Shear Orientation of Lyotropic Hexagonal Phases

Schmidt, Gudrun; Müller, Stefan; Lindner, Peter; Schmidt, Claudia; Richtering, Walter

doi:10.1021/jp9725745

Cited by 265 publications

(395 citation statements)

References 41 publications

(86 reference statements)

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“…However, the perfect fluid becomes negligible as the expansion proceeds and the universe subsequently enters a phase of power law, inflationary expansion driven by the exponential potential of a scalar field. For n = 3, the fluid is pressureless and current observations indicate that the universe is undergoing such a transition at the present epoch [4,5,6].…”

Section: Exact Cosmologies Sourced By Scalar Fields and Perfect Fluidsmentioning

confidence: 99%

“…It then follows that Eq. (3) can be expressed as [20] dρ φ dφ = −3Hφ (4) and the Friedmann equation (2) then takes the form…”

Section: The Ermakov-pinney Equation In Cosmologymentioning

confidence: 99%

“…The simplest mechanism for inflation utilises the potential energy associated with the self-interaction of a scalar inflaton field to drive the accelerated expansion. High redshift observations of type Ia supernovae suggest that the universe is experiencing another phase of accelerated expansion at the present epoch [4]. This, combined with the CMB data, presents a picture of the universe dominated by a dark energy component [5,6].…”

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confidence: 99%

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Ermakov-Pinney equation in scalar field cosmologies

2002

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It is shown that the dynamics of cosmologies sourced by a mixture of perfect fluids and self-interacting scalar fields are described by the non-linear, Ermakov-Pinney equation. The general solution of this equation can be expressed in terms of particular solutions to a related, linear differential equation. This characteristic is employed to derive exact cosmologies in the inflationary and quintessential scenarios. The relevance of the Ermakov-Pinney equation to the braneworld scenario is discussed. reviews, see, e.g., [3]). The simplest mechanism for inflation utilises the potential energy associated with the self-interaction of a scalar inflaton field to drive the accelerated expansion. High redshift observations of type Ia supernovae suggest that the universe is experiencing another phase of accelerated expansion at the present epoch [4]. This, combined with the CMB data, presents a picture of the universe dominated by a dark energy component [5,6]. One possible source of this dark energy is a scalar quintessence field that interacts with baryonic and non-baryonic matter in such a way that its potential energy is currently dominating the cosmic dynamics [7]. The observations favour a model of structure formation where 70% of the energy density of the universe is presently in the form of quintessence [6]. The remaining fraction of the energy density is comprised of visible and cold dark matter which collectively act as a pressureless perfect fluid.The ekpyrotic scenario has recently been proposed as an alternative to the standard inflationary cosmology [8]. In this scenario the big bang is interpreted as the collision of two domain walls or branes travelling through a fifth dimension. Before the collision, the effective dynamics on the four dimensional branes is described by Einstein's gravity minimally coupled to a self-interacting scalar field. The field parametrizes the separation between the branes and at early times slowly rolls down a negative potential. This results in an accelerated collapse of the universe and since the field is minimally coupled, its energy density is related to the Hubble parameter by the standard Friedmann equation. Thus, self-interacting scalar fields play a central role in modern cosmology and in view of the above developments, it is important to investigate cosmologies that contain both a scalar field and a perfect fluid.In this paper, we develop an analytical approach to models of this type by expressing the cosmological field equations in terms of an Ermakov system [9,10,11]. In general, an Ermakov system is a pair of coupled, second-order, non-linear ordinary differential equations (ODEs) [11] and such systems often arise in studies of nonlinear optics [12], nonlinear elasticity [13], molecular structures [14] and quantum cosmology [15]. (For further references, see, e.g., Refs. [16]). In the one-dimensional case, the two equations decouple and the system reduces to a single equation known as the Ermakov-Pinney equation [9,17]. This is given by 1

