The diffuse cosmic background radiation in the GALEX far ultraviolet (FUV, 1300Å-1700Å) is deduce... more The diffuse cosmic background radiation in the GALEX far ultraviolet (FUV, 1300Å-1700Å) is deduced to originate only partially in the dust-scattered radiation of FUV-emitting stars: the source of a substantial fraction of the FUV background radiation remains a mystery. The radiation is remarkably uniform at both far northern and far southern Galactic latitudes, and it increases toward lower Galactic latitudes at all Galactic longitudes. We examine speculation that it might be due to interaction of the dark matter with the nuclei of the interstellar medium but we are unable to point to a plausible mechanism for an effective interaction. We also explore the possibility that we are seeing radiation from bright FUV-emitting stars scattering from a "second population" of interstellar grains-grains that are small compared with FUV wavelengths. Such grains are known to exist (Draine 2011) and they scatter with very high albedo, with an isotropic scattering pattern. However, comparison with the observed distribution (deduced from their 100 µm emission) of grains at high Galactic latitudes shows no correlation between the grains' location and the observed FUV emission. Our modeling of the FUV scattering by small grains also shows that there must be remarkably few such "smaller" grains at high Galactic latitudes, both North and South; this likely means simply that there is very little interstellar dust of any kind at the Galactic poles, in agreement with Perry & Johnston (1982). We also review our limited knowledge of the cosmic diffuse background at ultraviolet wavelengths shortward of Lyman α-it could be that our "second component" of the diffuse far-ultraviolet background persists shortward of the Lyman limit, and is the cause of the re-ionization of the Universe (Kollmeier et al. 2014).
The standard cosmological model posits a spatially flat universe of infinite extent. However, no ... more The standard cosmological model posits a spatially flat universe of infinite extent. However, no observation, even in principle, could verify that the matter extends to infinity. In this work we model the universe as a finite spherical ball of dust and dark energy, and obtain a lower limit estimate of its mass and present size: the mass is at least 5 × 10 23 M ⊙ and the present radius is at least 50 Gly. If we are not too far from the dust-ball edge we might expect to see a cold spot in the cosmic microwave background, and there might be suppression of the low multipoles in the angular power spectrum. Thus the model may be testable, at least in principle. We also obtain and discuss the geometry exterior to the dust ball; it is Schwarzschild-de Sitter with a naked singularity, and provides an interesting picture of cosmogenesis. Finally we briefly sketch how radiation and inflation eras may be incorporated into the model.
Inflation is the idea that the very early universe may have been dominated by vacuum energy, givi... more Inflation is the idea that the very early universe may have been dominated by vacuum energy, giving rise to a brief period of vastly accelerated expansion. Its roots go back to the late 1960s and the quest for singularity avoidance in the wake of the discovery of the cosmic microwave background. A tentative connection to what would later be called the horizon problem within relativistic cosmology also goes back to this period. But inflation did not gain wide recognition until high-energy particle physicists became involved. Stimulated by the successes of electroweak unification, they began to explore the implications of spontaneous symmetry breaking for cosmology, with the attendant possibility of a false vacuum state. These models implied a universe dominated by massive relic particles from the early universe. This “monopole problem” was the trigger for the explosion of interest in inflation in the 1980s. A possible explanation for flatness was noted at about the same time. Only later was it appreciated that the most compelling argument for something like inflation is its potential to link the observed large-scale structure in the present-day universe to quantum fluctuations in the earliest moments after the big bang.
During the first half of the 1920s the hypothesis of zero-point energy and the associated hypothe... more During the first half of the 1920s the hypothesis of zero-point energy and the associated hypothesis of half-integral quantum numbers remained controversial. It was not until 1924 that they received solid confirmation from molecular spectroscopy. Although they could not be ignored any longer, they could not be understood on the basis of existing semi-classical quantum theory. Only with the emergence of quantum mechanics in 1925–1926 was the zero-point energy of material systems justified by a fundamental physical theory. The effect can be seen as a consequence of the uncertainty principle that Werner Heisenberg formulated in 1927.
The Casimir effect predicted in 1948 was not initially seen as relevant to cosmology. For a long ... more The Casimir effect predicted in 1948 was not initially seen as relevant to cosmology. For a long time the cosmological constant and the quantum mechanics of the vacuum lived separate lives. The situation only changed in the late 1960s. Inspired by a brief revival of interest in cosmological models with a positive cosmological constant, in 1968 Yakov Zel’dovich pointed out the significance of the constant in the context of quantum field theory. He also formulated the first version of what would be known as the cosmological-constant problem. With Zel’dovich’s work two historical strands were finally joined: the quantum vacuum and the energy density related to the cosmological constant.
