reach us now.

Figure 8.8
(
a
)
Light emitted long ago from a distant galaxy gets closer and closer to the Milky Way on subsequent time slices.
(
b
)
When we finally see the distant galaxy, we are looking at it across both space and time, since the light we see was emitted long ago. The path through spacetime followed by the light is highlighted.
(
c
)
The paths through spacetime taken by light emitted from various astronomical bodies that we see today.

The figures dramatically show how light from space can be used as a cosmic time capsule. When we look at the Andromeda galaxy, the light we receive was emitted some 3 million years ago, so we are seeing Andromeda as it was in the distant past. When we look at the Coma cluster, the light we receive was emitted some 300 million years ago and hence we are seeing the Coma cluster as it was in an even earlier epoch. If right now all the stars in all the galaxies in this cluster were to go supernova, we would still see the same undisturbed image of the Coma cluster and would do so for another 300 million years; only then would light from the exploding stars have had enough time to reach us. Similarly, should an astronomer in the Coma cluster who is on our current now-slice turn a superpowerful telescope toward earth, she will see an abundance of ferns, arthropods, and early reptiles; she won't see the Great Wall of China or the Eiffel Tower for almost another 300 million years. Of course, this astronomer, well trained in basic cosmology, realizes that she is seeing light emitted in earth's distant past, and in laying out her own cosmic spacetime loaf will assign earth's early bacteria to their appropriate epoch, their appropriate set of time slices.

All of this assumes that both we and the Coma cluster astronomer are moving only with the cosmic flow from spatial expansion, since this ensures that her slicing of the spacetime loaf coincides with ours—it ensures that her
now
-lists agree with ours. However, should she break ranks and move through space substantially in excess of the cosmic flow, her slices will tilt relative to ours, as in Figure 8.9. In this case, as we found with Chewie in Chapter 5, this astronomer's
now
will coincide with what we consider to be our future or our past (depending on whether the additional motion is toward or away from us). Notice, though, that her slices will no longer be spatially homogeneous. Each angled slice in Figure 8.9 intersects the universe in a range of different epochs and so the slices are far from uniform. This significantly complicates the description of cosmic history, which is why physicists and astronomers generally don't contemplate such perspectives. Instead, they usually consider only the perspective of observers moving solely with the cosmic flow, since this yields slices that are homogeneous—but fundamentally speaking, each viewpoint is as valid as any other.

Figure 8.9 The time slice of an observer moving significantly in excess of the cosmic flow from spatial expansion.

As we look farther to the left on the cosmic spacetime loaf, the universe gets ever smaller and ever denser. And just as a bicycle tire gets hotter and hotter as you squeeze more and more air into it, the universe gets hotter and hotter as matter and radiation are compressed together more and more tightly by the shrinking of space. If we head back to a mere ten millionths of a second after the beginning, the universe gets so dense and so hot that ordinary matter disintegrates into a primordial plasma of nature's elementary constituents. And if we continue our journey, right back to nearly time zero itself—the time of the
big bang—
the entire known universe is compressed to a size that makes the dot at the end of this sentence look gargantuan. The densities at such an early epoch were so great, and the conditions were so extreme, that the most refined physical theories we currently have are unable to give us insight into what happened. For reasons that will become increasingly clear, the highly successful laws of physics developed in the twentieth century break down under such intense conditions, leaving us rudderless in our quest to understand the beginning of time. We will see shortly that recent developments are providing a hopeful beacon, but for now we acknowledge our incomplete understanding of what happened at the beginning by putting a fuzzy patch on the far left of the cosmic spacetime loaf—our verson of the terra incognita on maps of old. With this finishing touch, we present Figure 8.10 as a broad-brush illustration of cosmic history.

Figure 8.10 Cosmic history—the spacetime "loaf"—for a universe that is flat and of finite spatial extent. The fuzziness at the top denotes our lack of understanding near the beginning of the universe.

We've so far assumed that space is shaped like a video game screen, but the story has many of the same features for the other possibilities. For example, if the data ultimately show that the shape of space is spherical, then, as we go ever farther back in time, the size of the sphere gets ever smaller, the universe gets ever hotter and denser, and at time zero we encounter some kind of big bang beginning. Drawing an illustration analogous to Figure 8.10 is challenging since spheres don't neatly stack one next to the other (you can, for example, imagine a "spherical loaf" with each slice being a sphere that surrounds the previous), but aside from the graphic complications, the physics is largely the same.

The cases of infinite flat space and of infinite saddle-shaped space also share many features with the two shapes already discussed, but they do differ in one essential way. Take a look at Figure 8.11, in which the slices represent flat space that goes on forever (of which we can show only a portion, of course). As you look at ever earlier times, space shrinks; galaxies get closer and closer together the farther back you look in Figure 8.11b. However, the overall size of space stays the same. Why? Well, infinity is a funny thing. If space is infinite and you shrink all distances by a factor of two, the size of space becomes half of infinity, and that is still infinite. So although everything gets closer together and the densities get ever higher as you head further back in time, the overall size of the universe stays infinite; things get dense everywhere on an infinite spatial expanse. This yields a rather different image of the big bang.

Normally, we imagine the universe began as a dot, roughly as in Figure 8.10, in which there is no exterior space or time. Then, from some kind of eruption, space and time unfurled from their compressed form and the expanding universe took flight. But if the universe is spatially infinite,
there was already an infinite spatial expanse at the moment of the big
bang.
At this initial moment, the energy density soared and an incomparably large temperature was reached, but these extreme conditions existed everywhere, not just at one single point. In this setting, the big bang did not take place at one point; instead, the big bang eruption took place
everywhere
on the infinite expanse. Comparing this to the conventional single-dot beginning, it is as though there were many big bangs, one at each point on the infinite spatial expanse. After the bang, space swelled, but its overall size didn't increase since something already infinite can't get any bigger. What did increase are the separations between objects like galaxies (once they formed), as you can see by looking from left to right in Figure 8.11b. An observer like you or me, looking out from one galaxy or another, would see surrounding galaxies all rushing away, just as Hubble discovered.

Bear in mind that this example of infinite flat space is far more than academic. We will see that there is mounting evidence that the overall shape of space is not curved, and since there is no evidence as yet that space has a video game shape, the flat, infinitely large spatial shape is the front-running contender for the large-scale structure of spacetime.

Figure 8.11
(
a
)
Schematic depiction of infinite space, populated by galaxies.
(
b
)
Space shrinks at ever earlier times—so galaxies are closer and more densely packed at earlier times—but the overall size of infinite space stays infinite. Our ignorance of what happens at the earliest times is again denoted by a fuzzy patch, but here the patch extends through the infinite spatial expanse.