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Recent findings show that single, non-neuronal cells are also able to learn signalling responses developing cellular memory. In cellular learning nodes of signalling networks strengthen their interactions e.g. by the conformational memory of intrinsically disordered proteins, protein translocation, miRNAs, lncRNAs, chromatin memory and signalling cascades. This can be described by a generalized, unicellular Hebbian learning process, where those signalling connections, which participate in learning, become stronger. Here we review those scenarios, where cellular signalling is not only repeated in a few times (when learning occurs), but becomes too frequent, too large, or too complex and overloads the cell. This leads to desensitisation of signalling networks by decoupling signalling components, receptor internalization, and consequent downregulation. These molecular processes are examples of anti-Hebbian learning and forgetting of signalling networks. Stress can be perceived as signalling overload inducing the desensitisation of signalling pathways. Aging occurs by the summative effects of cumulative stress downregulating signalling. We propose that cellular learning desensitisation, stress and aging may be placed along the same axis of more and more intensive (prolonged or repeated) signalling. We discuss how cells might discriminate between repeated and unexpected signals, and highlight the Hebbian and anti-Hebbian mechanisms behind the fold-change detection in the NF-\k{appa}B signalling pathway. We list drug design methods using Hebbian learning (such as chemically-induced proximity) and clinical treatment modalities inducing (cancer, drug allergies) desensitisation or avoiding drug-induced desensitisation. A better discrimination between cellular learning, desensitisation and stress may open novel directions in drug design, e.g., helping to overcome drug-resistance., Comment: 19 pages, 4 figures

Hexapeptides are increasingly applied as model systems for studying the amyloidogenecity properties of oligo- and polypeptides. It is possible to construct 64 million different hexapeptides from the twenty proteinogenic amino acid residues. Today's experimental amyloid databases contain only a fraction of these annotated hexapeptides. For labeling all the possible hexapeptides as "amyloidogenic" or "non-amyloidogenic" there exist several computational predictors with good accuracies. It may be of interest to define and study a simple graph structure on the 64 million hexapeptides as nodes when two hexapeptides are connected by an edge if they differ by only a single residue. For example, in this graph, HIKKLM is connected to AIKKLM, or HIKKNM, or HIKKLC, but it is not connected with an edge to VVKKLM or HIKNPM. In the present contribution, we consider our previously published artificial intelligence-based tool, the Budapest Amyloid Predictor (BAP for short), and demonstrate a spectacular property of this predictor in the graph defined above. We show that for any two hexapeptides predicted to be "amyloidogenic" by the BAP predictor, there exists an easily constructible path of length at most 6 that passes through neighboring hexapeptides all predicted to be "amyloidogenic" by BAP. For example, the predicted amyloidogenic ILVWIW and FWLCYL hexapeptides can be connected through the length-6 path ILVWIW-IWVWIW-IWVCIW-IWVCIL-FWVCIL-FWLCIL-FWLCYL in such a way that the neighbors differ in exactly one residue, and all hexapeptides on the path are predicted to be amyloidogenic by BAP. The symmetric statement also holds for non-amyloidogenic hexapeptides. It is noted that the mentioned property of the Budapest Amyloid Predictor \url{https://pitgroup.org/bap} is not proprietary; it is also true for any linear Support Vector Machine (SVM)-based predictors.

We apply a recently developed 2+1+1 decomposition of spacetime, based on a nonorthogonal double foliation for the study of spherically symmetric, static black hole solutions of Horndeski scalar-tensor theory. Our discussion proceeds in an effective field theory (EFT) of modified gravity approach, with the action depending on metric and embedding scalars adapted to the nonorthogonal 2+1+1 decomposition. We prove that the most generic class of Horndeski Lagrangians compatible with observations can be expressed in this EFT form. By studying the first order perturbation of the EFT action we derive three equations of motion, which reduce to those derived earlier in an orthogonal 2+1+1 decomposition, and a fourth equation for the metric parameter N related to the nonorthogonality of the foliation. For the Horndeski class of theories with vanishing $G_3$ and $G_5$, but generic functions $G_2(\phi,X)$ (k-essence) and $G_4(\phi)$ (nonminimal coupling to the metric) we prove the unicity theorem that no action beyond Einstein--Hilbert allows for the Schwarzschild solution. Next we integrate the EFT field equations for the case with only one independent metric function obtaining new solutions characterized by a parameter interpreted as either mass or tidal charge, the cosmological constant and a third parameter. These solutions represent naked singularities, black holes with scalar hair or have the double horizon structure of the Schwarzschild--de Sitter spacetime. Solutions with homogeneous Kantowski--Sachs type regions also emerge. Finally, one of the solutions obtained for the function $G_4$ linear in the curvature coordinate, in certain parameter range exhibits an intriguing logarithmic singularity lying outside the horizon. The newly derived hairy black hole solutions evade previously known unicity theorems by being asymptotically nonflat, even in the absence of the cosmological constant., Comment: 20 pages, 4 figures