Despite the success of inflation in addressing many puzzles of the early universe, theoretical co... more Despite the success of inflation in addressing many puzzles of the early universe, theoretical cosmologists were generally reluctant to entertain the idea that vacuum energy might also dominate the universe at late times, until they were obliged to do so by astronomers. The reality of quantum zero-point fields was attested to by the Casimir effect, but this line of reasoning implied an impossibly large value for the cosmological constant. Most who were aware of the issue concluded that the latter was probably zero due to some as-yet unknown cancellation effect within quantum field theory. Some speculated that the cosmological “constant” might be a dynamical variable, perhaps associated with a scalar field like the ones proposed in models of spontaneous symmetry breaking. It might then have decayed from large primordial values to the much smaller ones compatible with present-day observational cosmology. These ideas were revived in the 1990s under the name of quintessence. Quintessence cosmology remains a very active field of research, but may raise as many new questions as it answers.
Well into the 1990s, most cosmologists preferred not to speak of the cosmological constant. This ... more Well into the 1990s, most cosmologists preferred not to speak of the cosmological constant. This attitude was justified partly by the deep theoretical uncertainty surrounding the status of vacuum energy, and partly by the degree of fine-tuning that seemed to be implied in models whose density of vacuum energy was comparable to that of matter. Nevertheless the cosmological constant was trotted out whenever some crisis arose within cosmology that could not be explained any other way. Two examples that received attention in the 1960s were the concentration of quasars within a narrow range of high redshifts, and the tension between the age of the universe implied by measurements of the Hubble expansion rate and the age of the oldest stars. In the 1980s, vacuum energy was revived again to bridge the gap between the observed low density of matter and the expectation (based on inflation) that the total density of the universe should be exactly critical. The lack of anisotropy observed in the cosmic microwave background prior to 1992 was also taken as possible evidence for a \(\varLambda \) term. Tentative measurements of a nonzero dark-energy density were first obtained with counts of faint galaxies and analyses of absorption lines in the Lyman-\(\alpha \) forest, but seemed to conflict with upper limits based on the statistics of gravitational lenses.
Submitted for the APR15 Meeting of The American Physical Society The gravitational analog of Fara... more Submitted for the APR15 Meeting of The American Physical Society The gravitational analog of Faraday's induction law DANIEL ZILE 1 , JAMES OVERDUIN 2 , Towson University-Michael Faraday, the discoverer of electromagnetic induction, was convinced that there must also be a gravitational analog of this law, and he carried out drop-tower experiments in 1849 to look for the electric current induced in a coil by changes in gravitational flux through the coil. This work, now little remembered, was in some ways the first investigation of what we would now call a unified-field theory. We revisit Faraday's experiments in the light of current knowledge and ask what might be learned if they were to be performed today. We then review the gravitational analog for Faraday's law that arises within the vector (or gravito-electromagnetic) approximation to Einstein's theory of general relativity in the weak-field, low-velocity limit. This law relates spinning masses and induced "mass currents" rather than spinning charges and electric currents, but is otherwise remarkably similar to its electromagnetic counterpart. The predicted effects are completely unobservable in everyday settings like those envisioned by Faraday, but are thought to be relevant in astrophysical contexts like the accretion disks around collapsed stars, thus bearing out Faraday's remarkable intuition.
Wolfgang Priester was one of Germany's most versatile and quixotic astrophysicists, re-inventing ... more Wolfgang Priester was one of Germany's most versatile and quixotic astrophysicists, re-inventing himself successively as a radio astronomer, space physicist and cosmologist, and making a lasting impact on each field. We focus in this personal account on his contributions to cosmology, where he will be most remembered for his association with quasars, his promotion of the idea of a nonsingular "big bounce" at the beginning of the current expansionary phase, and his recognition of the importance of dark energy (Einstein's cosmological constant Λ) well before this became the standard paradigm in cosmology.
