Free Origins: Fourteen Billion Years of Cosmic Evolution by Donald Goldsmith, Neil deGrasse Tyson Page A

roughly even distribution, space cannot be “static.” The cosmos cannot just “sit there,” as our intuition insists that it should, and as all astronomical observations until that time implied. Instead, the totality of space must always be either expanding or contracting: space must behave something like the surface of an inflating or deflating balloon, but never like the surface of a balloon with constant size.
    This worried Einstein. For once, this bold theorist, who mistrusted authority and had never hesitated to oppose conventional physics ideas, felt that he had gone too far. No astronomical observations suggested an expanding universe, because astronomers had only documented the motions of nearby stars and had not yet determined the faraway distances to what we now call galaxies. Rather than announcing to the world that the universe must either be expanding or contracting, Einstein returned to his equation, seeking a way to immobilize the cosmos.
    He soon found one. Einstein’s basic equation allowed for a term with a constant but unknown value that represents the amount of energy contained in every cubic centimeter of empty space. Because nothing suggested that this constant term should have one value or another, in his first pass Einstein had set it equal to zero. Now Einstein published a scientific article to demonstrate that if this constant term, which cosmologists later named the “cosmological constant,” had a particular value, then space could be static. Then theory would no longer conflict with observations of the universe, and Einstein could regard his equation as valid.
    Einstein’s solution encountered grave difficulties. In 1922, a Russian mathematician named Alexander Friedmann proved that Einstein’s static universe must be unstable, like a pencil balanced on its point. The slightest ripple or disturbance would cause space either to expand or to contract. Einstein first proclaimed Friedmann mistaken, but then, in a generous act typical of the man, published an article retracting that claim and pronouncing Friedmann correct after all. As the 1920s ended, Einstein was delighted to learn of Hubble’s discovery that the universe is expanding. According to George Gamow’s recollections, Einstein pronounced the cosmological constant his “greatest blunder.” Except for a few cosmologists who continued to invoke a non-zero cosmological constant (with a value different from the one that Einstein had used) to explain certain puzzling observations, most of which later proved to be incorrect, scientists the world over sighed with relief that space had proven to have no need of this constant.
    Or so they thought. The great cosmological story at the end of the twentieth century, the surprise that stood the world of cosmology on one ear and sang a different tune into the other, resides in the stunning discovery, first announced in 1998, that the universe does have a non-zero cosmological constant. Empty space does indeed contain energy, named “dark energy,” and possesses highly unusual characteristics that determine the future of the entire universe.
    To understand, and possibly even to believe, these dramatic assertions, we must follow the crucial themes in cosmologists’ thinking during the seventy years following Hubble’s discovery of the expanding universe. Einstein’s fundamental equation allows for the possibility that space can have curvature, described mathematically as positive, zero, or negative. Zero curvature describes “flat space,” the kind that our minds insist on as the only possibility, which extends to infinity in all directions, like the surface of an infinite chalkboard. In contrast, a positively curved space corresponds in analogy to the surface of a sphere, a two-dimensional space whose curvature we can see by using the third dimension. Notice that the center of the sphere, the point that appears to remain stationary as its two-dimensional surface expands or contracts,