arXiv subjects

Francisco S. N. Lobo

Publications and source records attributed to Francisco S. N. Lobo.

At least 217 records · Page 12Linked to original sources

arXiv2014

A Riccati equation based approach to isotropic scalar field cosmologies

Gravitationally coupled scalar fields $ϕ$, distinguished by the choice of an effective self-interaction potential $V(ϕ)$, simulating a temporarily non-vanishing cosmological term, can generate both inflation and late time acceleration. In scalar field cosmological models the evolution of the Hubble function is determined, in terms of the interaction potential, by a Riccati type equation. In the present work we investigate scalar field cosmological models that can be obtained as solutions of the Riccati evolution equation for the Hubble function. Four exact integrability cases of the field equations are presented, representing classes of general solutions of the Riccati evolution equation. The solutions correspond to cosmological models in which the Hubble function is proportional to the scalar field potential plus a linearly decreasing function of time, models with the time variation of the scalar field potential proportional to the potential minus its square, models in which the potential is the sum of an arbitrary function and the square of the function integral, and models in which the potential is the sum of an arbitrary function and the derivative of its square root, respectively. The cosmological properties of all models are investigated in detail, and it is shown that they can describe the inflationary or the late accelerating phase in the evolution of the Universe

gr-qc↗

arXiv2014

Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates

In this paper, the exact analytical solution of the Susceptible-Infected-Recovered (SIR) epidemic model is obtained in a parametric form. By using the exact solution we investigate some explicit models corresponding to fixed values of the parameters, and show that the numerical solution reproduces exactly the analytical solution. We also show that the generalization of the SIR model, including births and deaths, described by a nonlinear system of differential equations, can be reduced to an Abel type equation. The reduction of the complex SIR model with vital dynamics to an Abel type equation can greatly simplify the analysis of its properties. The general solution of the Abel equation is obtained by using a perturbative approach, in a power series form, and it is shown that the general solution of the SIR model with vital dynamics can be represented in an exact parametric form.

q-bio.PE↗

arXiv2014

Dark matter density profile and galactic metric in Eddington-inspired Born-Infeld gravity

We consider the density profile of pressureless dark matter in Eddington-inspired Born-Infeld (EiBI) gravity. The gravitational field equations are investigated for a spherically symmetric dark matter galactic halo, by adopting a phenomenological tangential velocity profile for test particles moving in stable circular orbits around the galactic center. The density profile and the mass distribution, as well as the general form of the metric tensor is obtained by numerically integrating the gravitational field equations, and in an approximate analytical form by using the Newtonian limit of the theory. In the weak field limit the dark matter density distribution is described by the Lane-Emden equation with polytropic index $n=1$, and is non-singular at the galactic center. The parameter $κ$ of the theory is determined so that that the theory could provide a realistic description of the dark matter halos. The gravitational properties of the dark matter halos are also briefly discussed in the Newtonian approximation.

gr-qc↗

arXiv2014

Arbitrary scalar field and quintessence cosmological models

The mechanism of the initial inflationary scenario of the universe and of its late-time acceleration can be described by assuming the existence of some gravitationally coupled scalar fields $ϕ$, with the inflaton field generating inflation and the quintessence field being responsible for the late accelerated expansion. Various inflationary and late-time accelerated scenarios are distinguished by the choice of an effective self-interaction potential $V(ϕ)$, which simulates a temporarily non-vanishing cosmological term. In this work, we present a new formalism for the analysis of scalar fields in flat isotropic and homogeneous cosmological models. The basic evolution equation of the models can be reduced to a first order non-linear differential equation. Approximate solutions of this equation can be constructed in the limiting cases of the scalar field kinetic energy and potential energy dominance, respectively, as well as in the intermediate regime. Moreover, we present several new accelerating and decelerating exact cosmological solutions, based on the exact integration of the basic evolution equation for scalar field cosmologies. More specifically, exact solutions are obtained for exponential, generalized cosine hyperbolic, and power law potentials, respectively. Cosmological models with power law scalar field potentials are also analyzed in detail.

gr-qc↗

arXiv2014

Energy conditions in modified gravity

We consider generalized energy conditions in modified theories of gravity by taking into account the further degrees of freedom related to scalar fields and curvature invariants. The latter are usually recast as generalized {\it geometrical fluids} that have different meanings with respect to the standard matter fluids generally adopted as sources of the field equations. More specifically, in modified gravity the curvature terms are grouped in a tensor $H^{ab}$ and a coupling $g(Ψ^i)$ that can be reorganized in effective Einstein field equations, as corrections to the energy-momentum tensor of matter. The formal validity of such inequalities does not assure some basic requirements such as the attractive nature of gravity, so that the energy conditions have to be considered in a wider sense.

gr-qc↗

arXiv2014

A class of exact solutions of the Liénard type ordinary non-linear differential equation

