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Foundations of modern cosmology
Recent discoveries in astronomy, especially those made with data collected by satellites such as the Hubble Space Telescope and the Wilkinson Microwave Anisotropy Probe, have revolutionized the science of cosmology. These new observations offer the possibility that some long-standing mysteries in cosmology might be answered, including such fundamental questions as the ultimate fate of the universe. Foundations of modern cosmology provides an accessible, thorough and descriptive introduction to the physical basis for modern cosmological theory, from the big bang to a distant future dominated by dark energy. This second edition includes the latest observational results and provides the detailed background material necessary to understand their implications, with a focus on the specific model supported by these observations, the concordance model. Consistent with the book’s title, emphasis is given to the scientific framework for cosmology, particularly the basics concepts of physics that underlie modern theories of relativity and cosmology; the importance of data and observations is stressed throughout. The book sketches the historical background of cosmology, and provides a review of the relevant basic physics and astronomy. After this introduction, both special and general relativity are treated, before proceeding to an in-depth discussion of the big bang theory and physics of the early universe. The book includes current research areas, including dark matter and structure formation, dark energy, the inflationary universe, and quantum cosmology.
eBook
Einstein gravity in a nutshell
\"This unique textbook provides an accessible introduction to Einstein's general theory of relativity, a subject of breathtaking beauty and supreme importance in physics. With his trademark blend of wit and incisiveness, A. Zee guides readers from the fundamentals of Newtonian mechanics to the most exciting frontiers of research today, including de Sitter and anti-de Sitter spacetimes, Kaluza-Klein theory, and brane worlds. Unlike other books on Einstein gravity, this book emphasizes the action principle and group theory as guides in constructing physical theories. Zee treats various topics in a spiral style that is easy on beginners, and includes anecdotes from the history of physics that will appeal to students and experts alike. He takes a friendly approach to the required mathematics, yet does not shy away from more advanced mathematical topics such as differential forms. The extensive discussion of black holes includes rotating and extremal black holes and Hawking radiation. The ideal textbook for undergraduate and graduate students, Einstein Gravity in a Nutshell also provides an essential resource for professional physicists and is accessible to anyone familiar with classical mechanics and electromagnetism. It features numerous exercises as well as detailed appendices covering a multitude of topics not readily found elsewhere. Provides an accessible introduction to Einstein's general theory of relativity Guides readers from Newtonian mechanics to the frontiers of modern research Emphasizes symmetry and the Einstein-Hilbert action Covers topics not found in standard textbooks on Einstein gravity Includes interesting historical asides Features numerous exercises and detailed appendices Ideal for students, physicists, and scientifically minded lay readers Solutions manual (available only to teachers) \"-- Provided by publisher.
Book
Light deflection and Gauss–Bonnet theorem: definition of total deflection angle and its applications
In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild–de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle α of the light ray by constructing a quadrilateral Σ4 on the optical reference geometry Mopt determined by the optical metric g¯ij . On the basis of the definition of the total deflection angle α and the Gauss–Bonnet theorem, we derive two formulas to calculate the total deflection angle α ; (1) the angular formula that uses four angles determined on the optical reference geometry Mopt or the curved (r,ϕ) subspace Msub being a slice of constant time t and (2) the integral formula on the optical reference geometry Mopt which is the areal integral of the Gaussian curvature K in the area of a quadrilateral Σ4 and the line integral of the geodesic curvature κg along the curve CΓ . As the curve CΓ , we introduce the unperturbed reference line that is the null geodesic Γ on the background spacetime such as the Minkowski or the de Sitter spacetime, and is obtained by projecting Γ vertically onto the curved (r,ϕ) subspace Msub . We demonstrate that the two formulas give the same total deflection angle α for the Schwarzschild and the Schwarzschild–de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein–Shapiro’s formula when the source S and the receiver R of the light ray are located at infinity. In addition, in the Schwarzschild–de Sitter case, there appear order O(Λm) terms in addition to the Schwarzschild-like part, while order O(Λ) terms disappear.
Journal Article
Testing the Universality of Self-organized Criticality in Galactic, Extragalactic, and Black Hole Systems
In this study, we test whether the power law slopes (α F ) for fluxes (F), and (α E ) for energies (E) are universal in their size distributions, N(F)∝F−αF and N(E)∝E−αE , in astrophysical observations of galactic, extragalactic, and black hole systems. This is a test of fundamental importance for self-organized criticality (SOC) systems. The test decides whether (i) power laws are a natural consequence of the scale-freeness and inherent universality of SOC systems, or (ii) if they depend on more complex physical scaling laws. The former criterion allows quantitative predictions of the power-law-like size distributions, while the latter criterion requires individual physical modeling for each SOC variable and data set. Our statistical test, carried out with 61 published data sets, is consistent with the former option, which implies that observed power laws can simply be derived from the scale-freeness and do not require specific physical models to understand their statistical distributions. The observations show a mean and standard deviation of α F = 1.78 ± 0.29 for SOC fluxes and α E = 1.66 ± 0.22 for SOC fluences, and thus are consistent with the prediction of the fractal-diffusive SOC model, with α F = 1.80 and α E = 1.67.
Journal Article
Frank Shu (1943–2023)
Astrophysicist who researched galactic structure and star formation.
Astrophysicist who researched galactic structure and star formation.
Credit: AIP Emilio Segrè Visual Archives, Physics Today Collection
Frank Shu.
