Anisotropic Initial Conditions Research Articles

From the string vacuum to FLRW or de Sitter via α' corrections

We first make more precise a recent “Hamiltonian” reformulation of the Hohm-Zwiebach approach to the tree-level, O(d,d)-invariant string cosmology equations at all orders in the α' expansion, and recall how it allows to give a simple characterization of a large class of cosmological scenarios connecting, through a non-singular bounce, two duality-related perturbative solutions at early and late times. We then discuss the effects of adding to the action a non-perturbative, O(d,d)-breaking, dilaton potential V(ϕ). The resulting cosmological solutions, assumed to approach at early times the perturbative string vacuum (with vanishing curvature and string coupling), can stabilize the dilaton at late times and simultaneously approach either a matter-dominated FLRW cosmology or a de-Sitter-like inflationary phase, depending on initial conditions and on the properties of V(ϕ) at moderate-coupling. We also identify a general mechanism for generating isotropic late-time attractors from a large basin of anisotropic initial conditions.

Flows into de Sitter space from anisotropic initial conditions: An effective field theory approach

For decades, physicists have analyzed various versions of a ``cosmic no-hair'' conjecture, to understand under what conditions a spacetime that is initially spatially anisotropic and/or inhomogeneous will flow into an isotropic and homogeneous state. Wald's theorem, in particular, established that homogeneous but anisotropic spacetimes, if filled with a positive cosmological constant plus additional matter sources that satisfy specific energy conditions, will necessarily flow toward an (isotropic) de Sitter state at late times. In this paper we study the flow of homogeneous but anisotropic spacetimes toward isotropic states under conditions more general than those to which Wald's theorem applies. We construct an effective field theory (EFT) treatment for generic ``single-clock'' systems in anisotropic spacetimes---which are not limited to realizations compatible with scalar-field constructions---and identify fixed points in the resulting phase space. We identify regions of this phase space that flow to isotropic fixed points---including a de Sitter fixed point---even in the absence of a bare cosmological constant, and for matter sources that do not obey the energy conditions required for Wald's theorem. Such flows into de Sitter reveal the emergence of an effective cosmological constant.

Data assimilation for the two-dimensional shallow water equations: Optimal initial conditions for tsunami modelling

Accurate modelling of tsunami waves requires complete boundary and initial data, coupled with the appropriate mathematical model. However, necessary data is often missing or inaccurate, and may not have sufficient resolution to capture the dynamics of such nonlinear waves accurately. We demonstrate that variational data assimilation for the continuous shallow water equations (SWE) is a feasible approach for recovering initial conditions. We showed that the necessary conditions for reconstructing one-dimensional initial conditions in Kevlahan et al. (2019) can be extended to the maximum Euclidean distance between pairwise observations to two-dimensions. We use Sadourny finite-difference finite volume simulations to verify convergence to the true initial conditions can be achieved for observations arranged in multiple configurations, for both isotropic and anisotropic initial conditions, and with realistic bathymetry data in two dimensions. We compare observations arranged in straight lines, in a grid, and along concentric circles, and assess the optimal number and configuration of observation points such that convergence to the true initial conditions is achieved. These idealised results with simplified two-dimensional geometry are a first step towards more physically realistic settings. Recent advances in altimetry observation data now permit much denser measurements of sea surface height than is possible with a fixed buoy network. This provides the opportunity to use the method developed here for more accurate tsunami forecasts in realistic settings.

The final Kasner regime inside black holes with scalar or vector hair

The final (close to the singularity) dynamical behavior of the metric inside black holes with massive charged scalar or vector hair is analyzed for general anisotropic and inhomogeneous initial conditions. These solutions are relevant to a holographic realization of superconductivity. It is shown that the dynamics falls within the scope of the “cosmological billiard” description and that in both cases, the corresponding hyperbolic billiard region has infinite volume so that the system ultimately settles down to a final Kasner regime. For massive vector hair, the conclusion holds because the longitudinal mode plays the same role as a scalar field. There exists, however, a measure-zero subset of solutions characterized by vanishing longitudinal modes that exhibit a chaotic behavior with an infinite number of BKL oscillations as one goes to the singularity.