Based on the secular spin evolution of black holes, neutron stars, gravastars, or boson stars in precessing compact binaries on eccentric orbit, we identify the aligned and more generic coplanar configurations of the spins and orbital angular momentum as fix points. Through a dynamical system analysis, we investigate their linear stability as function of the mass quadrupole parameter. Marginal stability holds for the binary configurations with both spins antialigned to the orbital angular momentum, for both spins aligned to the orbital angular momentum (with the exception of certain quadrupolar parameter ranges of neutron stars and boson stars), and for the extremal mass ratio. For equal masses, the configurations of one of the spins aligned and the other antialigned is stable for gravastar binaries, for neutron star binaries in the high quadrupolar parameter range, and for boson star binaries. For some unequal mass gravastar binaries, black hole binaries or neutron star binaries, a transition from stability to instability can occur during the inspiral, when one of the spins is aligned, while the other is antialigned to the orbital angular momentum. We discover a transitional instability regime during the inspiral of certain gravastar, neutron star, or boson star binaries with opposing spins. For coplanar configurations we find instabilities only for the gravastar - gravastar, boson star - boson star and black hole - boson star binaries. For a given spin configuration, marginal stability strongly depends on the value of the quadrupolar parameters. The stability region is larger for neutron star binaries than for black hole binaries, while the mixed systems have a restricted stability parameter region., Comment: 14 pages, 7 figures

We discuss precessing compact binaries on eccentric orbit with gravastar, black hole, neutron star, or boson star components. We derive secular evolution equations to second post-Newtonian--order accuracy, with leading-order spin-orbit, spin-spin, and mass quadrupole-monopole contributions. The emerging closed system of first-order differential equations evolves the pairs of polar and azimuthal angles of the spin and orbital angular momentum vectors together with the periastron angle. The secular dynamics is autonomous. We confirm numerically, that secular evolutions look like smoothed-out instantaneous evolutions over timescales where radiation reaction is negligible. The secular evolution of the spin polar angles and the difference of their azimuthal angles generates a closed subsystem. We study analytically this system for the particular cases of one spin dominating over the other and for black hole - boson star binaries of equal masses. In the first case known large flip-flops of the smaller spin are reproduced, when the larger spin is almost coplanar with the orbit. We also find new, quadrupole-induced flip-flops occurring when the neutron star with dominant spin has a quadrupolar parameter $w_1\approx 3$. Finally we analyze the evolutions of the spin angles numerically by comparing the cases when the black hole companion is either a gravastar, another black hole or a boson star with identical mass. We find that both the amplitude and period of the flip-flop are the largest, when the companion is a black hole. In the case of a boson star companion the frequency of the flip-flop increases significantly. Further, while in the case of gravastars and black holes a swinging-type azimuthal evolution occurs, with the spins of the components periodically overpassing each other, their sequence is conserved when the companion is a boson star., Comment: 24 pages, 6 figures

