Reheating temperature in non-minimal derivative coupling model

We consider the inflaton as a scalar field described by a non-minimal derivative coupling model with a power law potential. We study the slow roll inflation, the rapid oscillation phase, the radiation dominated and the recombination eras respectively, and estimate e-folds numbers during these epochs. Using these results and recent astrophysical data we determine the reheating temperature in terms of the spectral index and the amplitude of the power spectrum of scalar perturbations.Comment: 14 pages, 2 figures, discussions added, accepted by JCA

Temperature in warm inflation in non minimal kinetic coupling model

Warm inflation in the non minimal derivative coupling model with a general dissipation coefficient is considered. We investigate conditions for the existence of the slow roll approximation and study cosmological perturbations. The spectral index, and the power spectrum are calculated and the temperature of the universe at the end of the slow roll warm inflation is obtained.Comment: 18 pages, major revision, accepted by the European Physical Journal

Clique Vectors of kk-Connected Chordal Graphs

The clique vector $\mathfrak{c}(G)$ of a graph $G$ is the sequence $(c_1, c_2, \ldots,c_d)$ in $\mathbb{N}^d$, where $c_i$ is the number of cliques in $G$ with $i$ vertices and $d$ is the largest cardinality of a clique in $G$. In this note, we use tools from commutative algebra to characterize all possible clique vectors of $k$-connected chordal graphs

Warm inflation with an oscillatory inflaton in the non-minimal kinetic coupling model

In the cold inflation scenario, the slow roll inflation and reheating via coherent rapid oscillation, are usually considered as two distinct eras. When the slow roll ends, a rapid oscillation phase begins and the inflaton decays to relativistic particles reheating the Universe. In another model dubbed warm inflation, the rapid oscillation phase is suppressed, and we are left with only a slow roll period during which the reheating occurs. Instead, in this paper, we propose a new picture for inflation in which the slow roll era is suppressed and only the rapid oscillation phase exists. Radiation generation during this era is taken into account, so we have warm inflation with an oscillatory inflaton. To provide enough e-folds, we employ the non-minimal derivative coupling model. We study the cosmological perturbations and compute the temperature at the end of warm oscillatory inflation.Comment: 22 pages, typos fixed, accepted by EPJ

Proper Motions of Sunspots' Umbral Dots at High Temporal and Spatial Resolution

To deepen the analysis of the photometric properties of the umbra of a sunspot, we study proper motions of small features such as umbral dots (UDs) inside a single sunspot observed by the Solar Optical Telescope of Hinode close to the disk center. We consider horizontal flows with high precision and details to study the transient motion behavior of UDs in short time intervals. Blue continuum images were first deconvolved with the point-spread function, such that the stray light is precisely removed and the original resolution is improved. Several images were co-added to improve the signal-to-noise ratio, keeping a reasonable temporal resolution and checking that the results are reproducible. The Fourier local correlation tracking technique is applied to the new corrected time sequence of images, and horizontal velocity maps were obtained both for the whole umbra and for a high-resolution small region of the umbra to study the smallest details of the velocity fields. We used two different Gaussian tracking windows (0.8arcsec and 0.2arcsec), which reveals two types of horizontal motions for umbral features. First, a global inner penumbra and peripheral umbra inward motion directed to the central parts is revealed as an overall proper motion of bright peripheral fine structures. Second, motions matching small cells inside the darkest parts of the umbra with apparent sink and source areas are revealed, suggesting possible upflows and downflows appearing in different bright and dark locations without a definite answer regarding their brightness identification with a convective or a buoyant cell

Connectivity of pseudomanifold graphs from an algebraic point of view

The connectivity of graphs of simplicial and polytopal complexes is a classical subject going back at least to Steinitz, and the topic has since been studied by many authors, including Balinski, Barnette, Athanasiadis and Bjorner. In this note, we provide a unifying approach which allows us to obtain more general results. Moreover, we provide a relation to commutative algebra by relating connectivity problems to graded Betti numbers of the associated Stanley--Reisner rings.Comment: 4 pages, minor change