Is the DBI scalar field as fragile as other kk-essence fields?

Caustic singularity formations in shift-symmetric $k$-essence and Horndeski theories on a fixed Minkowski spacetime were recently argued. In $n$ dimensions, this singularity is the $(n-2)$-dimensional plane in spacetime at which second derivatives of a field diverge and the field loses single-valued description for its evolution. This does not necessarily imply a pathological behavior of the system but rather invalidates the effective description. The effective theory would thus have to be replaced by another to describe the evolution thereafter. In this paper, adopting the planar-symmetric $1$+$1$-dimensional approach employed in the original analysis, we seek all $k$-essence theories in which generic simple wave solutions are free from such caustic singularities. Contrary to the previous claim, we find that not only the standard canonical scalar but also the DBI scalar are free from caustics, as far as planar-symmetric simple wave solutions are concerned. Addition of shift-symmetric Horndeski terms does not change the conclusion.Comment: 11 pages, 7 figures, v2: appendix added, published versio

Does the detection of primordial gravitational waves exclude low energy inflation?

We show that a detectable tensor-to-scalar ratio $(r\ge 10^{-3})$ on the CMB scale can be generated even during extremely low energy inflation which saturates the BBN bound $\rho_{\rm inf}\approx (30 {\rm MeV})^4$. The source of the gravitational waves is not quantum fluctuations of graviton but those of $SU(2)$ gauge fields, energetically supported by coupled axion fields. The curvature perturbation, the backreaction effect and the validity of perturbative treatment are carefully checked. Our result indicates that measuring $r$ alone does not immediately fix the inflationary energy scale.Comment: 6 pages, 3 figure

On cell problems for Hamilton-Jacobi equations with non-coercive Hamiltonians and its application to homogenization problems

We study a cell problem arising in homogenization for a Hamilton-Jacobi equation whose Hamiltonian is not coercive. We introduce a generalized notion of effective Hamiltonians by approximating the equation and characterize the solvability of the cell problem in terms of the generalized effective Hamiltonian. Under some sufficient conditions, the result is applied to the associated homogenization problem. We also show that homogenization for non-coercive equations fails in general

Where does curvaton reside? Differences between bulk and brane frames

Some classes of inflationary models naturally introduce two distinct metrics/frames, and their equivalence in terms of observables has often been put in question. D-brane inflation proposes candidates for an inflaton embedded in the string theory and possesses descriptions on the brane and bulk metrics/frames, which are connected by a conformal/disformal transformation that depends on the inflaton and its derivatives. It has been shown that curvature perturbations generated by the inflaton are identical in both frames, meaning that observables such as the spectrum of cosmic microwave background (CMB) anisotropies are independent of whether matter fields---including those in the standard model of particle physics---minimally couple to the brane or the bulk metric/frame. This is true despite the fact that the observables are eventually measured by the matter fields and that the total action including the matter fields is different in the two cases. In contrast, in curvaton scenarios, the observables depend on the frame to which the curvaton minimally couples. Among all inflationary scenarios, we focus on two models motivated by the KKLMMT fine-tuning problem: a slow-roll inflation with an inflection-point potential and a model of a rapidly rolling inflaton that conformally couples to gravity. In the first model, the difference between the frames in which the curvaton resides is encoded in the spectral index of the curvature perturbations, depicting the nature of the frame transformation. In the second model, the curvaton on the brane induces a spectral index significantly different from that in the bulk and is even falsified by the observations. This work thus demonstrates that two frames connected by a conformal/disformal transformation lead to different physical observables such as CMB anisotropies in curvaton models.Comment: 16 pages, v2: published versio