Hexapeptides are widely applied as a model system for studying amyloid-forming properties of polypeptides, including proteins. Recently, large experimental databases have become publicly available with amyloidogenic labels. Using these datasets for training and testing purposes, one may build artificial intelligence (AI)-based classifiers for predicting the amyloid state of peptides. In our previous work (Biomolecules, 11(4) 500, (2021)) we described the Support Vector Machine (SVM)-based Budapest Amyloid Predictor (\url{https://pitgroup.org/bap}). Here we apply the Budapest Amyloid Predictor for discovering numerous amyloidogenic and non-amyloidogenic hexapeptide patterns with accuracy between 80\% and 84\%, as surprising and succinct novel rules for further understanding the amyloid state of peptides. For example, we have shown that for any independently mutated residue (position marked by ``x''), the patterns CxFLWx, FxFLFx, or xxIVIV are predicted to be amyloidogenic, while those of PxDxxx, xxKxEx, and xxPQxx non-amyloidogenic at all. We note that each amyloidogenic pattern with two x's (e.g.,CxFLWx) describes succinctly $20^2=400$ hexapeptides, while the non-amyloidogenic patterns comprising four point mutations (e.g.,PxDxxx) gives $20^4=160,000$ hexapeptides in total. To our knowledge, no similar applications of artificial intelligence tools or succinct amyloid patterns were described before the present work.

Determining important vertices in large graphs (e.g., Google's PageRank in the case of the graph of the World Wide Web) facilitated the construction of excellent web search engines, returning the most important hits corresponding to the submitted user queries. Interestingly, finding important edges -- instead of vertices -- in large graphs has received much less attention until now. Here we examine the human structural braingraph (or connectome), identified by diffusion magnetic resonance imaging (dMRI) methods, with edges connecting cortical and subcortical gray matter areas and weighted by fiber strengths, measured by the number of the discovered fiber tracts along the edge. We identify several "single" important edges in these braingraphs, whose high or low weights imply the sex or the age of the subject observed. We call these edges implicator edges since solely from their weight, one can infer the sex of the subject with more than 67 \% accuracy or their age group with more than 62\% accuracy. We argue that these brain connections are the most important ones characterizing the sex or the age of the subjects. Surprisingly, the edges implying the male sex are mostly located in the anterior parts of the brain, while those implying the female sex are mostly in the posterior regions. Additionally, most of the inter-hemispheric implicator edges are male ones, while the intra-hemispheric ones are predominantly female edges. Our pioneering method for finding the sex- or age implicator edges can also be applied for characterizing other biological and medical properties, including neurodegenerative- and psychiatric diseases besides the sex or the age of the subject, if large and high-quality neuroimaging datasets become available.

The amyloid state of proteins is widely studied with relevancy in neurology, biochemistry, and biotechnology. In contrast with amorphous aggregation, the amyloid state has a well-defined structure, consisting of parallel and anti-parallel $\beta$-sheets in a periodically repeated formation. The understanding of the amyloid state is growing with the development of novel molecular imaging tools, like cryogenic electron microscopy. Sequence-based amyloid predictors were developed by using mostly artificial neural networks (ANNs) as the underlying computational techniques. From a good neural network-based predictor, it is a very difficult task to identify those attributes of the input amino acid sequence, which implied the decision of the network. Here we present a Support Vector Machine (SVM)-based predictor for hexapeptides with correctness higher than 84\%, i.e., it is at least as good as the published ANN-based tools. Unlike the artificial neural networks, the decision of the SVMs are much easier to analyze, and from a good predictor, we can infer rich biochemical knowledge. Availability and Implementation: The Budapest Amyloid Predictor webserver is freely available at https://pitgroup.org/bap.

Gaussian blurring is a well-established method for image data augmentation: it may generate a large set of images from a small set of pictures for training and testing purposes for Artificial Intelligence (AI) applications. When we apply AI for non-imagelike biological data, hardly any related method exists. Here we introduce the "Newtonian blurring" in human braingraph (or connectome) augmentation: Started from a dataset of 1053 subjects, we first repeat a probabilistic weighted braingraph construction algorithm 10 times for describing the connections of distinct cerebral areas, then take 7 repetitions in every possible way, delete the lower and upper extremes, and average the remaining 7-2=5 edge-weights for the data of each subject. This way we augment the 1053 graph-set to 120 x 1053 = 126,360 graphs. In augmentation techniques, it is an important requirement that no artificial additions should be introduced into the dataset. Gaussian blurring and also this Newtonian blurring satisfy this goal. The resulting dataset of 126,360 graphs, each in 5 resolutions (i.e., 631,800 graphs in total), is freely available at the site https://braingraph.org/cms/download-pit-group-connectomes/. Augmenting with Newtonian blurring may also be applicable in other non-image related fields, where probabilistic processing and data averaging are implemented.

