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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

Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.

/pdf/electromagnetically-induced-transparency-optics-in-coherent-2dhges92td.pdf

Electromagnetically induced transparency : Optics in coherent media

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Table Of Integrals Series And Products

Modified Gravity and Cosmology

The Firoozbakht, Nicholson, and Farhadian conjectures can be phrased in terms of increasingly powerful conjectured bounds on the prime gaps g n : = p n + 1 - p n . While a general proof of any of these conjectures is far out of reach, I shall show that all three of these conjectures are unconditionally and explicitly verified for all primes below the as yet unknown location of the 81st maximal prime gap, certainly for all primes p < 2 64 . For the Firoozbakht conjecture itself this is a rather minor improvement on currently known results, but for the somewhat stronger Nicholson and Farhadian conjectures this may be considerably more interesting. Sequences: A005250 A002386 A005669 A000101 A107578 A246777 A246776.

https://www.mdpi.com/2227-7390/7/8/691/pdf

Verifying the Firoozbakht, Nicholson, and Farhadian Conjectures up to the 81st Maximal Prime Gap

Gravitational lensing in a weak but otherwise arbitrary gravitational field can be described in terms of a 3 x 3 tensor, the "effective refractive index". If the sources generating the gravitational field all have small internal fluxes, stresses, and pressures, then this tensor is automatically isotropic and the "effective refractive index" is simply a scalar that can be determined in terms of a classic result involving the Newtonian gravitational potential. In contrast if anisotropic stresses are ever important then the gravitational field acts similarly to an anisotropic crystal. We derive simple formulae for the refractive index tensor, and indicate some situations in which this will be important.

Effective refractive index tensor for weak field gravity

: Redshift drift is the phenomenon whereby the observed redshift between an emitter and observer comoving with the Hubble ﬂow in an expanding FLRW universe will slowly evolve — on a timescale comparable to the Hubble time. In a previous article [JCAP 04 (2020) 043; arXiv:2001.11964] three of the current authors had performed a cosmographic analysis of the redshift drift in a FLRW universe, temporarily putting aside the issue of dynamics (the Friedmann equations). In the current article we now add dynamics, still within the framework of an exact FLRW universe. We shall develop a suitable generic matter model, and study both the low-redshift asymptotic behaviour and the utility of using alternative variables to describe the redshift.

Dynamical analysis of the redshift drift in FLRW universes

We present a compact Baker-Campbell-Hausdorff-Dynkin formula for the composition of Lorentz transformations $e^{\sigma_i}$ in the spin representation (a.k.a. Lorentz rotors) in terms of their generators $\sigma_i$: $$ 
\ln(e^{\sigma_1}e^{\sigma_2}) = 
\tanh^{-1}\left(\frac{ 
\tanh \sigma_1 + \tanh \sigma_2 + \frac12[\tanh \sigma_1, \tanh \sigma_2] 
}{ 
1 + \frac12\{\tanh \sigma_1, \tanh \sigma_2\} 
}\right) $$ This formula is general to geometric algebras (a.k.a. real Clifford algebras) of dimension $\leq 4$, naturally generalising Rodrigues' formula for rotations in $\mathbb{R}^3$. In particular, it applies to Lorentz rotors within the framework of Hestenes' spacetime algebra, and provides an efficient method for composing Lorentz generators. Computer implementations are possible with a complex $2\times2$ matrix representation realised by the Pauli spin matrices. The formula is applied to the composition of relativistic $3$-velocities yielding simple expressions for the resulting boost and the concomitant Wigner angle.

Explicit Baker-Campbell-Hausdorff-Dynkin formula for Spacetime via Geometric Algebra

http://cds.cern.ch/record/284142/files/9506083.pdf

Matt Visser

Papers

Verifying the Firoozbakht, Nicholson, and Farhadian Conjectures up to the 81st Maximal Prime Gap

Effective refractive index tensor for weak field gravity

Dynamical analysis of the redshift drift in FLRW universes

Explicit Baker-Campbell-Hausdorff-Dynkin formula for Spacetime via Geometric Algebra

Thin-shell wormholes