How Big Is the Universe?

The nine-year-old’s eyes are wide with wonder as he asks the question. “I don’t know son, real big, the biggest thing there is,” answers the exasperated father, without moving his eyes from the morning paper.

But dad, if the Universe contains everything that exists, how can it be just big? What’s on the outside?” insists the boy. The dad takes a deep breath. “Son, the Universe is infinite, okay? There’s nothing on the outside.” “Oh, and how do we know that?” the son continues. “Has someone gone looking for the end of the Universe?”

Children ask these kinds of questions all the time, even if most of the adults around then rarely pay any attention. Sadly, most adults forget that, when they were kids, they also asked questions like this, difficult questions that live on the boundary between science and metaphysics. After years of schooling, many children lose their curiosity, as they must focus increasingly on their homework, sports, and other activities. In what appears to be the paradox of schooling, regular exposure to knowledge seems to sedate the will to learn more.

Milan Kundera, the Czech-born French writer, paid homage to the questions children ask in his famous novel The Unbearable Lightness of Being:

Indeed, the only truly serious questions are the ones that even a child can formulate. Only the most naïve of questions are truly serious. They are questions with no answers. A question with no answer is a barrier that cannot be breached. In other words, it is questions with no answers that set the limits of human possibilities, describe the boundaries of human existence.

Scientists, in a sense, are people who keep that curiosity burning, trying to find answers to some of the questions they asked as children. This may seem like a romanticized view of science, but it really isn’t. Science feeds on curiosity, on asking the right questions, the ones that open doors to new knowledge. And the harder the question, the more promising it is, even if it may not have a final answer.

Trying to figure out the size of the Universe is one of these questions, and it has a fascinating history. We may have (and actually do) have very compelling reasons to state that the Universe is indeed infinite, as the disgruntled dad told his son. But somewhat perversely, we can’t ever be completely sure. We have answers but not THE final answer.

The shape and size of the Universe is an old mystery. Since we are not going to summarize the whole thing here,* it’s good to remember that only during the late 17th century, the cosmos went from being closed and finite to being infinite. For a while. * (Learn more about this fascinating history in my book The Dancing Universe: From Creation Myths to the Big Bang.)

In his Letters to the Oxford theologian Richard Bentley, Newton hypothesized that his newly discovered law of gravity—every material body attracts other material bodies with a force proportional to their masses and inversely proportional to the square of their distance (F = G Mm/R2, where G is the proportionality constant)—implied that a finite Universe would be unstable, collapsing into a huge blob at the center. One mass attracts another, that attracts another, and then . . .

To counter this idea, Newton supposed that the Universe was infinite in all directions, with stars sufficiently distanced so as to balance one another, like a perfectly even tug-of-war. God would occasionally interfere, making sure small orbital instabilities didn’t grow to cause huge cataclysms, like having all the planets fall into the Sun. To Newton—and this is something we don’t learn in most schools—God was like a cosmic mechanic, an indispensable presence guaranteeing the longevity of the Universe.

The next two huge steps in our conception of the Universe came with the American astronomer Edwin Hubble in the 1920s. First, in 1924, Hubble showed convincingly that the Milky Way, our galaxy, was but one in a sea of countless other “island-universes.” (We now estimate that there are up to 200 billion galaxies in the visible Universe.) Up to then, it wasn’t clear whether the faint nebula seen with telescopes were other far away galaxies or just remains of dead stars, local to our galaxy. (It’s both, but one needs to measure distances accurately to make sure, a hard thing to do.) Then, in 1929, Hubble showed that the galaxies were not standing still but moving away from one another, receding with speeds that increased with their distance.

A good way to picture the cosmic expansion is to visualize a classroom filled with desks. Now, imagine that the floor starts to stretch equally north-south and east-west. The desks will all move away from one another, with speeds that grow with their mutual distance. Picture each desk as a galaxy and voilà, you have an analogous picture to an expanding two-dimensional cosmos. To go to three dimensions—like the space in which we live—add more desks on top of one another, and make space stretch also up and down, and you have a three-dimensional expanding space, like our own.

This cosmic expansion had been predicted in 1922 by Russian meteorologist-turned-cosmologist Alexander Friedmann, who showed it to be a natural solution of Einstein’s 1915 equations of general relativity, the new theory of gravity where matter bends space. That Hubble showed it to be true was a remarkable feat of observational astronomy.

If the Universe is expanding, it must have been much smaller in the past. The point where all the galaxies are atop one another is called the “singularity,” the beginning of everything. Of course, things are not so simple since matter dissociates into its simpler components when heated and squeezed. The young Universe was filled with what we call a “primordial soup” of elementary particles, not galaxies.

Modern cosmology studies both the properties of the current Universe and of its distant past. And guess what is one of the central questions we’d like to answer? Precisely the one the kid asked the dad at the beginning of this essay: Is the Universe infinite or not?

According to theory, there are two answers to this: either yes, the Universe extends forever; or no, the Universe is finite, like the surface of a ball. The hard part is that while we can easily visualize the surface of a ball or a tabletop—both examples of two-dimensional surfaces—it’s much harder to do that with a three-dimensional geometrical object, the space in which we live. (Remember that we can move east-west, north-south, and up and down, hence the three dimensions of space.)

Here, math comes to the rescue, and we can just write the equations that do that for us. And what we find is that there are only three possible geometries for the universe, that depend on how much matter it contains. A finite universe is closed on itself, and will stop expanding in the future, contracting back to its high-density initial state: it has more matter than a certain critical value. We say it is an “overdense universe.” An open universe is underdense and will expand forever. Finally, the third option is the critical universe, that has the exact amount to be flat, teetering between the closed and open ones. It will also expand forever, albeit slower than an open universe. (The critical density value is about six atoms of hydrogen per cubic meter on average, so pretty small.) A flat three-dimensional universe is one where we can move equally in three directions, without feeling any curvature effects.

But theory is not enough. We need data to get an answer, and getting this data is very complicated. What helps is the relation between the quantity of matter and its effects on the geometry of space around it. Too much matter means more curvature and distortions that can be seen as we look to distant objects in space. To make a long story short, both current astronomical data and studies of the remnant radiation from the epoch when the first hydrogen atoms formed (the so-called cosmic background radiation, or CMB, produced just 380,000 years after the “bang”) indicate that the portion of the Universe that we can see is flat, with an accuracy of about half of a percent. The answer to the kid is, finally, yes, the Universe seems to be infinite in its three directions. But we can’t be sure.

Why can’t we be sure? Because every physical measurement has a precision limit. If the geometry of the Universe is that of an enormous three-dimensional sphere, we could be fooled into thinking that the part that we can measure is flat. To see this, picture a big party balloon. The more you fill it with air, the more a small patch on its surface looks flat. Back to our Universe, it could be that the patch that we measure, the visible Universe, is almost flat, but still part of a larger closed cosmos.

It’s hard to imagine that we will have a final answer to this question, unless someone came up with a final theory of everything that explained also the geometry of the Universe. Such theories, however, have their own set of problems. Better stick to the way science as we know it works: our current measurements indicate with large certainty that the Universe is flat. But not ever with total certainty. That’s not science.

Now you can go back and answer that kid in your life who asks these kinds of questions. And maybe you will have a budding scientist on your hands.

Having trouble visualizing a flat universe? Here are three explainer videos that might help you grasp the concept.

Templeton Prize winner Marcelo Gleiser is a professor of natural philosophy, physics and astronomy at Dartmouth College.