The 2+1+1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double foliation has been employed in the framework of dark matter and dark energy motivated scalar-tensor gravitational theories for the discussion of the odd sector perturbations of spherically symmetric gravity. For the even sector however the perpendicularity has to be suppressed in order to allow for suitable gauge freedom, recovering the 10th metric variable. The 2+1+1 decomposition of the Einstein-Hilbert action leads to the identification of the canonical pairs, the Hamiltonian and momentum constraints. Hamiltonian dynamics is then derived via Poisson brackets., Comment: 7 pages, 1 figure, this article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications

We revisit the issue of the fluid description of minimally coupled scalar fields. While in a cosmological setup the interpretation of a time-evolving scalar field as a perfect fluid is well-understood, the situation is more intricate when the scalar field is static, but has a spatial gradient, a situation motivated by black hole perturbations in scalar-tensor theories. Then the scalar field is interpreted as either a particular imperfect fluid of type I or a superposition of a pair of leftgoing (incoming) and rightgoing (outgoing) null dusts with a perfect fluid. Finally, when the scalar gradient is null, it is equivalent to an imperfect fluid of type II, degenerating into null dust when the energy conditions are imposed. We also propose the suitable action in terms of the fluid pressure components for each case and discuss the variational principle for a generic class of minimally coupled scalar fields., Comment: 6 pages, to appear in Physical Review D

In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA, we present here a sample of what we view as particularly promising directions, based in part on the current research interests of the LISA scientific community in the area of fundamental physics. We organize these directions through a "science-first" approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics., Comment: 22 pages, 1 figure, to appear in General Relativity and Gravitation

For more than a decade now, we can discover and study thousands of cerebral connections with the application of diffusion magnetic resonance imaging (dMRI) techniques and the accompanying algorithmic workflow. While numerous connectomical results were published enlightening the relation between the braingraph and certain biological, medical, and psychological properties, it is still a great challenge to identify a small number of brain connections, closely related to those conditions. In the present contribution, by applying the 1200 Subjects Release of the Human Connectome Project (HCP), we identify just 102 connections out of the total number of 1950 connections in the 83-vertex graphs of 1065 subjects, which -- by a simple linear test -- precisely, without any error determine the sex of the subject. Very surprisingly, we were able to identify two graph edges out of these 102, if, whose weights, measured in fiber numbers, are all high, then the connectome always belongs to a female subject, independently of the other edges. Similarly, we have identified 3 edges from these 102, whose weights, if two of them are high and one is low, imply that the graph belongs to a male subject -- again, independently of the other edges. We call the former 2 edges superfeminine and the first two of the 3 edges supermasculine edges of the human connectome. Even more interestingly, one of the edges, connecting the right Pars Triangularis and the right Superior Parietal areas, is one of the 2 superfeminine edges, and it is also the third edge, accompanying the two supermasculine connections, if its weight is low; therefore it is also a "switching" connection.

We assemble a database of 12 dwarf galaxies, for which optical (R-band) and near-infrared ($3.6\mu m$) surface brightness density together with spectroscopic rotation curve data are available, in order to test the slowly rotating Bose-Einstein Condensate (srBEC) dark matter model. We aim to establish the angular velocity range compatible with observations, bounded from above by the requirement of finite size halos, to check the modelfits with the dataset, and the universality of the BEC halo parameter $\mathcal{R}$. We construct the spatial luminosity density of the stellar component of the dwarf galaxies based on their $3.6\mu m$ and R-band surface brightness profiles, assuming an axisymmetric baryonic mass distribution. We build up the gaseous component by employing a truncated disk model. We fit a baryonic plus dark matter combined model, parametrized by the M/L ratios of the baryonic components and parameters of the srBEC (the central density $\rho_c$, size of the static BEC halo $\mathcal{R}$, angular velocity $\omega$) to the rotation curves. The $3.6\mu m$ surface brightness of 6 galaxies indicates the presence of a bulge and a disk component. The shape of the $3.6\mu m$ and R-band spatial mass density profiles being similar is consistent with the stellar mass of the galaxies emerging wavelength-independent. The srBEC model fits the rotation curve of 11 galaxies out of 12 within $1\sigma$ significance level, with the average of $\mathcal{R}$ as 7.51 kpc and standard deviation of 2.96 kpc. This represents an improvement over the static BEC modelfit. For the well-fitting 11 galaxies the angular velocities allowing for a finite size srBEC halo are $<2.2\times 10^{-16}$ 1/s. For a scattering length of the BEC particle of $a\approx 10^6$ fm, the mass of the BEC particle is slightly better constrained than in the static case as $m\in[1.26\times10^{-17}\div3.08\times10^{-17}]$ eV/c$^2$., Comment: 9 pages, 4 tables, 5 figures, submitted to A&A