Dynamical attractors in contracting spacetimes dominated by kinetically coupled scalar fields

We present non-perturbative numerical relativity simulations of slowly contracting spacetimes in which the scalar field driving slow contraction is coupled to a second scalar field through an exponential non-linear σ model-type kinetic interaction. These models are important because they can generate a nearly scale-invariant spectrum of super-Hubble density fluctuations fully consistent with cosmic microwave background observations. We show that the non-linear evolution rapidly approaches a homogeneous, isotropic and flat Friedmann-Robertson-Walker (FRW) geometry for a wide range of inhomogeneous and anisotropic initial conditions. Ultimately, we find, the kinetic coupling causes the evolution to deflect away from flat FRW and towards a novel Kasner-like stationary point, but in general this occurs on time scales that are too long to be observationally relevant.

Neutrino flavor mixing breaks isotropy in the early universe

The neutrino field is commonly assumed to be isotropic and homogeneous in the early universe. However, due to the large neutrino density, a small perturbation of the isotropy of the neutrino field could potentially be amplified by the non-linear flavor mixing caused by neutrino self-interactions. We carry out the first numerical simulations of the neutrino flavor evolution in a multi-angle anisotropic setting. Due to the computational challenges involved, we adopt a simplified framework consisting of a homogeneous universe with two angle bins — left and right moving modes — for neutrinos and antineutrinos, together with an approximate form for the collision term which goes beyond the commonly adopted damping approximation. By assuming a small initial left-right asymmetry of \U0001d4aa(10-15), we convincingly demonstrate that flavor evolution can be affected in both mass orderings, with implications on the effective number of thermally excited neutrino species (N eff). Notably, the correction to N_ eff is comparable to higher order corrections from finite temperature QED effects in normal ordering. In addition, by assuming an initial lepton asymmetry in the neutrino sector of the same order as the baryon one [\U0001d4aa(10-9)], we find that the neutrino-antineutrino asymmetry grows by several orders of magnitude for isotropic as well as anisotropic initial conditions. This work clearly shows that it is imperative to critically revisit standard assumptions concerning neutrino flavor mixing in the early universe, especially in the light of possible implications on the cosmological observables.

Anisotropic cosmological dynamics in Einstein–Gauss–Bonnet gravity: an example of dynamical compactification in $$7+1$$ dimensions

We consider a particular example of dynamical compactification of an anisotropic 7+1 dimensional Universe in Einstein - Gauss - Bonnet gravity. Starting from rather general totally anisotropic initial conditions a Universe in question evolves towards a product of two isotropic subspaces. The first subspace expands isotropically, the second represents an "inner" isotropic subspace with stabilized size. The dynamical evolution does not require fine-tuning of initial conditions, though it is possible for a particular range of coupling constants. The corresponding condition have been found analytically and have been confirmed using numerical integration of equations of motion.

Diffusion and Superdiffusion in Lattice Models for Colliding Particles with Stored Momentum

We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension (with power law correction) and diffusive in three and higher dimensions. In two dimensions we demonstrate superdiffusivity (with logarithmic correction) for certain anisotropic initial conditions.

Effects of spatial curvature and anisotropy on the asymptotic regimes in Einstein\u2013Gauss\u2013Bonnet gravity

In this paper we address two important issues which could affect reaching the exponential and Kasner asymptotes in Einstein–Gauss–Bonnet cosmologies—spatial curvature and anisotropy in both three- and extra-dimensional subspaces. In the first part of the paper we consider the cosmological evolution of spaces that are the product of two isotropic and spatially curved subspaces. It is demonstrated that the dynamics in D=2 (the number of extra dimensions) and D ge 3 is different. It was already known that for the Lambda -term case there is a regime with “stabilization” of extra dimensions, where the expansion rate of the three-dimensional subspace as well as the scale factor (the “size”) associated with extra dimensions reaches a constant value. This regime is achieved if the curvature of the extra dimensions is negative. We demonstrate that it takes place only if the number of extra dimensions is D ge 3. In the second part of the paper we study the influence of the initial anisotropy. Our study reveals that the transition from Gauss–Bonnet Kasner regime to anisotropic exponential expansion (with three expanding and contracting extra dimensions) is stable with respect to breaking the symmetry within both three- and extra-dimensional subspaces. However, the details of the dynamics in D=2 and D ge 3 are different. Combining the two described effects allows us to construct a scenario in D ge 3, where isotropization of outer and inner subspaces is reached dynamically from rather general anisotropic initial conditions.