The diffuse cosmic background radiation in the GALEX far ultraviolet (FUV, 1300Å-1700Å) is deduce... more The diffuse cosmic background radiation in the GALEX far ultraviolet (FUV, 1300Å-1700Å) is deduced to originate only partially in the dust-scattered radiation of FUV-emitting stars: the source of a substantial fraction of the FUV background radiation remains a mystery. The radiation is remarkably uniform at both far northern and far southern Galactic latitudes, and it increases toward lower Galactic latitudes at all Galactic longitudes. We examine speculation that it might be due to interaction of the dark matter with the nuclei of the interstellar medium but we are unable to point to a plausible mechanism for an effective interaction. We also explore the possibility that we are seeing radiation from bright FUV-emitting stars scattering from a "second population" of interstellar grains-grains that are small compared with FUV wavelengths. Such grains are known to exist (Draine 2011) and they scatter with very high albedo, with an isotropic scattering pattern. However, comparison with the observed distribution (deduced from their 100µ and 25µ emission) of grains at high Galactic latitudes shows no correlation between the grains' location and the observed FUV emission. Our modeling of the FUV scattering by small grains also shows that there must be remarkably few such "smaller" grains at high Galactic latitudes, both North and South; this likely means simply that there is very little interstellar dust of any kind at the Galactic poles, in agreement with Perry and Johnston (1982).
The standard cosmological model posits a spatially flat universe of infinite extent. However, no ... more The standard cosmological model posits a spatially flat universe of infinite extent. However, no observation, even in principle, could verify that the matter extends to infinity. In this work we model the universe as a finite spherical ball of dust and dark energy, and obtain a lower limit estimate of its mass and present size: the mass is at least 5 × 10 23 M ⊙ and the present radius is at least 50 Gly. If we are not too far from the dust-ball edge we might expect to see a cold spot in the cosmic microwave background, and there might be suppression of the low multipoles in the angular power spectrum. Thus the model may be testable, at least in principle. We also obtain and discuss the geometry exterior to the dust ball; it is Schwarzschild-de Sitter with a naked singularity, and provides an interesting picture of cosmogenesis. Finally we briefly sketch how radiation and inflation eras may be incorporated into the model.
We discuss a recent provocative suggestion by Amelino-Camelia and others that classical spacetime... more We discuss a recent provocative suggestion by Amelino-Camelia and others that classical spacetime may break down into "quantum foam" on distance scales many orders of magnitude larger than the Planck length, leading to effects which could be detected using large gravitational wave interferometers. This suggestion is based on a quantum uncertainty limit obtained by Wigner using a quantum clock in a gedanken timing experiment. Wigner's limit, however, is based on two unrealistic and unneccessary assumptions: that the clock is free to move, and that it does not interact with the environment. Removing either of these assumptions makes the uncertainty limit invalid, and removes the basis for Amelino-Camelia's suggestion.
Evolution of the scale factor a(t) in Friedmann models (those with zero pressure and a constant c... more Evolution of the scale factor a(t) in Friedmann models (those with zero pressure and a constant cosmological term Λ) is well understood, and elegantly summarized in the review of Felten and Isaacman [Rev. Mod. Phys. 58, 689 (1986)]. Developments in particle physics and inflationary theory, however, increasingly indicate that Λ ought to be treated as a dynamical quantity. We revisit the evolution of the scale factor with a variable Λ-term, and also generalize the treatment to include nonzero pressure. New solutions are obtained and evaluated using a variety of observational criteria. Existing arguments for the inevitability of a big bang (ie., an initial state with a = 0) are substantially weakened, and can be evaded in some cases with Λ0 (the present value of Λ) well below current experimental limits. 98.80.Bp,04.20.Dw
Wolfgang Priester was one of Germany's most versatile and quixotic astrophysicists, re-inventing ... more Wolfgang Priester was one of Germany's most versatile and quixotic astrophysicists, re-inventing himself successively as a radio astronomer, space physicist and cosmologist, and making a lasting impact on each field. We focus in this personal account on his contributions to cosmology, where he will be most remembered for his association with quasars, his promotion of the idea of a nonsingular "big bounce" at the beginning of the current expansionary phase, and his recognition of the importance of dark energy (Einstein's cosmological constant Λ) well before this became the standard paradigm in cosmology.
We study here what it means for the Universe to be nearly flat, as opposed to exactly flat. We gi... more We study here what it means for the Universe to be nearly flat, as opposed to exactly flat. We give three definitions of nearly flat, based on density, geometry and dynamics; all three definitions are equivalent and depend on a single constant flatness parameter ε that quantifies the notion of nearly flat. Observations can only place an upper limit on ε, and always allow the possibility that the Universe is infinite with k = −1 or finite with k = 1. We use current observational data to obtain a numerical upper limit on the flatness parameter and discuss its implications, in particular the "naturalness" of the nearly flat Universe.
