Inflation with a class of concave inflaton potentials in Randall-Sundrum model

We investigate inflation with a class of concave inflaton potentials of the form $\sim \phi^n$ $(0<n<1)$ in the Randall-Sundrum model with an infinite extra spatial dimension. We show that this class of models is much more in good agreement with observations compared to the standard inflation. We also find the range of the five-dimensional Planck scale ($M_5$) and show that large tensor-to-scalar ratios do not eliminate small-field inflation in braneworld cosmology.Comment: 7 pages, 2 figures; matches EPJC version; comments are welcom

Unitary paradox of cosmological perturbations

If we interpret the Bekenstein-Hawking entropy of the Hubble horizon as thermodynamic entropy, then the entanglement entropy of the superhorizon modes of curvature perturbation entangled with the subhorizon modes will exceed the Bekenstein-Hawking bound at some point; we call this the unitary paradox of cosmological perturbations by analogy with black hole. In order to avoid a fine-tuned problem, the paradox must occur during the inflationary era at the critical time $t_c=\ln(3\sqrt{\pi}/\sqrt{2}\epsilon_HH_{inf})/2H_{inf}$ (in Planck units), where $\epsilon_H= -\dot{H}/H^2$ is the first Hubble slow-roll parameter and $H_{inf}$ is the Hubble rate during inflation. If we instead accept the fine-tuned problem, then the paradox will occur during the dark energy era at the critical time $t_c'=\ln(3\sqrt{\pi}H_{inf}/\sqrt{2}fe^{2N}H_\Lambda^2)/2H_\Lambda$, where $H_\Lambda$ is the Hubble rate dominated by dark energy, $N$ is the total number of e-folds of inflation, and $f$ is a purification factor that takes the range $0<f<3\sqrt{\pi}H_{inf}/\sqrt{2}e^{2N}H_\Lambda^2$.Comment: 13 pages, 3 figures; close to published versio

Folding model study of the elastic α+α\alpha + \alpha scattering at low energies

The folding model analysis of the elastic $\alpha + \alpha$ scattering at the incident energies below the reaction threshold of 34.7 MeV (in the lab system) has been done using the well-tested density dependent versions of the M3Y interaction and realistic choices for the $^4$He density. Because the absorption is negligible at the energies below the reaction threshold, we were able to probe the $\alpha + \alpha$ optical potential at low energies quite unambiguously and found that the $\alpha + \alpha$ overlap density used to construct the density dependence of the M3Y interaction is strongly distorted by the Pauli blocking. This result gives possible explanation of a long-standing inconsistency of the double-folding model in its study of the elastic $\alpha + \alpha$ and $\alpha$-nucleus scattering at low energies using the same realistic density dependent M3Y interaction

Insights of quantum time for quantum evolution

If time is emergent, quantum system is entangled with quantum time as it evolves. If the system contains entanglement within itself, which we can call \textit{internal entanglement} to distinguish it from the ``external" time-system entanglement, the speed of evolution is enhanced. In this paper, we explore the insights of quantum time for the evolution of a system that contains two entangled qubits. We consider two cases: (1) two initially entangled qubits that evolve under local dynamics; (2) two interacting qubits such that entanglement between them is generated over time. In both cases, the key message is that increasing internal entanglement speeds up the evolution and makes the system more entangled with time. This result could be useful to gain new insights of quantum time for black hole evaporation or cosmological perturbations in an expanding Universe, because we also have an evolving entangled bipartite system in those cases.Comment: 12 pages, 4 figure

Time-System Entanglement and Special Relativity

We know that space and time are treated almost equally in classical physics, but we also know that this is not the case for quantum mechanics. A quantum description of both space and time is important to really understand the quantum nature of reality. The Page-Wootters mechanism of quantum time is a promising starting point, according to which the evolution of the quantum system is described by the entanglement between it and quantum temporal degrees of freedom. In this paper, we use a qubit clock model to study how the time-system entanglement measures depend on the rapidity when the quantum system is Lorentz boosted. We consider the case of a spin-1/2 particle with Gaussian momentum distribution as a concrete example.Comment: 5 pages, 3 figure

Shaft inflation in Randall-Sundrum model

Shaft inflation is a model in which the inflaton potential approaches a plateau far from the origin, while it resembles chaotic inflation near the origin. Meanwhile, the Randall-Sundrum type II model (RSII) is an interesting extra-dimensional model to study cosmological phenomenology. In this paper, we study shaft inflation in the RSII model. We find that the predictions are in excellent agreement with observation. The fundamental five-dimensional Planck scale is found to be $M_5\simeq 10^{16}$ GeV, which is consistent with the lower bound $M_5\gtrsim 10^{9}$ GeV obtained from experimental Newtonian gravitational bound. This is an important result that can be used to explore further the implications of extra dimension in other contexts.Comment: 14 pages, 5 figures, 2 tables; published version in JCA

Gauss Digitization of Simple Polygons

Digitization is a process of discretizing a continuous object $X ⊂ R 2$ to obtain a digital object $X ⊂ Z 2$. This document addresses the Gauss digitization of continuous objects. In particular, we are interested in computing the digitized object of simple polygons. The Gauss digitization of X , denoted by X, is defined as the set of integer points being inside X. More specifically, $X = X ∩ Z 2$. This problem of digitization is related to the point-in-polygon (PIP) problem in computational geometry. Indeed, computing the digitized object X of a given polygonal object X is equivalent to finding all integer points laying inside or on the boundary of X. In this document, we present an implementation of computing the Gauss digitization of polygons using a ray casting based approach

Constraint on the Higgs-Dilaton potential via Warm inflation in Two-Time Physics

Within the $SP(2,R)$ symmetry, the Two-time model (2T model) has six dimensions with two dimensions of time and the dilaton field that can be identified as inflaton in a warm inflation scenario with potential of the form $\sim\phi^4$. From that consideration, we derive the range of parameters for the Higgs-Dilaton potential, the coupling constant between Higgs and Dialton ($\alpha$) is lager than $1.598$ or smaller than $2.13\times 10^{-7}$ when the mass of Dilaton is lager than $200$ GeV. Therefore, the 2T-model indirectly suggests that extra-dimension can also be a source of inflation.Comment: 11 pages and 2 figure

Combinatorial structure of rigid transformations in 2D digital images

International audienceRigid transformations are involved in a wide range of digital image processing applications. When applied on such discrete images, rigid transformations are however usually performed in their associated continuous space, then requiring a subsequent digitization of the result. In this article, we propose to study rigid transformations of digital images as a fully discrete process. In particular, we investigate a combinatorial structure modelling the whole space of digital rigid transformations on any subset of Z^2 of size N*N. We describe this combinatorial structure, which presents a space complexity O(N^9) and we propose an algorithm enabling to build it in linear time with respect to this space complexity. This algorithm, which handles real (i.e. non-rational) values related to the continuous transformations associated to the discrete ones, is however defined in a fully discrete form, leading to exact computation