Experimental study of the hydro-mechanical response of Opalinus Clay – Part 2: Influence of the stress path on the pore pressure response

Triaxial tests on back-saturated specimens using different controlled stress paths were conducted to study the influence of the stress path on the hydro-mechanical behavior of a clay shale. Opalinus Clay, a clay shale chosen for the disposal of high-level nuclear waste in Switzerland, was utilized. Three different stress paths approximating a tunnel excavation were applied: a two-dimensional stress path with isotropic initial stress conditions (i.e. pure shear compression), a two-dimensional stress path with anisotropic initial stress conditions, and a three-dimensional stress path. The influence of the stress path was investigated with respect to the specimens' geometry. Two end members were tested: specimens where the axial load was applied parallel to bedding (P-specimens) and specimens where the load was applied normal to bedding (S-specimens).Differences in the hydro-mechanical response were identified with respect to the specimens' geometry but also to the stress paths. When subjected to the two-dimensional stress paths, positive excess pore pressure was measured for S-specimens at low differential stresses whereas P-specimens showed negative excess pore pressure. The magnitudes of excess pore pressure were higher for the anisotropic two-dimensional stress path. Dilation associated with yielding was observed for all specimens. The application of the three-dimensional stress path revealed pore pressure responses that were conceptually comparable to the pore pressure response observed in situ. Pore pressure increase in front of the tunnel face can be related to poroelastic response of the rock mass to a change in differential and mean stress. Again, differences between P- and S-specimens were identified. Decrease in pore pressure before the tunnel face can be related to the dilation associated with yielding.No difference in peak strength between P- and S-specimens and the different stress paths was found. Nevertheless, it was shown that the state of failure is affected by the transversal isotropy as S-specimens fail at lower effective stresses compared to P-specimens.

A viable compactification scenario in Gauss-Bonnet gravity

In this talk we address two important issues which could affect reaching the exponential and Kasner asymptotes in Einstein-Gauss-Bonnet cosmologies – spatial curvature and anisotropy in both three- and extra-dimensional subspaces. In the first part we consider cosmological evolution of spaces being the product of two isotropic and spatially curved subspaces. We consider all possible number of spatial dimensions and provide description of the curvature effects in these dimensions. It is demonstrated that the dynamics in D = 2 (the number of extra dimensions) and D ≥ 3 is different. In particular, the regime with the “stabilization” of extra dimensions could be reached only if D ≥ 3. In the second part we study the influence of initial anisotropy. Our study of reveals that transition from Gauss-Bonnet Kasner regime to anisotropic exponential expansion (with expanding three and contracting extra dimensions) is stable with respect to breaking the symmetry within both three- and extra-dimensional subspaces in any number of extra dimensions. This allows us to construct a scenario where isotropisation of outer and inner subspaces is reached dynamically from rather general anisotropic initial conditions.

Molecular plasmonics: The role of rovibrational molecular states in exciton-plasmon materials under strong-coupling conditions

We extend the model of exciton-plasmon materials to include a ro-vibrational structure of molecules using wave-packet propagations on electronic potential energy surfaces. The new model replaces conventional two-level emitters with more complex molecules allowing to examine the influence of alignment and vibrational dynamics on strong coupling with surface plasmon-polaritons. We apply the model to a hybrid system comprising a thin layer of molecules placed on top of a periodic array of slits. Rigorous simulations are performed for two types of molecular systems described by vibrational bound-bound and bound-continuum electronic transitions. Calculations reveal new features in transmission, reflection and absorption spectra including the observation of significantly higher values of the Rabi splitting and vibrational patterns clearly seen in the corresponding spectra. We also examine the influence of anisotropic initial conditions on optical properties of hybrid materials demonstrating that the optical response of the system is significantly affected by an initial pre-alignment of the molecules. Our work demonstrates that pre-aligned molecules could serve as an efficient probe for the sub-diffraction characterization of the near-field near metal interfaces.

