1,488 research outputs found
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 whose finite
topological charges are given by the fourth Chern number. We show that our
construction reproduces the known 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 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
and show that the curvature and tensor perturbations on the uniform
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
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