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

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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

The Jordan frame action for general disformal theories is presented and studied for the first time, motivated by several unresolved mysteries that arise when working in the Einstein frame. We present the Friedmann equations and, specialising to exponential functions, study the late-time cosmology using dynamical systems methods and by finding approximate solutions. Our analysis reveals that either the disformal effects are irrelevant or the universe evolves towards a phantom phase where the equation of state of dark energy is $-3$. There is a marginal case where the asymptotic state of the universe depends on the model parameters and de-Sitter solutions can be obtained. Our findings indicate that the metric singularity found using the Einstein frame construction corresponds phantom behaviour in the Jordan frame and we argue that this is the case for general disformal theories.

/pdf/disformal-gravity-theories-a-jordan-frame-analysis-1of4pvjjwq.pdf

Disformal gravity theories: a Jordan frame analysis

Modern instruments and observational programs in astrophysics and cosmology have opened new perspectives for probing general relativity on previously unexplored scales. This review provides both a methodological and an observational survey of the constraints on modified-gravity models using astrophysical objects in the cosmological, weak-field regime. It is embedded in the framework of the novel probes project, a forum connecting observers and theorists involved in the study of astrophysical tests of dark sector interactions.

/pdf/novel-probes-project-tests-of-gravity-on-astrophysical-2dqlkvpbp6.pdf

Novel Probes Project: Tests of gravity on astrophysical scales

The LIGO-Virgo Collaboration has recently announced the detection of a heavy binary black hole merger, with component masses that are difficult to account for in standard stellar structure theory. In this Letter, we propose several explanations based on models of new physics, including new light particle losses, modified gravity, large extra dimensions, and a small magnetic moment of the neutrino. Each of these affect the physics of the pair instability differently, leading to novel mechanisms for forming black holes inside the mass gap.

Beyond the Standard Model Explanations of GW190521.

Future space-based tests of relativistic gravitation---laser ranging to Phobos, accelerometers in orbit, and optical networks surrounding Earth---will constrain the theory of gravity with unprecedented precision by testing the inverse-square law, the strong and weak equivalence principles, and the deflection and time delay of light by massive bodies. In this paper, we estimate the bounds that could be obtained on alternative gravity theories that use screening mechanisms to suppress deviations from general relativity in the Solar System: chameleon, symmetron, and Galileon models. We find that space-based tests of the parametrized post-Newtonian parameter $\ensuremath{\gamma}$ will constrain chameleon and symmetron theories to new levels, and that tests of the inverse-square law using laser ranging to Phobos will provide the most stringent constraints on Galileon theories to date. We end by discussing the potential for constraining these theories using upcoming tests of the weak equivalence principle, and conclude that further theoretical modeling is required in order to fully utilize the data.

Tests of Gravity with Future Space-Based Experiments

Theories of modified gravity where light scalars with non-trivial self-interactions and non-minimal couplings to matter-chameleon and symmetron theories-dynamically suppress deviations from general relativity in the solar system. On other scales, the environmental nature of the screening means that such scalars may be relevant. The highly-nonlinear nature of screening mechanisms means that they evade classical fifth-force searches, and there has been an intense effort towards designing new and novel tests to probe them, both in the laboratory and using astrophysical objects, and by reinterpreting existing datasets. The results of these searches are often presented using different parametrizations, which can make it difficult to compare constraints coming from different probes. The purpose of this review is to summarize the present state-of-the-art searches for screened scalars coupled to matter, and to translate the current bounds into a single parametrization to survey the state of the models. Presently, commonly studied chameleon models are well-constrained but less commonly studied models have large regions of parameter space that are still viable. Symmetron models are constrained well by astrophysical and laboratory tests, but there is a desert separating the two scales where the model is unconstrained. The coupling of chameleons to photons is tightly constrained but the symmetron coupling has yet to be explored. We also summarize the current bounds on $f(R)$ models that exhibit the chameleon mechanism (Hu \& Sawicki models). The simplest of these are well constrained by astrophysical probes, but there are currently few reported bounds for theories with higher powers of $R$. The review ends by discussing the future prospects for constraining screened modified gravity models further using upcoming and planned experiments.

Jeremy Sakstein

Papers

Disformal gravity theories: a Jordan frame analysis

Novel Probes Project: Tests of gravity on astrophysical scales

Beyond the Standard Model Explanations of GW190521.

Tests of Gravity with Future Space-Based Experiments

Tests of Chameleon Gravity