Anthropic versus cosmological solutions to the coincidence problem

In this paper we investigate possible solutions to the coincidence problem in flat phantom dark energy models with a constant dark energy equation of state and quintessence models with a linear scalar field potential. These models are representative of a broader class of cosmological scenarios in which the universe has a finite lifetime. We show that, in the absence of anthropic constraints, including a prior probability for the models inversely proportional to the total lifetime of the universe excludes models very close to the $\Lambda {\rm CDM}$ model. This relates a cosmological solution to the coincidence problem with a dynamical dark energy component having an equation of state parameter not too close to -1 at the present time. We further show, that anthropic constraints, if they are sufficiently stringent, may solve the coincidence problem without the need for dynamical dark energy.Comment: 7 pages, 7 figure

Layzer-Irvine equation: new perspectives and the role of interacting dark energy

We derive the Layzer-Irvine equation in the presence of a homogeneous (or quasi-homogeneous) dark energy component with an arbitrary equation of state. We extend the Layzer-Irvine equation to homogeneous and isotropic universes with an arbitrary number of dimensions and obtain the corresponding virial relation for sufficiently relaxed objects. We find analogous equations describing the dynamics of cosmic string loops and other p-branes of arbitrary dimensionality, discussing the corresponding relativistic and non-relativistic limits. Finally, we generalize the Layzer-Irvine equation to account for a non-minimal interaction between dark matter and dark energy, discussing its practical use as a signature of such an interaction.Comment: 4 page

Linear perturbations in K-mouflage cosmologies with massive neutrinos

We present a comprehensive derivation of linear perturbation equations for different matter species, including photons, baryons, cold dark matter, scalar fields, and massless and massive neutrinos in the presence of a generic conformal coupling. Starting from the Lagrangians, we show how the conformal transformation affects the dynamics. In particular, we discuss how to incorporate consistently the scalar coupling in the equations of the Boltzmann hierarchy for massive neutrinos and the subsequent fluid approximations. We use the recently proposed K-mouflage model as an example to demonstrate the numerical implementation of our linear perturbation equations. K-mouflage is a new mechanism to suppress the fifth force between matter particles induced by the scalar coupling, but in the linear regime the fifth force is unsuppressed and can change the clustering of different matter species in different ways. We show how the cosmic microwave background, lensing potential and matter power spectra are affected by the fifth force and find ranges of K-mouflage parameters whose effects could be seen observationally. We also find that the scalar coupling can have the nontrivial effect of shifting the amplitude of the power spectra of the lensing potential and density fluctuations in opposite directions, although both probe the overall clustering of matter. This paper can serve as a reference for those who work on generic coupled scalar field cosmology or those who are interested in the cosmological behavior of the K-mouflage model

Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces

The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion systemwith cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both u and v is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface

Cosmological tests of coupled Galileons

We investigate the cosmological properties of Galileon models which admit Minkowski space as a stable solution in vacuum. This is motivated by stable, positive tension brane world constructions that give rise to Galileons. We include both conformal and disformal couplings to matter and focus on constraints on the theory that arise because of these couplings. The disformal coupling to baryonic matter is extremely constrained by astrophysical and particle physics effects. The disformal coupling to photons induces a cosmological variation of the speed of light and therefore distorsions of the Cosmic Microwave Background spectrum which are known to be very small. The conformal coupling to baryons leads to a variation of particle masses since Big Bang Nucleosynthesis which is also tightly constrained. We consider the background cosmology of Galileon models coupled to Cold Dark Matter (CDM), photons and baryons and impose that the speed of light and particle masses respect the observational bounds on cosmological time scales. We find that requiring that the equation of state for the Galileon models must be close to -1 now restricts severely their parameter space and can only be achieved with a combination of the conformal and disformal couplings. This leads to large variations of particle masses and the speed of light which are not compatible with observations. As a result, we find that cosmological Galileon models are viable dark energy theories coupled to dark matter but their couplings, both disformal and conformal, to baryons and photons must be heavily suppressed making them only sensitive to CDM