The dynamics of spinning test bodies, moving in rotating black hole (Kerr, Bardeen-like and Hayward-like) spacetimes, are investigated. In Kerr spacetime, all the spherical, zoom-whirl and unbound orbits are considered numerically. Along spherical orbits and for high spin, an amplitude modulation is found in the harmonic evolution of the spin precessional angular velocity, caused by the spin-curvature coupling. Along the discussed zoom-whirl and unbound orbits, the test body approaches the center so much that it passes through the ergosphere. Near and inside the ergosphere, the variation of the spin direction can be very rapid. The effects of the spin-curvature coupling is also investigated. The initial values are chosen such a way, that the body and its spin move in the equatorial plane of the coordinate space and of the comoving frame, respectively. Hence, a clear effect of the spin-curvature coupling is observed as the orbit and the spin vector leave the equatorial plane. Additional effects in the spin precessional angular velocity and in the evolution of the Boyer-Lindquist coordinate components of the spin vector is also considered. Finally, in case of different regular black holes, the spin-curvature coupling influences differently the orbit and the spin evolutions., Comment: 24 pages; 14 figures

We confront a non-relativistic Bose--Einstein Condensate (BEC) model of light bosons interacting gravitationally either through a Newtonian or a Yukawa potential with the observed rotational curves of $12$ dwarf galaxies. The baryonic component is modelled as an axisymmetric exponential disk and its characteristics are derived from the surface luminosity profile of the galaxies. The purely baryonic fit is unsatisfactory, hence a dark matter component is clearly needed. The rotational curves of five galaxies could be explained with high confidence level by the BEC model. For these galaxies, we derive: (i) upper limits for the allowed graviton mass; and (ii) constraints on a velocity-type and a density-type quantity characterizing the BEC, both being expressed in terms of the BEC particle mass, scattering length and chemical potential. The upper limit for the graviton mass is of the order of $10^{-26}$ $\text{eV/c}^2$, three orders of magnitude stronger than the limit derived from recent gravitational wave detections., Comment: 13 pages, 1 figure, 2 tables, published in Symmetry

Motivated by situations with temporal evolution and spatial symmetries both singled out, we develop a new 2+1+1 decomposition of spacetime, based on a nonorthogonal double foliation. Time evolution proceeds along the leaves of the spatial foliation. We identify the gravitational variables in the velocity phase-space as the 2-metric (induced on the intersection $\Sigma_{t\chi }$ of the hypersurfaces of the foliations), the 2+1 components of the spatial shift vector, together with the extrinsic curvature, normal fundamental form and normal fundamental scalar of $\Sigma _{t\chi }$, all constructed with the normal to the temporal foliation. This work generalizes a previous decomposition based on orthogonal foliations, a formalism lacking one metric variable, now reintroduced. The new metric variable is related to (i) the angle of a Lorentz-rotation between the nonorthogonal bases adapted to the foliations, and (ii) to the vorticity of these basis vectors. As a first application of the formalism, we work out the Hamiltonian dynamics of general relativity in terms of the variables identified as canonical, generalizing previous work. As a second application we present the unambiguous gauge-fixing suitable to discuss the even sector scalar-type perturbations of spherically symmetric and static spacetimes in generic scalar-tensor gravitational theories, which has been obstructed in the formalism of orthogonal double foliation., Comment: 16 pages, 4 figures, to appear in Phys. Rev. D