The diffuse cosmic background radiation in the GALEX far ultraviolet (FUV, 1300Å-1700Å) is deduce... more The diffuse cosmic background radiation in the GALEX far ultraviolet (FUV, 1300Å-1700Å) is deduced to originate only partially in the dust-scattered radiation of FUV-emitting stars: the source of a substantial fraction of the FUV background radiation remains a mystery. The radiation is remarkably uniform at both far northern and far southern Galactic latitudes, and it increases toward lower Galactic latitudes at all Galactic longitudes. We examine speculation that it might be due to interaction of the dark matter with the nuclei of the interstellar medium but we are unable to point to a plausible mechanism for an effective interaction. We also explore the possibility that we are seeing radiation from bright FUV-emitting stars scattering from a "second population" of interstellar grains-grains that are small compared with FUV wavelengths. Such grains are known to exist (Draine 2011) and they scatter with very high albedo, with an isotropic scattering pattern. However, comparison with the observed distribution (deduced from their 100 µm emission) of grains at high Galactic latitudes shows no correlation between the grains' location and the observed FUV emission. Our modeling of the FUV scattering by small grains also shows that there must be remarkably few such "smaller" grains at high Galactic latitudes, both North and South; this likely means simply that there is very little interstellar dust of any kind at the Galactic poles, in agreement with Perry & Johnston (1982). We also review our limited knowledge of the cosmic diffuse background at ultraviolet wavelengths shortward of Lyman α-it could be that our "second component" of the diffuse far-ultraviolet background persists shortward of the Lyman limit, and is the cause of the re-ionization of the Universe (Kollmeier et al. 2014).
The standard cosmological model posits a spatially flat universe of infinite extent. However, no ... more The standard cosmological model posits a spatially flat universe of infinite extent. However, no observation, even in principle, could verify that the matter extends to infinity. In this work we model the universe as a finite spherical ball of dust and dark energy, and obtain a lower limit estimate of its mass and present size: the mass is at least 5 × 10 23 M ⊙ and the present radius is at least 50 Gly. If we are not too far from the dust-ball edge we might expect to see a cold spot in the cosmic microwave background, and there might be suppression of the low multipoles in the angular power spectrum. Thus the model may be testable, at least in principle. We also obtain and discuss the geometry exterior to the dust ball; it is Schwarzschild-de Sitter with a naked singularity, and provides an interesting picture of cosmogenesis. Finally we briefly sketch how radiation and inflation eras may be incorporated into the model.
Inflation is the idea that the very early universe may have been dominated by vacuum energy, givi... more Inflation is the idea that the very early universe may have been dominated by vacuum energy, giving rise to a brief period of vastly accelerated expansion. Its roots go back to the late 1960s and the quest for singularity avoidance in the wake of the discovery of the cosmic microwave background. A tentative connection to what would later be called the horizon problem within relativistic cosmology also goes back to this period. But inflation did not gain wide recognition until high-energy particle physicists became involved. Stimulated by the successes of electroweak unification, they began to explore the implications of spontaneous symmetry breaking for cosmology, with the attendant possibility of a false vacuum state. These models implied a universe dominated by massive relic particles from the early universe. This “monopole problem” was the trigger for the explosion of interest in inflation in the 1980s. A possible explanation for flatness was noted at about the same time. Only later was it appreciated that the most compelling argument for something like inflation is its potential to link the observed large-scale structure in the present-day universe to quantum fluctuations in the earliest moments after the big bang.
During the first half of the 1920s the hypothesis of zero-point energy and the associated hypothe... more During the first half of the 1920s the hypothesis of zero-point energy and the associated hypothesis of half-integral quantum numbers remained controversial. It was not until 1924 that they received solid confirmation from molecular spectroscopy. Although they could not be ignored any longer, they could not be understood on the basis of existing semi-classical quantum theory. Only with the emergence of quantum mechanics in 1925–1926 was the zero-point energy of material systems justified by a fundamental physical theory. The effect can be seen as a consequence of the uncertainty principle that Werner Heisenberg formulated in 1927.
The Casimir effect predicted in 1948 was not initially seen as relevant to cosmology. For a long ... more The Casimir effect predicted in 1948 was not initially seen as relevant to cosmology. For a long time the cosmological constant and the quantum mechanics of the vacuum lived separate lives. The situation only changed in the late 1960s. Inspired by a brief revival of interest in cosmological models with a positive cosmological constant, in 1968 Yakov Zel’dovich pointed out the significance of the constant in the context of quantum field theory. He also formulated the first version of what would be known as the cosmological-constant problem. With Zel’dovich’s work two historical strands were finally joined: the quantum vacuum and the energy density related to the cosmological constant.