Unravelling the path to create a cell sheet-based model of skin scar-like tissue

Regardless of the advances in understanding the mechanisms and the pathophysiology behind skin deformities, scaring continues to be an unsolved clinical problem. The underlying wound healing process involves a series of key cells which play different key roles. Fibroblasts are known to suffer the influence of local biochemical (e.g TGF-B1) and biomechanical signaling upon a wound scenario leading to a phenotypical change into myofibroblasts. The latter enhance immature extracellular matrix (ECM) synthesis and generate tensional forces that leads to ECM reorganization. Certain skin pathologies (e.g hypertrophic scars) rise from a dysfunction of this underlying regulatory mechanism which in turn drives myofibroblast persistence in the wound. When trying to study the mechanisms behind scarring human ex vivo samples are many times scarce and most of the current in vitro systems rely on standard 2D cultures of keloid/hypertrophic scar fibroblasts. Taking all of this into consideration we propose the use of cell sheet technology to create an in vitro 3D scar model. Herein we report the effect of TGF-B1 in human dermal fibroblast cell sheets as the first step to attain cell sheets with a myofibroblast-like phenotype in which cells are embedded in a scar-like ECM. To further strengthen our concept we performed the stacking of pre-formed cell sheets generating a cohesive 3D scar-like tissue. Human dermal fibroblast (hDFbs) cell sheets were produced as previously described1, and stimulated with TGF-B1 (10ng/ml) over 7, 14 and 21 days. Following phenotype and ECM characterization, cell sheets were stacked in order to obtain a 3D structure composed of 2 or 3 cell-sheets. The analysis of key genes (q-PCR) and proteins (Western blot and immunocytochemistry) showed that hDFbs cell sheets, when stimulated with TGF-B1 present an increased expression of a-SMA, fibronectin (FN) ED- A and FN ED-B, characteristic of a myofibroblast-like phenotype. When looking into the expression of scar ECM-associated proteins, hDFbs cell sheets obtained in the presence of TGF-B1 produced higher amounts of fibronectin and collagen I. Stable 3D constructs with a noticeable level of integration after a total of 21 days of culture, were further created upon stacking of the cell sheets obtained after 7days of culture in the presence of TGF-B1. In conclusion, this work suggested that it is possible to promote the secretion of scar-like ECM in hDFbs cell sheets due to phenotypic changes into myofibroblast-like cells when stimulated with TGF-B1. Cohesive 3D scar-like tissue structures were obtained which opens the possibility to develop a highly accurate in vitro 3D scar model to study underlying cellular mechanisms involved in the wound healing deregulation. Grant IF/00945/2014 funded by FCT/MCTES, Project “NORTE-08-5369-FSE-000044”, funded by Programa Operacional Norte 2020 Fundo Social Europeu, and GENE2SKIN Twinning Project, Horizon 2020, funded by the European Commissioninfo:eu-repo/semantics/publishedVersio

In vitro 3D cell sheet-based model for unraveling scar pathophysiology

Fibroblasts are key players in the scarring process. In hypertrophic scars, fibroblasts suffer phenotypical changes into myofibroblasts persisting in the wound under the influence of local biochemical (TGFb1) and biomechanical signaling leading to enhanced immature extracellular matrix (ECM) synthesis. Benchtop models of hypertrophic scars rely on scarce human ex vivo samples or standard 2D cultures of hypertrophic scar fibroblasts. We therefore propose the use of human dermal fibroblast cell sheets (hDFbsCS) as the first step to attain cell sheets with a myofibroblast-like phenotype to generate cohesive in vitro 3D scar-like tissues. hDFbsCS were produced as previously described (Cerqueira, 2014), and stimulated with TGFb1 up to 21 days. Following phenotype and ECM characterization, 3 hDFbsCS were stacked to obtain a 3D structure. Gene and protein analysis showed that upon TGFb1 stimulation, hDFbsCS present a higher expression of aSMA, fibronectin EDA and EDB, characteristic of amyofibroblast-like phenotype. Regarding the expression of scar ECM-associated proteins, TGFb1 stimulated hDFbsCS produced increased fibronectin and collagen I. Upon stacking of hDFbsCS obtained after 7 days of culture in the presence of TGFb1, stable and integrated 3D constructs were obtained. This work suggests that it is possible to create cohesive 3D scar-like tissue structures from hDFbsCS opening the possibility to develop in vitro 3D scar models to study wound healing deregulation pathophysiology. Acknowledgments: Grant IF.00945.2014 and SFRH.BD. 119756.2016 (FCT MCTES), NORTE.08.5369.FSE.000044 (funded by Programa Operacional Norte 2020 Fundo Social Europeu), GENE2SKIN Twinning Project, Horizon 2020 (European Commission).Grant IF.00945.2014 and SFRH.BD.119756.2016 (FCT_MCTES), NORTE.08.5369.FSE.000044 (funded by Programa_Operacional_Norte_2020 Fundo Social Europeu), GENE2SKIN Twinning Project, Horizon_2020 (European Commission).info:eu-repo/semantics/publishedVersio

Dominated Splitting and Pesin's Entropy Formula

Let $M$ be a compact manifold and $f:\,M\to M$ be a $C^1$ diffeomorphism on $M$. If $\mu$ is an $f$-invariant probability measure which is absolutely continuous relative to Lebesgue measure and for $\mu$ $a.\,\,e.\,\,x\in M,$ there is a dominated splitting $T_{orb(x)}M=E\oplus F$ on its orbit $orb(x)$, then we give an estimation through Lyapunov characteristic exponents from below in Pesin's entropy formula, i.e., the metric entropy $h_\mu(f)$ satisfies $$h_{\mu}(f)\geq\int \chi(x)d\mu,$$ where $\chi(x)=\sum_{i=1}^{dim\,F(x)}\lambda_i(x)$ and $\lambda_1(x)\geq\lambda_2(x)\geq...\geq\lambda_{dim\,M}(x)$ are the Lyapunov exponents at $x$ with respect to $\mu.$ Consequently, by using a dichotomy for generic volume-preserving diffeomorphism we show that Pesin's entropy formula holds for generic volume-preserving diffeomorphisms, which generalizes a result of Tahzibi in dimension 2

Entropy of semiclassical measures for nonpositively curved surfaces

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. We follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus on the main differences and refer the reader to (arXiv:0809.0230) for the details of analogous lemmas.Comment: 20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work (arXiv:0809.0230, version 2