Cosmological disformal invariance

The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.Comment: 23 pages + Appendix, updated versio

ADHM Construction of (Anti-)Self-dual Instantons in Eight Dimensions

We study the ADHM construction of (anti-)self-dual instantons in eight dimensions. We propose the general scheme to construct the (anti-)self-dual gauge field configurations $F \wedge F = \pm *_8 F \wedge F$ whose finite topological charges are given by the fourth Chern number. We show that our construction reproduces the known $\text{SO}(8)$ one-instanton solution. We also construct multi-instanton solutions of 't Hooft and Jackiw-Nohl-Rebbi (JNR) types in the dilute instanton gas approximation. The well-separated configurations of multi-instantons reproduce the correct topological charges with high accuracy. We also show that our construction is generalized to (anti-)self-dual instantons in $4n \ (n=3,4, \ldots)$ dimensions.Comment: 35 pages, 1 figure, minor correction

Multi-disformal invariance of nonlinear primordial perturbations

We study disformal transformations of the metric in the cosmological context. We first consider the disformal transformation generated by a scalar field $\phi$ and show that the curvature and tensor perturbations on the uniform $\phi$ slicing, on which the scalar field is homogeneous, are non-linearly invariant under the disformal transformation. Then we discuss the transformation properties of the evolution equations for the curvature and tensor perturbations at full non-linear order in the context of spatial gradient expansion as well as at linear order. In particular, we show that the transformation can be described in two typically different ways: one that clearly shows the physical invariance and the other that shows an apparent change of the causal structure. Finally we consider a new type of disformal transformation in which a multi-component scalar field comes into play, which we call a "multi-disformal transformation". We show that the curvature and tensor perturbations are invariant at linear order, and also at non-linear order provided that the system has reached the adiabatic limit.Comment: 8 page

Sigma Model BPS Lumps on Torus

We study doubly periodic Bogomol'nyi-Prasad-Sommerfield (BPS) lumps in supersymmetric CP^{N-1} non-linear sigma models on a torus T^2. Following the philosophy of the Harrington-Shepard construction of calorons in Yang-Mills theory, we obtain the n-lump solutions on compact spaces by suitably arranging the n-lumps on R^2 at equal intervals. We examine the modular invariance of the solutions and find that there are no modular invariant solutions for n=1,2 in this construction.Comment: 15 pages, 3 figures, published versio

Large non-Gaussianity from multi-brid inflation

A model of multi-component hybrid inflation, dubbed multi-brid inflation, in which various observable quantities including the non-Gaussianity parameter f_{NL} can be analytically calculated was proposed recently. In particular, for a two-brid inflation model with an exponential potential and the condition that the end of inflation is an ellipse in the field space, it was found that, while keeping the other observational quantities within the range consistent with observations, large non-Gaussianity is possible for certain inflationary trajectories, provided that the ratio of the two masses is large. One might question whether the resulting large non-Gaussianity is specific to this particular form of the potential and the condition for the end of inflation. In this paper, we consider a model of multi-brid inflation with a potential given by an exponential function of terms quadratic in the scalar field components. We also consider a more general class of ellipses for the end of inflation than those studied previously. Then, focusing on the case of two-brid inflation, we find that large non-Gaussianity is possible in the present model even for the equal-mass case. Then by tuning the model parameters, we find that there exist models for which both the non-Gaussianity and the tensor-to-scalar ratio are large enough to be detected in the very near future.Comment: 13 pages, 3 figures; Typos corrected, references and one figure adde

Ab initio Study of Valley Line on a Total-Energy Surface for Zone-Center Distortions of Ferroelectric Perovskite Oxides BaTiO3 and PbTiO3

An ab initio structure optimization technique is newly developed to determine the valley line on a total-energy surface for zone-center distortions of ferroelectric perovskite oxides and is applied to barium titanate BaTiO3 and lead titanate PbTiO3. The proposed technique is an improvement over King-Smith and Vanderbilt's scheme [Phys. Rev. B 49, p.5828 (1994)] of evaluating total energy as a function of the amplitude of atomic displacements. The results of numerical calculations show that total energy can be expressed as a fourth-order function of the amplitude of atomic displacements in BaTiO3 but not in PbTiO3.Comment: 4 pages, 5 figure