Despite the success of inflation in addressing many puzzles of the early universe, theoretical co... more Despite the success of inflation in addressing many puzzles of the early universe, theoretical cosmologists were generally reluctant to entertain the idea that vacuum energy might also dominate the universe at late times, until they were obliged to do so by astronomers. The reality of quantum zero-point fields was attested to by the Casimir effect, but this line of reasoning implied an impossibly large value for the cosmological constant. Most who were aware of the issue concluded that the latter was probably zero due to some as-yet unknown cancellation effect within quantum field theory. Some speculated that the cosmological “constant” might be a dynamical variable, perhaps associated with a scalar field like the ones proposed in models of spontaneous symmetry breaking. It might then have decayed from large primordial values to the much smaller ones compatible with present-day observational cosmology. These ideas were revived in the 1990s under the name of quintessence. Quintessence cosmology remains a very active field of research, but may raise as many new questions as it answers.
Well into the 1990s, most cosmologists preferred not to speak of the cosmological constant. This ... more Well into the 1990s, most cosmologists preferred not to speak of the cosmological constant. This attitude was justified partly by the deep theoretical uncertainty surrounding the status of vacuum energy, and partly by the degree of fine-tuning that seemed to be implied in models whose density of vacuum energy was comparable to that of matter. Nevertheless the cosmological constant was trotted out whenever some crisis arose within cosmology that could not be explained any other way. Two examples that received attention in the 1960s were the concentration of quasars within a narrow range of high redshifts, and the tension between the age of the universe implied by measurements of the Hubble expansion rate and the age of the oldest stars. In the 1980s, vacuum energy was revived again to bridge the gap between the observed low density of matter and the expectation (based on inflation) that the total density of the universe should be exactly critical. The lack of anisotropy observed in the cosmic microwave background prior to 1992 was also taken as possible evidence for a \(\varLambda \) term. Tentative measurements of a nonzero dark-energy density were first obtained with counts of faint galaxies and analyses of absorption lines in the Lyman-\(\alpha \) forest, but seemed to conflict with upper limits based on the statistics of gravitational lenses.
Submitted for the APR15 Meeting of The American Physical Society The gravitational analog of Fara... more Submitted for the APR15 Meeting of The American Physical Society The gravitational analog of Faraday's induction law DANIEL ZILE 1 , JAMES OVERDUIN 2 , Towson University-Michael Faraday, the discoverer of electromagnetic induction, was convinced that there must also be a gravitational analog of this law, and he carried out drop-tower experiments in 1849 to look for the electric current induced in a coil by changes in gravitational flux through the coil. This work, now little remembered, was in some ways the first investigation of what we would now call a unified-field theory. We revisit Faraday's experiments in the light of current knowledge and ask what might be learned if they were to be performed today. We then review the gravitational analog for Faraday's law that arises within the vector (or gravito-electromagnetic) approximation to Einstein's theory of general relativity in the weak-field, low-velocity limit. This law relates spinning masses and induced "mass currents" rather than spinning charges and electric currents, but is otherwise remarkably similar to its electromagnetic counterpart. The predicted effects are completely unobservable in everyday settings like those envisioned by Faraday, but are thought to be relevant in astrophysical contexts like the accretion disks around collapsed stars, thus bearing out Faraday's remarkable intuition.
Wolfgang Priester was one of Germany's most versatile and quixotic astrophysicists, re-inventing ... more Wolfgang Priester was one of Germany's most versatile and quixotic astrophysicists, re-inventing himself successively as a radio astronomer, space physicist and cosmologist, and making a lasting impact on each field. We focus in this personal account on his contributions to cosmology, where he will be most remembered for his association with quasars, his promotion of the idea of a nonsingular "big bounce" at the beginning of the current expansionary phase, and his recognition of the importance of dark energy (Einstein's cosmological constant Λ) well before this became the standard paradigm in cosmology.
