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 review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Dynamics of dark energy

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.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

We find new exact analytical solutions in three-dimensional gravity applying the Minimal Geometric Deformation approach in a cloud of strings.

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Minimal geometric deformation in a cloud of strings

We study for the first time the stability against scalar perturbations, and we compute the spectrum of quasinormal modes of three-dimensional charged black holes in Einstein-power-Maxwell nonlinear electrodynamics assuming running couplings. Adopting the sixth order Wentzel-Kramers-Brillouin (WKB) approximation we investigate how the running of the couplings change the spectrum of the classical theory. Our results show that all modes corresponding to nonvanishing angular momentum are unstable both in the classical theory and with the running of the couplings, while the fundamental mode can be stable or unstable depending on the running parameter and the electric charge.

Quasinormal modes of scale dependent black holes in ( 1+2 )-dimensional Einstein-power-Maxwell theory

The role of brane-bulk energy exchange and of an induced gravity term on a single braneworld of negative tension and vanishing effective cosmological constant is studied. It is shown that for the physically interesting cases of dust and radiation a unique global attractor which can realize our present universe (accelerating and 0 < Ωm0 < 1) exists for a wide range of the parameters of the model. For Ωm0 = 0.3, independently of the other parameters, the model predicts that the equation of state for the dark energy today is wDE,0 = −1.4, while Ωm0 = 0.03 leads to wDE,0 = −1.03. In addition, during its evolution, wDE crosses the wDE = −1 line to smaller values.

Brane-bulk energy exchange: a model with the present universe as a global attractor

The author A. R. acknowledges DI-VRIEA for financial support through Proyecto Postdoctorado VRIEA-PUCV. The author G. P. thanks the Fundacao para a Ciencia e Tecnologia (FCT), Portugal, for the financial support to the Center for Astrophysics and Gravitation-CENTRA, Instituto Superior T´ecnico, Universidade de Lisboa, through the Project No. UIDB/00099/2020. The author P. B. is founded by the Beatriz Galindo Contract No. BEAGAL 18/00207.

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Black hole shadow of a rotating scale-dependent black hole

In the present work, we compute the spectrum of quasinormal frequencies of four-dimensional (4D) charged black holes (BHs) in Einstein-power-Maxwell (EpM) theory. In particular, we study scalar perturbations adopting the sixth-order WKB approximation. We analyze in detail, the behavior of the spectrum depending on the charge of the BH, the quantum number of angular momentum and the overtone number. In addition, a comparison is made between the results obtained here and the results valid for charged BHs in other theories as well as for the Reissner–Nordstrom BH. Finally, we have provided an analytical expression for the quasinormal spectrum in the eikonal limit.

Grigoris Panotopoulos

Papers

Minimal geometric deformation in a cloud of strings

Quasinormal modes of scale dependent black holes in ( 1+2 )-dimensional Einstein-power-Maxwell theory

Brane-bulk energy exchange: a model with the present universe as a global attractor

Black hole shadow of a rotating scale-dependent black hole

Quasinormal modes of black holes in Einstein-power-Maxwell theory