On a continuum theory of brittle materials with microstructure

In this work we study localization of a Kalb-Ramond tensorial gauge field on a membrane described by real scalar fields. The membrane is embedded in an AdS-type five-dimensional bulk space, which mimics a Randall-Sundrum scenario. First, we consider a membrane described by only a single real scalar field. In that scenario we find that there is no localized tensorial zero mode. When we take into account branes described by two real scalar fields with internal structures, we obtain again a nonlocalized zero mode for a Kalb-Ramond tensorial gauge field. After modifying our model of one single scalar field by coupling the dilaton to the Kalb-Ramond field, we find that this result is changed. Furthermore, we analyze Kaluza-Klein massive modes and resonance structures.

Noncommutative universe and chameleon field dynamics

At energies higher than the brane tension, the dynamics of a scalar field rolling down a potential are modified relative to the predictions of General Relativity. The modifications imply, among other things, that steeper potentials can be used to drive an epoch of slow–roll inflation. We investigate the evolution of entropy and adiabatic modes during inflation driven by two scalar fields confined on the brane. We show that the amount of entropy perturbations produced during inflation is suppressed compared to the predictions made by General Relativity. As a consequence, the initial conditions do not matter in multiple field inflation in brane worlds if inflation is driven at energies much higher than the brane tension. DAMTP-2002-107 Inflation provides an explanation for the origin of structures in the universe. In its simplest form, inflation is driven by a single scalar field, called the inflaton, which slowly rolls down a potential. Perturbations in the inflaton field are adiabatic and obey Gaussian statistics [1]. However, this picture might be over simplistic as there is no reason to believe that inflation is driven solely by a single scalar field. Instead, the possibility that inflation is driven by a system of several scalar fields must be considered. In particular, perturbations are, in general, no longer purely adiabatic. Entropy (or isocurvature) per

The relative values of a single 2D scalar field can be effectively perceived when the field is represented by height and rendered as a surface in three dimensions. When multiple scalar fields are simultaneously rendered on the same domain, control of additional rendering attributes such as color, transparency, texturing, and lighting is needed for effective perception. However, the transition from foreground to background due to surface intersections can confound accurate surface perception, even for techniques that work well for overlapping non-intersecting surfaces. We propose a general method for decomposing and stratifying multiple intersecting surfaces into layered components to permit complete rendering control of each surface component. We explore different rendering schemes based on stratification values and report initial results from experimentation.

We study a class of unified dark matter (UDM) models based on generalized K-essence, where a single scalar field with non-canonical kinetic terms accounts for dark radiation, dark matter, and dark energy. Starting from the purely kinetic Lagrangian proposed by Scherrer (2004 Phys. Rev. Lett. 93 011301), we extend the analysis to quadratic and exponential scalar potentials and explore their phenomenology. All models are implemented in a modified version of Hi_CLASS (a Horndeski capable extension of CLASS) and confronted with data from Planck 2018, DESI DR1, and Big Bang Nucleosynthesis. The scenarios reproduce the full sequence of cosmic epochs: an early radiation-like phase, a matter-dominated era, and late-time accelerated expansion. The new models predict slightly higher values of the Hubble constant compared to ΛCDM, thereby partially alleviating the respective tensions from ∼ 4.4 σ to ∼ 3.4 σ . The quadratic potential requires an ultralight mass that makes it effectively indistinguishable from the Scherrer solution. Overall, generalized K-essence provides a minimal (single field and minimally coupled) and observationally viable realization of UDM, offering a unified description of the dark sector with distinctive signatures in both early- and late-time cosmology.

