REVIEWS OF MODERN PHYSICS, VOLUME 84, JULY–SEPTEMBER 2012 Nobel Lecture: Accelerating expansion of the Universe through observations of distant supernovae* Brian P. Schmidt (published 13 August 2012) DOI: 10.1103/RevModPhys.84.1151 This is not just a narrative of my own scientific journey, but constant, and suggested that Hubble’s data and Slipher’s also my view of the journey made by cosmology over the data supported this conclusion (Lemaˆitre, 1927). His work, course of the 20th century that has lead to the discovery of the published in a Belgium journal, was not initially widely read, accelerating Universe. It is complete from the perspective of but it did not escape the attention of Einstein who saw the the activities and history that affected me, but I have not tried work at a conference in 1927, and commented to Lemaˆitre, to make it an unbiased account of activities that occurred ‘‘Your calculations are correct, but your grasp of physics is around the world. abominable.’’ (Gaither and Cavazos-Gaither, 2008). 20th Century Cosmological Models: In 1907 Einstein had In 1928, Robertson, at Caltech (just down the road from what he called the ‘‘wonderful thought’’ that inertial accel- Edwin Hubble’s office at the Carnegie Observatories), pre- eration and gravitational acceleration were equivalent. It took dicted the Hubble law, and claimed to see it when he com- Einstein more than 8 years to bring this thought to its fruition, pared Slipher’s redshift versus Hubble’s galaxy brightness his theory of general Relativity (Norton and Norton, 1984)in measurements, but this observation was not substantiated November, 1915. Within a year, de Sitter had already inves- (Robertson, 1928). Finally, in 1929, Hubble presented a paper tigated the cosmological implications of this new theory (de in support of an expanding universe, with a clear plot of Sitter, 1917) which predicted spectral redshift of objects in galaxy distance versus redshift—it is for this paper that the Universe dependent on distance. In 1917, Einstein pub- Hubble is given credit for discovering the expanding lished his Universe model (Einstein, 1917)—one that added Universe (Hubble, 1929). Assuming that the brightest stars an extra term—the cosmological constant—with which he he could see in a galaxy were all the same intrinsic brightness, attempted to balance gravitational attraction with the negative Hubble found that the faster an object was moving away from pressure associated with an energy density inherent to the Slipher’s measurements, the fainter its brightest stars were. vacuum. This addition, completely consistent with his theory, That is, the more distant the galaxy, the faster its speed of allowed him to create a static model consistent with the recession. It is from this relationship that Hubble inferred that Universe as it was understood at that time. Finally, in 1922, the Universe was expanding. Friedmann published his family of models for an isotropic With the expansion of the Universe as an anchor, theory and homogenous universe (Friedmann, 1922). converged on a standard model of the Universe, which was Observational cosmology really got started in 1917 when still in place in 1998, at the time of our discovery of the Vesto Slipher (to whose family I am indebted for helping fund accelerating Universe. This standard model was based on the my undergraduate education through a scholarship set up at theory of general relativity, and two assumptions: one, that the University of Arizona in his honor) observed about 25 the Universe is homogenous and isotropic on large scales; and nearby galaxies, spreading their light out using a prism, and two, it is composed of normal matter—matter whose density recording the results onto film (Slipher, 1917). The results falls directly in proportion to the volume of space which it occupies. Within this framework, it was possible to devise confounded him and the other astronomers of the day. Almost observational tests of the overall theory, as well as provide every object he observed had its light stretched to redder values for the fundamental constants within this model—the colors, indicating that essentially everything in the Universe current expansion rate (Hubble’s constant), and the average was moving away from us. Slipher’s findings created a conun- density of matter in the Universe. For this model, it was also drum for astronomers of the day: Why would our position as possible to directly relate the density of the Universe to the observer seemingly be repulsive to the rest of the Universe? rate of cosmic deceleration: the more material, the faster the The contact between theory and observations at this time deceleration; and the geometry of space: above a critical appears to have been mysteriously poor, even for