Journal Article
A Comprehensive Analysis of Textbook-version Afterglow Light Curves of Gamma-Ray Bursts and Implication for Universal Radiation Physics of Baryonic Jets
The standard external shock model in the thin-shell scenario predicts an onset bump in the early optical afterglow light curves of gamma-ray bursts (GRBs). We collect such a textbook-version light-curve sample of 30 GRBs and derive the jet properties from our joint fit to their X-ray and optical afterglow light curves. It is found that the distributions of the isotropic initial Lorentz factors (Γ0), the deceleration radii (R dec), and the magnetic field strength (B 0) are log-normal, but the distributions of the isotropic kinetic energy (E k,iso), medium density (n 0), and magnetization parameter (σ B ≡ ϵ B /ϵ e ) are tentatively bimodal. A tight R dec–B 0–σ B relation is found. It infers a universal ϵ e E k,iso among bursts, plausibly supporting the previous argument of a universal GRB radiation energy among GRBs. A jet break is required for modeling the light curves of 26 GRBs. The distributions of the jet opening angles and the jet-corrected kinetic energies log-normally center at logθj,c/rad=−1.51 (standard deviation σ = 0.27) and log(Ek,j,c/erg)=51.78 (σ = 0.54), respectively. Those GRBs (19 GRBs), whose prompt gamma-ray emission is well estimated with broad energy-band observations, satisfy the previously discovered L γ,p,iso–E p,z–Γ0 relation, and their gamma-ray radiation efficiencies log-normally distribute in the range from 0.04% to 10% with a central value of 0.42%. Such a low efficiency favors the baryonic fireball model, and the distribution of their baryon mass loading in the GRB ejecta log-normally centers at log(Mfb,c/M☉)=−5 (σ = 0.75).
Journal Article
A stress test of global PDF fits: closure testing the MSHT PDFs and a first direct comparison to the neural net approach
We present a first global closure test of the fixed parameterisation (MSHT) approach to PDF fitting. We find that the default MSHT20 parameterisation can reproduce the features of the input set in such a closure test to well within the textbook uncertainties. This provides strong evidence that parameterisation inflexibility in the MSHT20 fit is not a significant issue in the data region. We also present the first completely like-for-like comparison between two global PDF fits, namely MSHT and NNPDF, where the only difference is guaranteed to be due to the fitting methodology. To achieve this, we present a fit to the NNPDF4.0 data and theory inputs, but with the MSHT fixed parameterisation. We find that this gives a moderately, but noticeably, better fit quality than the central NNPDF4.0 fits, both with perturbative and fitted charm, and that this difference persists at the level of the PDFs and benchmark cross sections. The NNPDF4.0 uncertainties are found to be broadly in line with the MSHT results if a textbook
T
2
=
1
tolerance is applied, but to be significantly smaller if a tolerance typical of the MSHT20 fit is applied. This points to an inherent inconsistency between these approaches. We discuss the need for an enlarged tolerance criterion in global PDF fits in detail, and demonstrate the impact of data/theory inconsistencies in the closure test setting; namely, these do not lead to any increase in the
T
2
=
1
PDF uncertainty. We also investigate the impact of restricting the PDF parameterisation to have fewer free parameters than the default MSHT20 case, and find this can be significant at the level of both closure tests and the full fit.
Journal Article
Methods for relativistic self-gravitating fluids: from binary neutron stars to black hole-disks and magnetized rotating neutron stars
The cataclysmic observations of event GW170817, first as gravitational waves along the inspiral motion of two neutron stars, then as a short γ -ray burst, and later as a kilonova, launched the era of multimessenger astronomy, and played a pivotal role in furthering our understanding on a number of longstanding questions. Numerical modeling of such multimessenger sources is an important tool to understand the physics of compact objects and, more generally, the physics of matter under extreme conditions. In this review we present a unified view of various techniques used to obtain equilibrium and quasiequilibrium solutions for three astrophysically relevant relativistic, self-gravitating fluid systems: Binary neutron stars, black hole-disks, and magnetized rotating neutron stars. These solutions are necessary not only for modeling such compact objects, but equally important, for providing self-consistent initial data in numerical relativity simulations. Instead of presenting the full details of the formulations and numerical algorithms, we focus on painting the broadbrush picture of the methods developed to address these problems, and facilitate future work in the area.
Journal Article
Horizon, homogeneity and flatness problems: do their resolutions really depend upon inflation?
The horizon problem, encountered in cosmology, is derived as such for world models based on Robertson–Walker metric where homogeneity and isotropy of the universe is assumed to begin with and is guaranteed for all epochs. Actually, the only thing that happens in this scenario is that in such a universe, described by a single, time-dependent scale factor, which may otherwise be independent of spatial coordinates, the light signals in a finite time might not cover all the available space. Further, the flatness problem, as it is posed, is not even falsifiable. The usual argument offered in the literature is that the present density of the universe is very close to the critical density value and that the universe must be flat since otherwise in past at
∼
10
-
35
second (near the epoch of inflation) there will be extremely low departures of density from the critical density value (of the order
∼
10
-
53
), requiring a sort of fine tuning. We show that even if the present value of the density parameter were very different, still at
10
-
35
second it would differ from unity by the same fraction. Thus a use of fine tuning argument to promote
k
=
0
model amounts to a priori rejection of all models with
k
≠
0
. Without casting any aspersions on the inflationary theory, which after all is the most promising paradigm to explain the pattern of anisotropies observed in the cosmic microwave background, we argue that one cannot use homogeneity and flatness in support of inflation.
Journal Article