Static, spherically symmetric solutions with a scalar field in Rastall gravity

Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except in a very special case. When a canonical scalar field is coupled to the gravity sector in this theory, new exact solutions appear for some values of the Rastall parameter $a$. Some of these solutions describe the same space-time geometry as the recently found solutions in the $k$-essence theory with a power function for the kinetic term of the scalar field. There is a large class of solutions (in particular, those describing wormholes and regular black holes) whose geometry coincides with that of solutions of GR coupled to scalar fields with nontrivial self-interaction potentials; the form of these potentials, however, depends on the Rastall parameter $a$. We also note that all solutions of GR with a zero trace of the energy-momentum tensor, including black-hole and wormhole ones, may be re-interpreted as solutions of Rastall's theory.Comment: Latex file, 18 pages. To fit published versio

A note on acoustic black holes in neo-Newtonian theory

Newtonian fluid dynamics allows the construction of acoustic metrics from which black hole configurations can be studied. However, relativistic pressure effects are neglected within Newtonian theory. We study acoustic black holes in the framework of neo-Newtonian hydrodynamics, which is designed to take into account relativistic inertial effects of the pressure $p$. Within this new hydrodynamical context we show how $p$ can influence the formation of the acoustic horizons.Comment: Latex file, 10 pages. Some discussions extended. Accepted for publication in MPL

Viscous Cosmology

We discuss the possibility to implement a viscous cosmological model, attributing to the dark matter component a behaviour described by bulk viscosity. Since bulk viscosity implies negative pressure, this rises the possibility to unify the dark sector. At the same time, the presence of dissipative effects may alleviate the so called small scale problems in the $\Lambda$CDM model. While the unified viscous description for the dark sector does not lead to consistent results, the non-linear behaviour indeed improves the situation with respect to the standard cosmological model.Comment: Latex file, 7 pages, 6 figures. To appear in the proceedings of the XIIth International Conference on Gravitation, Astrophysics and Cosmology, June 28-July 5, 2015, PFUR, Moscow, Russi

Rastall Cosmology and the \Lambda CDM Model

Rastall's theory is based on the non-conservation of the energy-momentum tensor. We show that, in this theory, if we introduce a two-fluid model, one component representing vacuum energy whereas the other pressureless matter (e.g. baryons plus cold dark matter), the cosmological scenario is the same as for the \Lambda CDM model, both at background and linear perturbative levels, except for one aspect: now dark energy may cluster. We speculate that this can lead to a possibility of distinguishing the models at the non-linear perturbative level.Comment: 9 pages, 1 figure. Accepted for publication in Physical Review

Observational constraints on Rastall's cosmology

Rastall's theory is a modification of General Relativity, based on the non-conservation of the stress-energy tensor. The latter is encoded in a parameter $\gamma$ such that $\gamma = 1$ restores the usual $\nabla_\nu T^{\mu\nu} = 0$ law. We test Rastall's theory in cosmology, on a flat Robertson-Walker metric, investigating a two-fluid model and using the type Ia supernovae Constitution dataset. One of the fluids is pressureless and obeys the usual conservation law, whereas the other is described by an equation of state $p_x = w_x\rho_x$, with $w_x$ constant. The Bayesian analysis of the Constitution set does not strictly constrain the parameter $\gamma$ and prefers values of $w_x$ close to -1. We then address the evolution of small perturbations and show that they are dramatically unstable if $w_x \neq -1$ and $\gamma \neq 1$, i.e. General Relativity is the favored configuration. The only alternative is $w_x = -1$, for which the dynamics becomes independent from $\gamma$.Comment: Latex file, 14 pages, 6 figures in eps format. Substantial modifications performed, main conclusions change

Disrupted Resting-State Functional Connectivity in Progressive Supranuclear Palsy