Far-from-equilibrium dynamics of a strongly coupled non-Abelian plasma with non-zero charge density or external magnetic field

Using holography, we study the evolution of a spatially homogeneous, far from equilibrium, strongly coupled $$ \mathcal{N}=4 $$ supersymmetric Yang-Mills plasma with a non-zero charge density or a background magnetic field. This gauge theory problem corresponds, in the dual gravity description, to an initial value problem in Einstein-Maxwell theory with homogeneous but anisotropic initial conditions. We explore the dependence of the equilibration process on different aspects of the initial departure from equilibrium and, while controlling for these dependencies, examine how the equilibration dynamics are affected by the presence of a non-vanishing charge density or an external magnetic field. The equilibration dynamics are remarkably insensitive to the addition of even large chemical potentials or magnetic fields; the equilibration time is set primarily by the form of the initial departure from equilibrium. For initial deviations from equilibrium which are well localized in scale, we formulate a simple model for equilibration times which agrees quite well with our results.

Consolidation around a tunnel in a general poroelastic medium under anisotropic initial stress conditions

In this study, a solution for the response of a poroelastic medium around a deeply excavated circular tunnel is analytically formulated based on Biot’s consolidation theory. The proposed solution considers the initial anisotropic stress in the medium around lined or unlined tunnels and is an improvement over previous solutions (Carter and Booker, 1982, 1984) because it considers Biot’s coefficient, the combined compressibility of liquid and solid phases in the porous medium, and a thick-walled liner. The solution is expressed using the Laplace transform domain, and numerical inversion techniques are used to obtain real time domain results. The new solution is verified by comparing it with previous analytical solutions and numerical results obtained using the commercial finite element software COMSOL Multiphysics (COMSOL AB, Stockholm, Sweden). Parametric studies are performed to determine the influences of Biot’s coefficient and the combined compressibility and liner properties during the consolidation process.

A quantum gravitational inflationary scenario in Bianchi-I spacetime

We investigate the ϕ2 inflationary model in the Bianchi-I spacetime using the effective spacetime description of loop quantum cosmology to understand the issues of the resolution of initial singularity, isotropization, effect of anisotropies on the amount of inflation, and the phase-space attractors in the presence of non-perturbative quantum gravitational modifications. A comparative analysis with the classical theory by including more general initial conditions than the ones previously considered in the latter is also performed. We show that, in general, the classical singularity is replaced by a bounce of the mean scale factor in loop quantum cosmology. Due to the underlying quantum geometric effects, the energy density of the inflaton and the anisotropic shear remain bounded throughout the non-singular evolution. Starting from arbitrary anisotropic initial conditions, a loop quantum universe isotropizes either before or soon after the onset of slow-roll inflation. We find a double attractor behavior in the phase-space dynamics of loop quantum cosmology, similar to the one in classical theory, but with some additional subtle features. Quantum modifications to the dynamical equations are such that, unlike the classical theory, the amount of inflation does not monotonically depend on the initial anisotropy in loop quantum cosmology. Our results suggest that a viable non-singular inflationary model can be constructed from highly anisotropic initial conditions in the Planck regime.

Experimental study of asphaltic concrete dynamic properties as an impervious core in embankment dams

The seismic behaviour of asphaltic concrete used as an impervious core in embankment dams was investigated.To evaluate the specimen’s dynamic behaviour, an extensive series of monotonic and cyclic triaxial tests were carried out. Bitumen content between 5.5% and 7.0% with 0.5% increments were selected for the tests. Isotropic and anisotropic initial stress conditions with different principal stress ratio were also considered in this study. Thousands of cycles were imposed on some of the specimens, to study their fatigue behaviour due to seismic loading. A small degradation could be seen but no cracking was observed on the cutting surfaces. All tests were carried out at a constant temperature of 22°C simulating a constant temperature inside a dam in tropical climate regions. Shear modulus in the compression region (Gc) and tension region (Ge) are presented for different Bitumen content, confining stress, stress ratio (Kc) and loading type. The damping ratio was also presented for different loading states. A regression equation was also derived for determining cyclic and maximum shear modulus (Gmax) of the asphaltic concrete for different Bitumen content as a function of confining stress which can be used in numerical studies.