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Section: Exact Cosmologies Sourced By Scalar Fields and Perfect Fluidsmentioning

confidence: 99%

“…It then follows that Eq. (3) can be expressed as [20] dρ φ dφ = −3Hφ (4) and the Friedmann equation (2) then takes the form…”

Section: The Ermakov-pinney Equation In Cosmologymentioning

confidence: 99%

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confidence: 99%

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Ermakov-Pinney equation in scalar field cosmologies

2002

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“…It must be mentioned at this stage that current astrophysical evidence (either by direct measurements of the acceleration of the Universe using supernovae type -Ia data content. Best-fit models to the current data are consistent with a Cosmological Constant Λ-Universe [4,6].It is physically interesting, therefore, to ask what happens with CPT invariance of a quantum field theory when placed in such Universes (global gravitational backgrounds). From the previous arguments [3] one expects Cosmological Breaking of the CPT theorem.…”

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confidence: 91%

On CPT Symmetry: Cosmological, Quantum-Gravitational and Other Possible Violations and Their Phenomenology

Mavromatos

2004

Springer Proceedings in Physics

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Abstract. I discuss various ways in which CPT symmetry may be violated, and their phenomenology in current or immediate future experimental facilities, both terrestrial and astrophysical. Specifically, I discuss first violations of CPT symmetry due to the impossibility of defining a scattering matrix as a consequence of the existence of microscopic or macroscopic space-time boundaries, such as Planck-scale Black-Hole (event) horizons, or cosmological horizons due to the presence of a (positive) cosmological constant in the Universe. Second, I discuss CPT violation due to breaking of Lorentz symmetry, which may characterize certain approaches to quantum gravity, and third, I describe models of CPT non invariance due to violations of locality of interactions. In each of the above categories I discuss experimental sensitivities. I argue that the majority of Lorentz-violating cases of CPT breaking, with minimal (linear) suppression by the Planck-mass scale, are already excluded by current experimental tests. There are however some (stringy) models which can evade these constraints. CPT Breaking and the Scattering MatrixThe symmetry under the successive operations (in any order) of charge conjugation, C, parity (reflexion), P, and time reversal, T, known as CPT, is a fundamental symmetry of any local quantum field theory in flat space time, under the following assumptions [1]:• (i) Unitarity and the proper definition of a scattering matrix, • (ii) Lorentz Invariance and • (iii) Locality of InteractionsIn the presence of gravity, i.e. non-Minkowski,non-flat space time backgrounds, CPT symmetry may be violated, at least in in its strong form. This is indeed the case of singular space-time gravitational backgrounds, such as black holes, or in general space times with boundaries. The reason is that in such cases the presence of these boundaries jeopardizes requirements (i) and (ii) of the CPT theorem. In a quantum context, a Black hole evaporates due to Hawking radiation, and as such it may 'capture' for ever information on matter states passing nearby, as depicted schematically in figure 1. In such a case, one may not be able to define properly asymptotic state vectors |ψ > in a quantum context, given that Planck size black hole horizons appear as fluctuations of the geometry, and hence an asymptotic observer will necessarily trace out the information captured by the horizons. This means that the out states will be necessarily described by density matrices, ρ = Tr unobs |ψ >< ψ|. One has therefore an evolution from pure states to mixed, and unitarity is lost. The problem in defining asymptotic state vectors also implies the impossibility of defining a proper scattering S-matrix, since the latter connects by definition "in" and "out" state vectors: |OU T >= S|IN >. Instead, one can only define a Hawking $-matrix [2], which connects IN and OUT mixed states described by density matrices:where $ = SS † , with S = e iHt the S-matrix, and H the Hamiltonian of the matter subsystem. The $-matrix has no inverse, as a consequence...

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“…Morphological features in the form of striations forming a crosshatch [126,127] are attributed to the columnar rectangular phase, A 8 . A typical fan-shaped texture resulting from the thermomechanical undulation of the columns [128,129] was observed from the columnar hexagonal phase, E 10 .…”

Section: Figure 33mentioning

confidence: 99%