the days density, the Universe has a finite (closed) geometry, below before the internet. In 1927, Georges Lemaˆitre, a Belgian this critical density, a hyperbolic (open) geometry. monk who, as part of his MIT Ph.D. thesis, independently In more mathematical terms: If the universe is isotropic derived the Freidmann cosmological solutions to general and homogenous on large scales, the geometric relationship relativity, predicted the expansion of the Universe as de- of space and time are described by the Robertson-Walker scribed now by Hubble’s law. He also noted that the age of metric, the Universe was approximately the inverse of the Hubble dr2 ds2 ¼ dt2 À a2ðtÞ þ r2d2 : (1) *The 2011 Nobel Prize for Physics was shared by Saul Perlmutter, 1 À kr2 Adam G. Riess, and Brian P. Schmidt. These papers are the text of the address given in conjunction with the award. In this expression, which is independent of the theory of 0034-6861= 2012=84(3)=1151(13) 1151 Ó 2012 Nobel Foundation, Published by The American Physical Society 1152 Brian P. Schmidt: Nobel Lecture: Accelerating expansion of the ... gravitation, the line element distance (s) between two objects parameter, q0, is defined as depends on coordinates r and , and time separation, t. The a€0 M Universe is assumed to have a simple topology such that if it q À a ¼ : 0 2 0 2 (7) has negative, zero, or positive curvature, k takes the value a_ 0 f1; 0; 1g, respectively. These universes are said, in order, to The equivalence of M and q0 is provided through solu- be open, flat, or closed. The Robertson-Walker metric also tions of the Friedmann equation assuming a universe consist- requires the dynamic evolution of the Universe to be given ing solely of normal matter. The Taylor expansion is accurate through the evolution of the scale factor aðtÞ, which gives the to a few percent over the region of interest of the day radius of curvature of the Universe—or more simply put, (z<0:5), but was perfected by Mattig (1958), who found a tracks the relative size of a piece of space over time. This closed solution, c pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dynamic equation of the Universe is derived from general D q z q 1 1 2q z 1 : L ¼ 2 ½ 0 þð 0 À Þð þ 0 À Þ (8) relativity, and was first given by Friedmann in the equation H0q0 which we now name after him: These equations provide one of the classic tests of cos- a_ 2 8G k H2 ¼ À : (2) mology—the luminosity distance versus redshift relationship. a 3 a2 For an object of known luminosity, a single measurement at a moderate redshift [not so low that gravitationally induced The expansion rate of the Universe (H), called the Hubble motions, typically z 0:002, are important—and not so high parameter (or the Hubble constant, H0, at the present epoch), that the second order term in Eq. (6) is important], of its evolves according to the content of the Universe. Through the redshift and brightness, will yield an estimate of H0.By 20th century, the content of the Universe was assumed to be measuring a standard candle’s (an object of fixed luminosity) dominated by a single component of matter with density, i, brightness as a function of redshift, one can fit the curvature compared to a critical density, crit. The ratio of the average in the line, and solve for q0. density of matter compared to the critical density is called the In principal, from Eq. (6), measuring H0 does not appear to density parameter, M and is defined as be difficult. An accurately measured distance and redshift to a 0:02 <z<0:1 i i : single object at a redshift between is all that it i ¼ 2 (3) crit ð3H0=8GÞ takes, with their ratio providing the answer. But making accurate absolute measurements of distance in astronomy is The critical density is the value where the gravitational effect challenging—the only geometric distances that were typi- of material in the Universe causes space to become geomet- cally available were parallax measurements (measurement rically flat [k ¼ 0 in Eq. (1)]. Below this density, the Universe of the wobbles in the positions of nearby stars due to the has an open, hyperbolic geometry (k ¼1); above, a closed, Earth’s motion around the Sun) of a handful of nearby stars. spherical geometry (k ¼þ1). From these few objects, through a bootstrapping process of As experimentalists, what we need are observables with comparing the brightnesses of similar objects in progressive which to test and constrain the theory. Several such tests were steps, known as the extragalactic distance ladder, researchers developed and described in detail in 1961 by Allan Sandage came to conclusions which varied by more than a factor of 2, (Sandage, 1961) and are often described as the classical tests a discordance which persisted until the beginning of the new of cosmology.