The diffuse cosmic background radiation in the GALEX far ultraviolet (FUV, 1300Å-1700Å) is deduce... more The diffuse cosmic background radiation in the GALEX far ultraviolet (FUV, 1300Å-1700Å) is deduced to originate only partially in the dust-scattered radiation of FUV-emitting stars: the source of a substantial fraction of the FUV background radiation remains a mystery. The radiation is remarkably uniform at both far northern and far southern Galactic latitudes, and it increases toward lower Galactic latitudes at all Galactic longitudes. We examine speculation that it might be due to interaction of the dark matter with the nuclei of the interstellar medium but we are unable to point to a plausible mechanism for an effective interaction. We also explore the possibility that we are seeing radiation from bright FUV-emitting stars scattering from a "second population" of interstellar grains-grains that are small compared with FUV wavelengths. Such grains are known to exist (Draine 2011) and they scatter with very high albedo, with an isotropic scattering pattern. However, comparison with the observed distribution (deduced from their 100µ and 25µ emission) of grains at high Galactic latitudes shows no correlation between the grains' location and the observed FUV emission. Our modeling of the FUV scattering by small grains also shows that there must be remarkably few such "smaller" grains at high Galactic latitudes, both North and South; this likely means simply that there is very little interstellar dust of any kind at the Galactic poles, in agreement with Perry and Johnston (1982).
The standard cosmological model posits a spatially flat universe of infinite extent. However, no ... more The standard cosmological model posits a spatially flat universe of infinite extent. However, no observation, even in principle, could verify that the matter extends to infinity. In this work we model the universe as a finite spherical ball of dust and dark energy, and obtain a lower limit estimate of its mass and present size: the mass is at least 5 × 10 23 M ⊙ and the present radius is at least 50 Gly. If we are not too far from the dust-ball edge we might expect to see a cold spot in the cosmic microwave background, and there might be suppression of the low multipoles in the angular power spectrum. Thus the model may be testable, at least in principle. We also obtain and discuss the geometry exterior to the dust ball; it is Schwarzschild-de Sitter with a naked singularity, and provides an interesting picture of cosmogenesis. Finally we briefly sketch how radiation and inflation eras may be incorporated into the model.
We discuss a recent provocative suggestion by Amelino-Camelia and others that classical spacetime... more We discuss a recent provocative suggestion by Amelino-Camelia and others that classical spacetime may break down into "quantum foam" on distance scales many orders of magnitude larger than the Planck length, leading to effects which could be detected using large gravitational wave interferometers. This suggestion is based on a quantum uncertainty limit obtained by Wigner using a quantum clock in a gedanken timing experiment. Wigner's limit, however, is based on two unrealistic and unneccessary assumptions: that the clock is free to move, and that it does not interact with the environment. Removing either of these assumptions makes the uncertainty limit invalid, and removes the basis for Amelino-Camelia's suggestion.
Evolution of the scale factor a(t) in Friedmann models (those with zero pressure and a constant c... more Evolution of the scale factor a(t) in Friedmann models (those with zero pressure and a constant cosmological term Λ) is well understood, and elegantly summarized in the review of Felten and Isaacman [Rev. Mod. Phys. 58, 689 (1986)]. Developments in particle physics and inflationary theory, however, increasingly indicate that Λ ought to be treated as a dynamical quantity. We revisit the evolution of the scale factor with a variable Λ-term, and also generalize the treatment to include nonzero pressure. New solutions are obtained and evaluated using a variety of observational criteria. Existing arguments for the inevitability of a big bang (ie., an initial state with a = 0) are substantially weakened, and can be evaded in some cases with Λ0 (the present value of Λ) well below current experimental limits. 98.80.Bp,04.20.Dw
Wolfgang Priester was one of Germany's most versatile and quixotic astrophysicists, re-inventing ... more Wolfgang Priester was one of Germany's most versatile and quixotic astrophysicists, re-inventing himself successively as a radio astronomer, space physicist and cosmologist, and making a lasting impact on each field. We focus in this personal account on his contributions to cosmology, where he will be most remembered for his association with quasars, his promotion of the idea of a nonsingular "big bounce" at the beginning of the current expansionary phase, and his recognition of the importance of dark energy (Einstein's cosmological constant Λ) well before this became the standard paradigm in cosmology.
We study here what it means for the Universe to be nearly flat, as opposed to exactly flat. We gi... more We study here what it means for the Universe to be nearly flat, as opposed to exactly flat. We give three definitions of nearly flat, based on density, geometry and dynamics; all three definitions are equivalent and depend on a single constant flatness parameter ε that quantifies the notion of nearly flat. Observations can only place an upper limit on ε, and always allow the possibility that the Universe is infinite with k = −1 or finite with k = 1. We use current observational data to obtain a numerical upper limit on the flatness parameter and discuss its implications, in particular the "naturalness" of the nearly flat Universe.
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Papers by James Overduin