In this work we consider perturbations of homogeneous and hypersurface orthogonal cosmological backgrounds with local rotational symmetry (LRS), using a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds, of LRS class II, are characterised by that the vorticity, the twist of the 2-sheets, and the magnetic part of the Weyl tensor all vanish. They include the flat Friedmann universe as a special case. The matter contents of the perturbed spacetimes are given by vorticity-free perfect fluids, but otherwise the perturbations are arbitrary and describe gravitational, shear, and density waves. All the perturbation variables can be given in terms of the time evolution of a set of six harmonic coefficients. This set decouples into one set of four coefficients with the density perturbations acting as source terms, and another set of two coefficients describing damped source-free gravitational waves with odd parity. We also consider the flat Friedmann universe, which~has been considered by several others using the 1 + 3 covariant split, as a check of the isotropic limit. In agreement with earlier results we find a second-order wavelike equation for the magnetic part of the Weyl tensor which decouples from the density gradient for the flat Friedmann universes. Assuming vanishing vector perturbations, including the density gradient, we find a similar equation for the electric part of the Weyl tensor, which was previously unnoticed., Comment: 26 pages

We derive the conservative secular evolution of precessing compact binaries to second post-Newtonian order accuracy, with leading-order spin-orbit, spin-spin and mass quadrupole-monopole contributions included. The emerging closed system of first-order differential equations evolves the pairs of polar and azimuthal angles of the spin and orbital angular momentum vectors together with the periastron angle. In contrast with the instantaneous dynamics, the secular dynamics is autonomous. This secular dynamics reliably characterizes the system over timescales starting from a few times the radial period to several precessional periods, but less than the radiation reaction timescale. We numerically compare the instantaneous and secular evolutions and estimate the number of periods for which dissipation has no significant effect, e.g. the conservative timescale. We apply the analytic equations to study the spin flip-flop effect, recently found by numerical relativity methods. Our investigations show that the effect does not generalize beyond its original parameter settings, although we reveal distinct configurations exhibiting one half flip-flops. In addition, we find a flip-flopping evolution of the orbital angular momentum vector, which ventures from one pole to another through several precessional periods. This is a new effect, occurring for mass ratios much less than one., Comment: 24 pages, 10 figure panels, figure resolution downscaled for arXiv version, LIGO document P1600207

We assemble a database of 15 HSB and 15 LSB galaxies, for which surface brightness density and spectroscopic rotation curve data are both available and representative for various morphologies. We use this dataset to test the Navarro-Frenk-White, the Einasto, and the pseudo-isothermal sphere dark matter (DM) models. We investigate the compatibility of the pure baryonic model and baryonic plus one of the three DM models with observations on the assembled galaxy database. When a DM component improves the fit with the spectroscopic rotational curve, we rank the models according to the goodness of fit to the datasets. We constructed the spatial luminosity density of the baryonic component based on the surface brightness profile of the galaxies. We estimated the mass-to-light (M/L) ratio of the stellar component through a previously proposed color-mass-to-light ratio relation (CMLR). We assumed an axissymetric baryonic mass model with variable axis ratios together with one of the three DM models to provide the theoretical rotational velocity curves, and we compared them with the dataset. In a second attempt, we addressed the question whether the dark component could be replaced by a pure baryonic model with fitted M/L ratios. We employed the Akaike information criterion (AIC) to establish the performance of the best-fit models. For 7 galaxies, neither model fits the dataset within the 1{\sigma} confidence level. For the other 23 cases, one of the models with DM explains the rotation curve data best. According to the AIC, the PSE emerges as most favored in 14 cases, followed by the NFW (6 cases) and the Einasto (3 cases) DM models. We find that the pure baryonic model with fitted M/L ratios falls within the 1{\sigma} confidence level for 10 HSB and 2 LSB galaxies, at the price of growing the M/Ls on average by a factor of two, but the fits are inferior compared to the best-fitting DM model., Comment: 14 pages, 5 figures, 8 tables. Accepted to publish in A&A

