There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

We present cosmological parameter results from the ﬁnal full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to signiﬁcant gains in the precision of other correlated parameters Improved modelling of the small-scale polarization leads to more robust constraints on manyparameters,withresidualmodellinguncertaintiesestimatedtoaﬀectthemonlyatthe05σlevelWeﬁndgoodconsistencywiththestandard spatially-ﬂat6-parameter ΛCDMcosmologyhavingapower-lawspectrumofadiabaticscalarperturbations(denoted“base ΛCDM”inthispaper), from polarization, temperature, and lensing, separately and in combination A combined analysis gives dark matter density Ωch2 = 0120±0001, baryon density Ωbh2 = 00224±00001, scalar spectral index ns = 0965±0004, and optical depth τ = 0054±0007 (in this abstract we quote 68% conﬁdence regions on measured parameters and 95% on upper limits) The angular acoustic scale is measured to 003% precision, with 100θ∗ = 10411±00003Theseresultsareonlyweaklydependentonthecosmologicalmodelandremainstable,withsomewhatincreasederrors, in many commonly considered extensions Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: HubbleconstantH0 = (674±05)kms−1Mpc−1;matterdensityparameterΩm = 0315±0007;andmatterﬂuctuationamplitudeσ8 = 0811±0006 We ﬁnd no compelling evidence for extensions to the base-ΛCDM model Combining with baryon acoustic oscillation (BAO) measurements (and consideringsingle-parameterextensions)weconstraintheeﬀectiveextrarelativisticdegreesoffreedomtobe Neﬀ = 299±017,inagreementwith the Standard Model prediction Neﬀ = 3046, and ﬁnd that the neutrino mass is tightly constrained toPmν < 012 eV The CMB spectra continue to prefer higher lensing amplitudesthan predicted in base ΛCDM at over 2σ, which pulls some parameters that aﬀect thelensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAOdataThejointconstraintwithBAOmeasurementsonspatialcurvatureisconsistentwithaﬂatuniverse, ΩK = 0001±0002Alsocombining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = −103±003, consistent with a cosmological constant We ﬁnd no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r0002 < 006 Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower ﬂuctuation amplitudes or matter density parameters), and in signiﬁcant, 36σ, tension with local measurements of the Hubble constant (which prefer a higher value) Simple model extensions that can partially resolve these tensions are not favoured by the Planck data

/pdf/planck-2018-results-vi-cosmological-parameters-3d8tp95x87.pdf

Planck 2018 results. VI. Cosmological parameters

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

/pdf/the-observation-of-gravitational-waves-from-a-binary-black-58srpupgg9.pdf

The Observation of Gravitational Waves from a Binary Black Hole Merger

To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

This paper is concerned with theories of gravity that contain a scalar coupled both conformally and disformally to matter through the metric. By systematically deriving the non-relativistic limit, it is shown that no new non-linear screening mechanisms are present beyond the Vainshtein mechanism and chameleon-like screening. If one includes the cosmological expansion of the universe, disformal effects that are usually taken to be absent can be present in the solar system. When the conformal factor is absent, fifth-forces can be screened on all scales when the cosmological field is slowly-rolling. We investigate the cosmology of these models and use local tests of gravity to place new constraints on the disformal coupling and find $\mathcal{M}>\mathcal{O}(\textrm{eV})$, which is not competitive with laboratory tests. Finally, we discuss the future prospects for testing these theories and the implications for other theories of modified gravity. In particular, the Vainshtein radius of solar system objects can be altered from the static prediction when cosmological time-derivatives are non-negligible.

Disformal Theories of Gravity: From the Solar System to Cosmology

The splashback radius is a physical scale in dark matter halos that is set by the gravitational dynamics of recently accreted shells. We use analytical models and N-body simulations to study the dependence of splashback on dark energy and screened modified gravity theories. In modified gravity models, the transition from screened to unscreened regions typically occurs in the cluster outskirts, suggesting potentially observable signatures in the splashback feature. We investigate the location of splashback in both chameleon and Vainshtein screened models and find significant differences compared with ΛCDM predictions. We also find an interesting interplay between dynamical friction and modified gravity, providing a distinctive signature for modified gravity models in the behavior of the splashback feature as a function of galaxy luminosity.

/pdf/splashback-in-galaxy-clusters-as-a-probe-of-cosmic-expansion-4bt7bpqm7z.pdf

Splashback in galaxy clusters as a probe of cosmic expansion and gravity

In the Standard Model, the so-called pair instability from creation of electron-positron pairs reduces the mass of low-metallicity population-III stars as they collapse, unless they are heavy enough to make the process inefficient, leading to an expected mass gap in the black hole spectrum. In this work, the authors argue that future observations of the black hole population will allow one to test this prediction, and use it to put constraints on new particles, such as axions, that would cause an additional instability.

New physics and the black hole mass gap

Screened modified gravity models evade solar system tests of relativistic gravitation but exhibit novel and interesting effects on scales between the solar system and the Hubble flow: astrophysical...

Astrophysical tests of screened modified gravity

Chameleon and similar (symmetron and dilation) theories of gravity can exhibit new and interesting features on cosmological scales whilst screening the modifications on small scales thereby satisfying solar system tests of general relativity. This thesis explores the regime between these two scales: astrophysics. The majority of this thesis is focused on discerning new and novel astrophysical probes of chameleon gravity in the form of stellar structure and oscillation tests. These are used to place new constraints on the theory parameters and the implications of these are discussed, as are the future prospects for improving them using planned future surveys. The final two chapters review supersymmetric completions of these theories.

/pdf/astrophysical-tests-of-modified-gravity-1jqmfcytcb.pdf

Jeremy Sakstein

Papers

Disformal Theories of Gravity: From the Solar System to Cosmology

Splashback in galaxy clusters as a probe of cosmic expansion and gravity

New physics and the black hole mass gap

Astrophysical tests of screened modified gravity

Astrophysical Tests of Modified Gravity