One Hundred Years of General Relativity

The following sections are included:

• Foreword
• Contents
• Color plates

This year marks the 100th anniversary of Einstein’s 1915 landmark paper “Die Feldgleichungen der Gravitation” in which the field equations of general relativity were correctly formulated for the first time, thus rendering general relativity a complete theory. Over the subsequent hundred years, physicists and astronomers have struggled with uncovering the consequences and applications of these equations. This paper, which was written as an introduction to six chapters dealing with the connection between general relativity and cosmology that will appear in the two-volume book One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, endeavors to provide a historical overview of the connection between general relativity and cosmology, two areas whose development has been closely intertwined.

The history of cosmic structure goes back to the time of Einstein’s youth, although few scientists actually thought of the problem of galaxy and cluster formation. The data and ideas were collected slowly as astronomers slowly realized the nature of the problem of large-scale structure. This paper will review several of the key episodes in the history of the field. Starting with the discovery of dark matter in the 30s, the CMBR discovery in the 1960s to the idea of an early episode of inflation in the 1980s, the field has had an acceleration of discovery. In the 80s it was realized that the initial conditions of the universe were specified by the cold dark matter (CDM). Now initial conditions for the formation of structure could be specified for any type of dark matter. With the advent of computing resources, highly nonlinear phases of galaxy formation could be simulated and scientists could ask whether cold dark matter was the correct theory, even on the scale of dwarf spheroidal galaxies, or do the properties of the dwarfs require a different type of dark matter? In an idiosyncratic list, we review several of the key events of the history of cosmic structure, including the first measurements of ξ(r), then the remarkable success of Λ CDM explanations of the large-scale universe. We next turn to velocity fields, the large-scale flow problem, a field which was so promising 20 years ago, and to the baryon acoustic oscillations, a field of remarkable promise today. We review the problem of dwarf galaxies and Lyman-α absorption systems, asking whether the evidence is pointing toward a major switch in our understanding of the nature of dark matter. Finally, we discuss flux anomalies in multiply-lensed systems, which set constraints on the number of dwarf galaxies associated with the lensing galaxy, a topic that is now very interesting since simulations have indicated there should be hundreds of dwarfs orbiting the Milky Way, rather than the 10 that are known. It is quite remarkable that many of the today’s results are dependent on techniques first used by Einstein.

Observations of the cosmic microwave background (CMB), especially of its frequency spectrum and its anisotropies, both in temperature and in polarization, have played a key role in the development of modern cosmology and of our understanding of the very early universe. We review the underlying physics of the CMB and how the primordial temperature and polarization anisotropies were imprinted. Possibilities for distinguishing competing cosmological models are emphasized. The current status of CMB experiments and experimental techniques with an emphasis toward future observations, particularly in polarization, is reviewed. The physics of foreground emissions, especially of polarized dust, is discussed in detail, since this area is likely to become crucial for measurements of the B modes of the CMB polarization at ever greater sensitivity.

Type Ia supernovae (SNe Ia) luminosities can be corrected in order to render them useful as standard candles that are able to probe the expansion history of the universe. This technique was successfully applied to discover the present acceleration of the universe. As the number of SNe Ia observed at high redshift increases and analysis techniques are perfected, people aim to use this technique to probe the equation-of-state of the dark energy (EOSDE). Nevertheless, the nature of SNe Ia progenitors remains controversial and concerns persist about possible evolution effects that may be larger and harder to characterize than the more obvious statistical uncertainties.

Gravitational lensing is a unique and direct probe of mass in the universe. It depends only on the law of gravity and does not depend on the dynamical state nor the composition of matter. Thus it is used to study the distribution of the dark matter in the lensing object. Combined with the traditional observations such as optical and X-ray, it gives us useful information on the structure formation in the universe. The lensing observables depend also on the global geometry as well as on the large scale structure of the universe. Therefore it is possible to derive useful constraints on cosmological parameters once the distribution of lensing mass is accurately known. Since the first discovery of a lensing event by a galaxy in 1979, various kinds of lensing phenomena caused by stars, galaxies, clusters of galaxies and large scale structure have been observed and are used to study the mass distribution at various scales and cosmology. Gravitational lensing is now regarded as an indispensable research tool in observational cosmology. In this article we give a pedagogical introduction to gravitational lensing and its applications to cosmology.

Starting with an account of historical developments in Japan and Russia, we review inflationary cosmology and its basic predictions in a pedagogical manner. We also introduce the generalized G-inflation model, in terms of which all the known single-field inflation models may be described. This formalism allows us to analyze and compare the many inflationary models that have been proposed simultaneously and within a common framework. Finally, current observational constraints on inflation are reviewed, with particular emphasis on the sensitivity of the inferred constraints to the choice of datasets used.

At its very beginning, the universe is believed to have grown exponentially in size via the mechanism of inflation. The almost scale-invariant density perturbation spectrum predicted by inflation is strongly supported by cosmological observations, in particular the cosmic microwave background (MB) radiation. However, the universe’s precise inflationary scenario remains a profound problem for cosmology and for fundamental physics. String theory, the most-studied theory as the final physical theory of nature, should provide an answer to this question. Some of the proposals on how inflation is realized in string theory are reviewed. Since everything is made of strings, some string loops of cosmological sizes are likely to survive in the hot big bang that followed inflation. They appear as cosmic strings, which can have intricate properties. Because of the warped geometry in flux compactification of the extra spatial dimensions in string theory, some of the cosmic strings may have tensions substantially below the Planck or string scale. Such strings cluster in a manner similar to dark matter leading to hugely enhanced densities. As a result, numerous fossil remnants of the low tension cosmic strings may exist within the galaxy. They can be revealed through the optical lensing of background stars in the near future and studied in detail through gravitational wave emission. We anticipate that these cosmic strings will permit us to address central questions about the properties of string theory as well as the birth of our universe.

We present a bird’s-eye survey on the development of fundamental ideas of quantum gravity, placing emphasis on perturbative approaches, string theory, loop quantum gravity (LQG) and black hole thermodynamics. The early ideas at the dawn of quantum gravity as well as the possible observations of quantum gravitational effects in the foreseeable future are also briefly discussed.

I argue that cosmological data from the epoch of primordial inflation is catalyzing the maturation of quantum gravity from speculation into a hard science. I explain why quantum gravitational effects from primordial inflation are observable. I then review what has been done, both theoretically and observationally, and what the future holds. I also discuss what this tells us about quantum gravity.

The discovery in the early 1970s that black holes radiate as black bodies has radically affected our understanding of general relativity, and offered us some early hints about the nature of quantum gravity. In this paper, I will review the discovery of black hole thermodynamics and summarize the many independent ways of obtaining the thermodynamic and (perhaps) statistical mechanical properties of black holes. I will then describe some of the remaining puzzles, including the nature of the quantum microstates, the problem of universality, and the information loss paradox.

This paper presents an “in-a-nutshell” yet self-contained introductory review on loop quantum gravity (LQG) — a background-independent, nonperturbative approach to a consistent quantum theory of gravity. Instead of rigorous and systematic derivations, it aims to provide a general picture of LQG, placing emphasis on the fundamental ideas and their significance. The canonical formulation of LQG, as the central topic of the paper, is presented in a logically orderly fashion with moderate details, while the spin foam theory, black hole thermodynamics, and loop quantum cosmology are covered briefly. Current directions and open issues are also summarized.

The following sections are included:

• Subject Index
• Author Index