We consider cosmological tests of a scalar-vector-tensor gravitational model, in which the dark energy is included in the total action through a gauge invariant, electromagnetic type contribution. The ground state of dark energy, corresponding to a constant potential $V$ is a Bose-Einstein type condensate with spontaneously broken U(1) symmetry. In another words dark energy appears as a massive vector field emerging from a superposition of a massless vector and a scalar field, the latter corresponding to the Goldstone boson. Two particular cosmological models, corresponding to pure electric and pure magnetic type potentials, respectively are confronted with Type IA Supernovae and Hubble parameter data. In the electric case good fit is obtained along a narrow inclined stripe in the $\Omega _{m}-\Omega _{V}\,$ parameter plane, which includes the $\Lambda $CDM limit as the best fit. The other points on this admissible region represent superconducting dark energy as a sum of a cosmological constant and a time-evolving contribution. In the magnetic case the cosmological test selects either i) parameter ranges of the superconducting dark energy allowing for the standard baryonic plus dark matter or ii) a unified superconducting dark matter and dark energy model, additionally including only the baryonic sector., Comment: 12 pages, 10 figures

A general treatment of vorticity-free, perfect fluid perturbations of Kantowski-Sachs models with a positive cosmological constant are considered within the framework of the 1+1+2 covariant decomposition of spacetime. The dynamics is encompassed in six evolution equations for six harmonic coefficients, describing gravito-magnetic, kinematic and matter perturbations, while a set of algebraic expressions determine the rest of the variables. The six equations further decouple into a set of four equations sourced by the perfect fluid, representing forced oscillations and two uncoupled damped oscillator equations. The two gravitational degrees of freedom are represented by pairs of gravito-magnetic perturbations. In contrast with the Friedmann case one of them is coupled to the matter density perturbations, becoming decoupled only in the geometrical optics limit. In this approximation, the even and odd tensorial perturbations of the Weyl tensor evolve as gravitational waves on the anisotropic Kantowski-Sachs background, while the modes describing the shear and the matter density gradient are out of phase dephased by $\pi /2$ and share the same speed of sound.

The evolution of a closed Friedmann universe filled by a tachyon scalar field with a trigonometric potential and cold dark matter (CDM) is investigated. A subset of the evolutions consistent to 1$\sigma $ confidence level with the Union 2.1 supernova data set is identified. The evolutions of the tachyon field are classified. Some of them evolve into a de Sitter attractor, while others proceed through a pseudo-tachyonic regime into a sudden future singularity. Critical evolutions leading to Big Brake singularities in the presence of CDM are found and a new type of cosmological evolution characterized by singularity avoidance in the pseudo-tachyon regime is presented., Comment: 7 pages, 5 figures, to be published in Phys. Rev. D

We analyse the conservative evolution of spinning compact binaries to second post-Newtonian (2PN) order accuracy, with leading order spin-orbit, spin-spin and mass quadrupole-monopole contributions included. As a main result we derive a closed system of first order differential equations in a compact form, for a set of dimensionless variables encompassing both orbital elements and spin angles. These evolutions are constrained by conservation laws holding at 2PN order. As required by the generic theory of constrained dynamical systems we perform a consistency check and prove that the constraints are preserved by the evolution. We apply the formalism to show the existence of chameleon orbits, whose local, orbital parameters evolve from elliptic (in the Newtonian sense) near pericenter, towards hyperbolic at large distances. This behavior is consistent with the picture that General Relativity predicts stronger gravity at short distances than Newtonian theory does., Comment: to be published in Phys. Rev. D, 19 pages, 3 figure panels