Cyclic and post-cyclic monotonic behavior of crushed conglomerate rockfill material under dry and saturated conditions

The seismic behavior of two conglomerate rockfill materials used in two high rockfill dams, subjected to earthquake loads, has been studied. In order to evaluate the dynamic behavior, an extensive series of monotonic and cyclic tests were carried out on large cylindrical specimens of conglomerate rockfill materials using triaxial tests. This paper first studies the effects of drainage (dry, saturation) conditions on the mechanical behavior of conglomerate rockfills at two compaction levels, and grain size distribution subjected to monotonic loading. Loading frequency and drainage condition effects on specimen behavior have been studied under cyclic loads under both isotropic and anisotropic initial stress conditions. To study any sign of material degradation due to cyclic loading, the post-cyclic monotonic stress–strain curves were compared under “dry” and “saturated” conditions. Geotechnical parameters to be used in static and dynamic numerical analyses models have also been presented.

Stability of a self-gravitating homogeneous resistive plasma

In this paper, we analyze the stability of a homogeneous self-gravitating plasma, having a non-zero resistivity. This study provides a generalization of the Jeans paradigm for determining the critical scale above which gravitational collapse is allowed.We start by discussing the stability of an ideal self-gravitating plasma embedded in a constant magnetic field. We outline the existence of an anisotropic feature of the gravitational collapse. In fact, while in the plane orthogonal to the magnetic field the Jeans length is enhanced by the contribution of the magnetic pressure, outside this plane perturbations are governed by the usual Jeans criterion. The anisotropic collapse of a density contrast is sketched in detail, suggesting that the linear evolution provides anisotropic initial conditions for the non-linear stage, where this effect could be strongly enforced.The same problem is then faced in the presence of non-zero resistivity and the conditions for the gravitational collapse are correspondingly extended. The relevant feature emerging in this resistive scenario is the cancelation of the collapse anisotropy in weakly conducting plasmas. In this case, the instability of a self-gravitating resistive plasma is characterized by the standard isotropic Jeans length in any directions. The limit of very small resistivity coefficient is finally addressed, elucidating how reminiscence of the collapse anisotropy can be found in the different values of the perturbation frequency inside and outside the plane orthogonal to the magnetic field.

Angular correlations and high energy evolution

We address the question of to what extent JIMWLK evolution is capable of taking into account angular correlations in a high energy hadronic wave function. Our conclusion is that angular (and indeed other) correlations in the wave function cannot be reliably calculated without taking into account Pomeron loops in the evolution. As an example we study numerically the energy evolution of angular correlations between dipole scattering amplitudes in the framework of the large ${N}_{c}$ approximation to JIMWLK evolution (the ``projectile dipole model''). Target correlations are introduced via averaging over an (isotropic) ensemble of anisotropic initial conditions. We find that correlations disappear very quickly with rapidity even inside the saturation radius. This is in accordance with our physical picture of JIMWLK evolution. The actual correlations inside the saturation radius in the target QCD wave function, on the other hand, should remain sizable at any rapidity.

Observable effects of anisotropic bubble nucleation

Our universe may have formed via bubble nucleation in an eternally-inflating background. Furthermore, the background may have a compact dimension — the modulus of which tunnels out of a metastable minimum during bubble nucleation — which subsequently grows to become one of our three large spatial dimensions. Then the reduced symmetry of the background is equivalent to anisotropic initial conditions in our bubble universe. We compute the inflationary spectrum in such a scenario and, as a first step toward understanding the effects of anisotropy, project it onto spherical harmonics. The resulting spectrum exhibits anomalous multipole correlations, their relative amplitude set by the present curvature parameter, which appear to extend to arbitrarily large multipole moments. This raises the possibility of future detection, if slow-roll inflation does not last too long within our bubble. A full understanding of the observational signal must account for the effects of background anisotropy on photon free streaming, and is left to future work.