BACKGROUND AND PURPOSE: Studies on functional connectivity in progressive supranuclear palsy have been restricted to the thalamus and midbrain tegmentum. The present study aims to evaluate functional connectivity abnormalities of the subcortical structures in these patients. Functional connectivity will be correlated with motor and nonmotor symptoms of the disease. MATERIALS AND METHODS: Nineteen patients with progressive supranuclear palsy (mean age, 70.93 ± 5.19 years) and 12 age-matched healthy subjects (mean age, 69.17 ± 5.20 years) underwent multimodal MR imaging, including fMRI at rest, 3D T1-weighted imaging, and DTI. fMRI data were processed with fMRI of the Brain Software Library tools by using the dorsal midbrain tegmentum, thalamus, caudate nucleus, putamen, and pallidum as seed regions. RESULTS: Patients had lower functional connectivity than healthy subjects in all 5 resting-state networks, mainly involving the basal ganglia, thalamus, anterior cingulate, dorsolateral prefrontal and temporo-occipital cortices, supramarginal gyrus, supplementary motor area, and cerebellum. Compared with healthy subjects, patients also displayed subcortical atrophy and DTI abnormalities. Decreased thalamic functional connectivity correlated with clinical scores, as assessed by the Hoehn and Yahr Scale and by the bulbar and mentation subitems of the Progressive Supranuclear Palsy Rating Scale. Decreased pallidum functional connectivity correlated with lower Mini-Mental State Examination scores; decreased functional connectivity in the dorsal midbrain tegmentum network correlated with lower scores in the Frontal Assessment Battery. CONCLUSIONS: The present study demonstrates a widespread disruption of cortical-subcortical connectivity in progressive supranuclear palsy and provides further insight into the pathophysiologic mechanisms of motor and cognitive impairment in this condition

Scalar models for the generalized Chaplygin gas and the structure formation constraints

The generalized Chaplygin gas model represents an attempt to unify dark matter and dark energy. It is characterized by a fluid with an equation of state $p = - A/\rho^\alpha$. It can be obtained from a generalization of the DBI action for a scalar, tachyonic field. At background level, this model gives very good results, but it suffers from many drawbacks at perturbative level. We show that, while for background analysis it is possible to consider any value for $\alpha$, the perturbative analysis must be restricted to positive values of $\alpha$. This restriction can be circumvented if the origin of the generalized Chaplygin gas is traced back to a self-interacting scalar field, instead of the DBI action. But, in doing so, the predictions coming from formation of large scale structures reduce the generalized Chaplygin gas model to a kind of quintessence model, and the unification scenario is lost, if the scalar field is the canonical one. However, if the unification condition is imposed from the beginning as a prior, the model may remain competitive. More interesting results, concerning the unification program, are obtained if a non-canonical self-interacting scalar field, inspired by Rastall's theory of gravity, is imposed. In this case, an agreement with the background tests is possible.Comment: Latex file, 25 pages, 33 figures in eps format. New section on scalar models. Accepted for publication in Gravitation&Cosmolog

Disrupted Resting-State Functional Connectivity in Progressive Supranuclear Palsy

BACKGROUND AND PURPOSE: Studies on functional connectivity in progressive supranuclear palsy have been restricted to the thalamus and midbrain tegmentum. The present study aims to evaluate functional connectivity abnormalities of the subcortical structures in these patients. Functional connectivity will be correlated with motor and nonmotor symptoms of the disease. MATERIALS AND METHODS: Nineteen patients with progressive supranuclear palsy (mean age, 70.93 ± 5.19 years) and 12 age-matched healthy subjects (mean age, 69.17 ± 5.20 years) underwent multimodal MR imaging, including fMRI at rest, 3D T1-weighted imaging, and DTI. fMRI data were processed with fMRI of the Brain Software Library tools by using the dorsal midbrain tegmentum, thalamus, caudate nucleus, putamen, and pallidum as seed regions. RESULTS: Patients had lower functional connectivity than healthy subjects in all 5 resting-state networks, mainly involving the basal ganglia, thalamus, anterior cingulate, dorsolateral prefrontal and temporo-occipital cortices, supramarginal gyrus, supplementary motor area, and cerebellum. Compared with healthy subjects, patients also displayed subcortical atrophy and DTI abnormalities. Decreased thalamic functional connectivity correlated with clinical scores, as assessed by the Hoehn and Yahr Scale and by the bulbar and mentation subitems of the Progressive Supranuclear Palsy Rating Scale. Decreased pallidum functional connectivity correlated with lower Mini-Mental State Examination scores; decreased functional connectivity in the dorsal midbrain tegmentum network correlated with lower scores in the Frontal Assessment Battery. CONCLUSIONS: The present study demonstrates a widespread disruption of cortical-subcortical connectivity in progressive supranuclear palsy and provides further insight into the pathophysiologic mechanisms of motor and cognitive impairment in this condition