The Inflationary Universe

The Gauss-Codazzi formalism is used to obtain exact solutions to Einstein's equations in the presence of domain walls. Domain walls are shown to have repulsive gravitational fields. The most general solution to Einstein's equations for a planar domain wall is obtained. Also, the motion of a spherical domain wall in an asymptotically flat space-time is derived.

The Gravitationally Repulsive Domain Wall

Classical solutions play an important role in quantum field theory, high energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on Yang–Mills instantons and on bounce solutions.

Classical Solutions in Quantum Field Theory

It has been recently shown that, contrary to an intuitive decoupling argument, the presence of new physics at very large energy scales (say around the Planck scale) can have a strong impact on the electroweak vacuum lifetime. In particular, the vacuum could be totally destabilized. This study was performed in a flat spacetime background, and it is important to extend the analysis to curved spacetime since these are Planckian-physics effects. It is generally expected that under these extreme conditions gravity should totally quench the formation of true vacuum bubbles, thus washing out the destabilizing effect of new physics. In this work we extend the analysis to curved spacetime and show that, although gravity pushes toward stabilization, the destabilizing effect of new physics is still (by far) the dominating one. In order to get model independent results, high energy new physics is parametrized in two different independent ways: as higher order operators in the Higgs field, or introducing new particles with very large masses. The destabilizing effect is observed in both cases, hinting at a general mechanism that does not depend on the parametrization details for new physics, thus maintaining the results obtained from the analysis performed in flat spacetime.

/pdf/impact-of-new-physics-on-the-ew-vacuum-stability-in-a-curved-305kkbeecg.pdf

Impact of New Physics on the EW vacuum stability in a curved spacetime background

Fubini instantons in Dilatonic Einstein–Gauss–Bonnet theory of gravitation

Abstract The bulk-boundary correspondence is an integral feature of topological analysis and the existence of boundary or interface modes offers direct insight into the topological structure of the Bloch wave function. While only the topology of the wave function has been considered relevant to boundary modes, we demonstrate that another geometric quantity, the so-called quantum distance, can also host a bulk-interface correspondence. We consider a generic class of two-dimensional flat band systems, where the flat band has a parabolic band-crossing with another dispersive band. While such flat bands are known to be topologically trivial, we show that the nonzero maximum quantum distance between the eigenstates of the flat band around the touching point guarantees the existence of boundary modes at the interfaces between two domains with different chemical potentials or different maximum quantum distance. Moreover, the maximum quantum distance can predict even the explicit form of the dispersion relation and decay length of the interface modes. 

/pdf/bulk-interface-correspondence-from-quantum-distance-in-flat-3t75sefn.pdf

Bulk-interface correspondence from quantum distance in flat band systems

We study Fubini instantons of a self-gravitating scalar field. The Fubini instanton describes the decay of a vacuum state under tunneling instead of rolling in the presence of a tachyonic potential. The tunneling occurs from the maximum of the potential, which is a vacuum state, to any arbitrary state, belonging to the tunneling without any barrier. We consider two different types of the tachyonic potential. One has only a quartic term. The other has both the quartic and quadratic terms. We show that, there exist several kinds of new O(4)-symmetric Fubini instanton solution, which are possible only if gravity is taken into account. One type of them has the structure with $Z_2$ symmetry. This type of the solution is possible only in the de Sitter background. We discuss on the interpretation of the solutions with $Z_2$ symmetry.

Fubini instantons in curved space

We investigate and classify the possible types of false vacuum bubbles in Einstein gravity The false vacuum bubbles can occur only if gravity is taken into account We show that there exist solutions only with compact geometries The analytic computations for the radius and nucleation rate of a vacuum bubble are evaluated using the thin-wall approximation We discuss possible cosmological implications of our new solutions

http://inspirehep.net/record/1264782/files/arXiv:1311.4279.pdf

The nucleation of false vacuum bubbles with compact geometries

Oscillating Instanton Solutions and Classification of Vacuum Bubbles

In the standard mean-field treatment of superconductors, the electron-electron interactions are assumed to be written in terms of local density operators. However, more general interactions, such as pair-hopping interactions, may exist or may be generated in a low-energy effective Hamiltonian. In this work, we study the effect of correlated hopping interactions toward the electromagnetic response of superconductors. When only the Hamiltonian after the mean-field approximation is provided, one cannot unambiguously determine its electromagnetic response whenever such interactions are allowed. We find that additional terms in the current operator are generated and the Meissner weight and the optical conductivities are modified from the textbook results.

pdf/electromagnetic-response-of-superconductors-in-mean-field-3r2d37v2.pdf

Electromagnetic response of superconductors in mean-field approximation

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