A recently investigated tachyonic scalar field dark energy dominated universe exhibits a bivalent future: depending on initial parameters can run either into a de Sitter exponential expansion or into a traversable future soft singularity followed by a contraction phase. We also include in the model (i) a tiny amount of radiation, (ii) baryonic matter ($\Omega _{b}h^{2}=0.022161$, where the Hubble constant is fixed as $h=0.706$) and (iii) cold dark matter (CDM). Out of a variety of six types of evolutions arising in a more subtle classification, we identify two in which in the past the scalar field effectively degenerates into a dust (its pressure drops to an insignificantly low negative value). These are the evolutions of type IIb converging to de Sitter and type III hitting the future soft singularity. We confront these background evolutions with various cosmological tests, including the supernova type Ia Union 2.1 data, baryon acoustic oscillation distance ratios, Hubble parameter-redshift relation and the cosmic microwave background (CMB) acoustic scale. We determine a subset of the evolutions of both types which at 1$\sigma $ confidence level are consistent with all of these cosmological tests. At perturbative level we derive the CMB temperature power spectrum to find the best agreement with the Planck data for $\Omega _{CDM}=0.22$. The fit is as good as for the $\Lambda $CDM model at high multipoles, but the power remains slightly overestimated at low multipoles, for both types of evolutions. The rest of the CDM is effectively generated by the tachyonic field, which in this sense acts as a combined dark energy and dark matter model., Comment: 25 pages, 15 figures

We present a comparative confrontation of both the Bose-Einstein Condensate (BEC) and the Navarro-Frenk-White (NFW) dark halo models with galactic rotation curves. We employ 6 High Surface Brightness (HSB), 6 Low Surface Brightness (LSB), and 7 dwarf galaxies with rotation curves falling into two classes. In the first class rotational velocities increase with radius over the observed range.The BEC and NFW models give comparable fits for HSB and LSB galaxies of this type, while for dwarf galaxies the fit is significantly better with the BEC model. In the second class the rotational velocity of HSB and LSB galaxies exhibits long flat plateaus, resulting in better fit with the NFW model for HSB galaxies and comparable fits for LSB galaxies. We conclude that due to its central density cusp avoidance the BEC model fits better dwarf galaxy dark matter distribution. Nevertheless it suffers from sharp cutoff in larger galaxies, where the NFW model performs better. The investigated galaxy sample obeys the Tully-Fisher relation, including the particular characteristics exhibited by dwarf galaxies. In both models the fitting enforces a relation between dark matter parameters: the characteristic density and the corresponding characteristic distance scale with an inverse power., Comment: published version

We discuss the origin of the low-energy cutoff, or LEC, seen in the radio spectra of many extragalactic jets and relate this to the spin of the supermassive black holes that presumably power them. Pion decay via proton-proton collisions is a possible mechanism to supply a secondary positron population with a low energy limit. We expect that pion production would occur in advection dominated accretion flows or ADAFs. In radiatively inefficient ADAFs the heat energy of the accreting gas is unable to radiate in less than the accretion time and the particle temperature could be high enough so that thermal protons can yield such pion production. Strong starbursts are another option for the injection of a truncated particle population into the jet. The role of both mechanisms is discussed with respect to the black hole spin estimate. The energy demanded to produce the pion decay process involves a minimum threshold for kinetic energy of the interacting protons. Therefore the mean proton speed in the flow can determine whether a LEC is generated. In ADAFs the random velocity of the protons can exceed the minimum speed limit of pion production around the jet launching region in the innermost part of the flow. Finally we summarize the additional work needed to put the model assumptions on a more rigorous basis.

The study of the rotation curves of spiral galaxies reveals a nearly constant cored density distribution of Cold Dark Matter. N-body simulations however lead to a cuspy distribution on the galactic scale, with a central peak. A Bose-Einstein condensate (BEC) of light particles naturally solves this problem by predicting a repulsive force, obstructing the formation of the peak. After succinctly presenting the BEC model, we test it against rotation curve data for a set of 3 High Surface Brightness (HSB), 3 Low Surface Brightness (LSB) and 3 dwarf galaxies. The BEC model gives a similar fit to the Navarro-Frenk-White (NFW) dark matter model for all HSB and LSB galaxies in the sample. For dark matter dominated dwarf galaxies the addition of the BEC component improved more upon the purely baryonic fit than the NFW component. Thus despite the sharp cut-off of the halo density, the BEC dark matter candidate is consistent with the rotation curve data of all types of galaxies., Comment: 25 pages, 3 figure panels, 4 tables. Chapter 6 of "Recent Development in Dark Matter Research", Eds. N. Kinjo, A. Nakajima, Nova Science Publishers (2014)