We examine the question as to whether the Palatini f(R) gravity theories permit space-times in which the causality is violated. We show that every perfect-fluid G\"{o}del-type solution of Palatini f(R) gravity with density $\rho$ and pressure $p$ that satisfy the weak energy condition $\rho+p \geq 0$ is necessarily isometric to the G\"odel geometry, demonstrating therefore that these theories present causal anomalies in the form of closed time-like curves. This result extends a theorem on G\"{o}del-type models to the framework of Palatini f(R) gravity theory. We concretely examine the G\"odel-type perfect-fluid solutions in specific $f(R) = R - \alpha/R^{n}$ Palatini gravity theory, where the free parameters $\alpha$ and $n$ have been recently constrained by a diverse set of observational data. We show that for positive matter density and for $\alpha$ and $n$ within the interval permitted by the observational data, this theory does not admit the G\"odel geometry as a perfect-fluid solution of its field equations. In this sense, this theory remedies the causal pathology in the form of closed time-like curves which is allowed in general relativity. We derive an expression for a critical radius $r_c$ (beyond which the causality is violated) for an arbitrary Palatini f(R) theory, thus making apparent that the violation of causality depends on the form of f(R) and on the matter content components. We also examine the violation of causality of G\"odel-type by considering a single scalar field as the matter content. For this source we show that Palatini f(R) gravity gives rise to a unique G\"odel-type solution with no violation of causality.

A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to the domain scientists. It has been shown in recent works that a single scalar field is insufficient to capture many important topological features in the data, instead one needs to consider topological relationships between multiple scalar fields. In the current paper, we propose a novel method of finding similarity between two multifield data by comparing their respective fiber component distributions. Given a time-varying multifield data, the method computes a metric plot for each pair of histograms at consecutive time stamps to understand the topological changes in the data over time. We validate the method using real and synthetic data. The effectiveness of the proposed method is shown by its ability to capture important topological features that are not always possible to detect using the individual component scalar fields.

We propose a cosmological framework in which neutrino masses evolve dynamically through coupling with a scalar field that simultaneously drives inflation. The neutrino mass is modeled as a power-law, exponential, or hybrid function of the scalar field, yielding an effective potential that includes neutrino backreaction. Starting from the Einstein–Hilbert action in a flat FLRW background, we derive the modified Friedmann and Klein–Gordon equations incorporating this coupling. Using the Fermi–Dirac integrals, we account for the continuous transition of neutrinos from relativistic to nonrelativistic regimes. The inflationary dynamics are investigated through the slow-roll parameters derived from the effective potential, together with the evaluation of the scalar spectral index , and the tensor-to-scalar ratio r for each model. The exponential and mixed MaVaN couplings emerge as the most flexible cases, allowing inflationary dynamics and neutrino mass variation to be accommodated within a single scalar field, only in a constrained region of the parameter space.

We revisit a propagating torsion gravity theory obtained by introducing a field coupled to the Holst term in the first-order Einstein-Cartan action. The resulting theory has second-order field equations, no adjustable coupling constants, and one more propagating degree of freedom as compared to general relativity. When no fermions are present the theory is known to be equivalent to that of a single massless scalar field canonically coupled to gravity. We extend this result to the case with fermions and obtain an effective interaction between the scalar field and the fermionic currents. We also describe a version of the theory with a potential for the scalar field and discuss whether it can be interpreted as the inflaton.

This thesis deals with the construction of perturbative methods for analyzing the phase transition of the electroweak gauge theory in a strong magnetic field at zero temperature. The first part is a self-contained description of the methods and results. The second part contains the articles on which the first part is based. It should be emphasized that this thesis is organized in a non-traditional manner in the sense that the first part contains all essential material from the articles as well as original results, for instance Theorem 4.2, Section 6.2 and both Appendices, which have not been published previously in journals. After the brief Introduction, Chapter 2 reviews the Weinberg--Salam model of electroweak interactions and proceeds to explain the instability in a strong magnetic field with respect to the production of W bosons. Chapter 3 describes how the instability, above a critical value of the magnetic field, leads to the formation of a new phase with a W-boson condensate. For the special case when the Higgs mass and the Z-boson mass are set equal, previous results by Ambj\o{}rn and Olesen are used to illustrate the properties of this new phase. In Chapter 4 a classical perturbative method is developed by means of which the W-boson phase can be analyzed near the critical value of the magnetic field for general values of the Higgs to Z-boson mass ratio. Great care is taken to label all possible perturbative solutions for the W condensate, so that the energy can be expressed in terms of simple geometric quantities. The classical solutions do correspond to coherent quantum states of W-boson pairs which are constructed in Chapter 5. Finally in Chapter 6 values of the energy for classical and quantum solutions are analyzed and compared, and it is found that, above the critical magnetic field and for a Higgs mass larger than the Z mass, the ground state corresponds to a condensate of W-boson pairs whose density forms an hexagonal pattern in the directions perpendicular to the magnetic field. It is also shown that quantum effects will shift the critical magnetic field to a slightly higher value if periodic boundary conditions are imposed in the direction of the magnetic field. Analogies with Type-II superconductivity are explored.

In this paper we systematically develop the flat/CFT holographic dictionary, building on AdS/CFT holography. After analysing the behaviour of scalar field modes on hyperbolic slices of Minkowski and performing the holographic renormalisation for the associated onshell action, we obtain a holography dictionary between the bulk theory and the corresponding dual theory on the celestial sphere. We propose that a single scalar field in the bulk is dual to two series of operators on the celestial sphere; the scaling dimension of these operators takes values on the principal series. The real time features of the bulk theory, such as the dynamical and the casual structure, are encoded in the construction of correlation functions on the boundary via the coefficients of the bulk modes. Moreover, we will see that the two series of operators can be interpreted as ingoing and outgoing waves in the bulk. We illustrate our dictionary with the example of a single shock wave. Our results lay foundations for further computation within the flat/celestial CFT correspondence.

Dark energy models with a single scalar field cannot cross the equation of state divide set by a cosmological constant. More general models that allow crossing require additional degrees of freedom to ensure gravitational stability. We show that a parameterized post-Friedmann description of cosmic accelerzation provides a simple but accurate description of multiple scalar field crossing models. Moreover the prescription provides a well-controlled approximation for a wide range of smooth dark energy models. It conserves energy and momentum and is exact in the metric evolution on scales well above and below the transition scale to relative smoothness. Standard linear perturbation tools have been altered to include this description and made publicly available for studies of the dark energy involving cosmological structure out to the horizon scale.

We explore a class of effective field theory models of cosmic accelerationinvolving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy theweak equivalence principle, assuming that one boson is lighter thanall the others, and integrating out the heavier fields.The result is a quintessence model with matter coupling,together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients.After eliminating higher derivative terms and exploiting the field redefinition freedom,we show that the resulting theory contains nine independent free functions of the scalar field when truncated at four derivatives. This is in contrast to the four free functions found insimilar theories of single-field inflation, where matter is notpresent. We discuss several different representations of the theorythat can be obtained using the field redefinition freedom.For perturbations to the quintessence field today on subhorizonlengthscales larger than the Compton wavelength of the heavy fields,the theory is weakly coupled and natural in the sense of t'Hooft. Thetheory admits a regime where the perturbations become modestly nonlinear, but very strongnonlinearities lie outside its domain of validity.

We describe a correspondence between domain wall solutions of Einstein gravity with a single scalar field and self-interaction potential. The correspondence we call conformal scale factor inversion (CSFI) is a map comprising the inversion of the scale factor in conformal coordinates, and a transformation of the field and its potential which preserves the form of the Einstein equations for static and isotropic domain walls. By construction, CSFI maps the asymptotic anti--de Sitter boundary to the vicinity of a naked singularity in a theory with a special Liouville (exponential) scalar field potential; it is also a map in the parameter space of exponential potentials. The correspondence can be extended to linear fluctuations, being akin to an S-duality, and can be interpreted in terms of ``SUSY quantum mechanics'' for the fluctuation modes. The holographic implementation of CSFI relates the UV and IR regimes of a pair of holographic renormalization group flows; in particular, it is a symmetry of the GPPZ flow.

We discuss how the ghost-free bigravity coupled with a single scalar field can be derived from a braneworld setup. We consider DGP two-brane model without radion stabilization. The bulk configuration is solved for given boundary metrics, and it is substituted back into the action to obtain the effective four-dimensional action. In order to obtain the ghost-free bigravity, we consider the gradient expansion in which the brane separation is supposed to be sufficiently small so that two boundary metrics are almost identical. The obtained effective theory is shown to be ghost free as expected, however, the interaction between two gravitons takes the Fierz-Pauli form at the leading order of the gradient expansion, even though we do not use the approximation of linear perturbation. We also find that the radion remains as a scalar field in the four-dimensional effective theory, but its coupling to the metrics is non-trivial.