A class of exact solutions is obtained for the Liénard type ordinary non-linear differential equation. As a first step in our study the second order Liénard type equation is transformed into a second kind Abel type first order differential equation. With the use of an exact integrability condition for the Abel equation (the Chiellini lemma), the exact general solution of the Abel equation can be obtained, thus leading to a class of exact solutions of the Liénard equation, expressed in a parametric form. We also extend the Chiellini integrability condition to the case of the general Abel equation. As an application of the integrability condition the exact solutions of some particular Liénard type equations, including a generalized van der Pol type equation, are explicitly obtained.

math-ph↗

arXiv2013

The Cauchy problem in hybrid metric-Palatini f(X)-gravity

The well-formulation and the well-posedness of the Cauchy problem is discussed for {\it hybrid metric-Palatini gravity}, a recently proposed modified gravitational theory consisting of adding to the Einstein-Hilbert Lagrangian an $f(R)$ term constructed {\it à la} Palatini. The theory can be recast as a scalar-tensor one predicting the existence of a light long-range scalar field that evades the local Solar System tests and is able to modify galactic and cosmological dynamics, leading to the late-time cosmic acceleration. In this work, adopting generalized harmonic coordinates, we show that the initial value problem can always be {\it well-formulated} and, furthermore, can be {\it well-posed} depending on the adopted matter sources.

gr-qc↗

arXiv2013

Analytical solutions of the Riccati equation with coefficients satisfying integral or differential conditions with arbitrary functions

Ten new exact solutions of the Riccati equation $dy/dx=a(x)+b(x)y+c(x)y^{2}$ are presented. The solutions are obtained by assuming certain relations among the coefficients $a(x)$, $b(x)$ and $c(x)$ of the Riccati equation, in the form of some integral or differential expressions, also involving some arbitrary functions. By appropriately choosing the form of the coefficients of the Riccati equation, with the help of the conditions imposed on the coefficients, we obtain ten new integrability cases for the Riccati equation. For each case the general solution of the Riccati equation is also presented. The possibility of the application of the obtained mathematical results for the study of anisotropic general relativistic stellar models is also briefly considered.

math.CA↗

arXiv2013

Quadratic Palatini gravity and stable black hole remnants

We present a four-dimensional Planck-scale corrected quadratic extension of General Relativity (GR) where no a priori relation between metric and connection is imposed (Palatini formalism). Static spherically symmetric electrovacuum solutions are obtained in exact analytical form. The macroscopic properties of these solutions are in excellent agreement with GR, though the region around the central singularity is modified. In fact, the singularity is generically replaced by a wormhole supported by the electric field, which provides a non-trivial topology to the space-time. Moreover, for a certain charge-to-mass ratio the geometry is completely regular everywhere. For such regular solutions, the horizon disappears in the microscopic regime below a critical number of charges ($N<17$), yielding a set of massive objects that could be naturally identified as black hole remnants.

hep-th↗

arXiv2013

Planck scale physics and topology change through an exactly solvable model

We consider the collapse of a charged radiation fluid in a Planck-suppressed quadratic extension of General Relativity (GR) formulated à la Palatini. We obtain exact analytical solutions that extend the charged Vaidya-type solution of GR, which allows to explore in detail new physics at the Planck scale. Starting from Minkowski space, we find that the collapsing fluid generates wormholes supported by the electric field. We discuss the relevance of our findings in relation to the quantum foam structure of space-time and the meaning of curvature divergences in this theory.

hep-th↗

arXiv2013

A Chiellini type integrability condition for the generalized first kind Abel differential equation

The Chiellini integrability condition of the first order first kind Abel equation $dy/dx=f(x)y^2+g(x)y^3$ is extended to the case of the general Abel equation of the form $dy/dx=a(x)+b(x)y+f(x)y^{α-1}+g(x)y^α$, where $α\in \Re$, and $α> 1$. In the case $α=2$ the generalized Abel equations reduces to a Riccati type equation, for which a Chiellini type integrability condition is obtained.

nlin.SI↗

arXiv2013

Galactic rotation curves in hybrid metric-Palatini gravity

Generally, the dynamics of test particles around galaxies, as well as the corresponding mass deficit, is explained by postulating the existence of a hypothetical dark matter. In fact, the behavior of the rotation curves shows the existence of a constant velocity region, near the baryonic matter distribution, followed by a quick decay at large distances. In this work, we consider the possibility that the behavior of the rotational velocities of test particles gravitating around galaxies can be explained within the framework of the recently proposed hybrid metric-Palatini gravitational theory. The latter is constructed by modifying the metric Einstein-Hilbert action with an $f(R)$ term in the Palatini formalism. It was shown that the theory unifies local constraints and the late-time cosmic acceleration, even if the scalar field is very light. In the intermediate galactic scale, we show explicitly that in the hybrid metric-Palatini model the tangential velocity can be explicitly obtained as a function of the scalar field of the equivalent scalar-tensor description. The possibility of constraining the form of the scalar field and the parameters of the model by using the stellar velocity dispersions is also analyzed. Furthermore, the Doppler velocity shifts are also obtained in terms of the scalar field. All the physical and geometrical quantities and the numerical parameters in the hybrid metric-Palatini model can be expressed in terms of observable/measurable parameters, such as the tangential velocity, the baryonic mass of the galaxy, the Doppler frequency shifts, and the stellar dispersion velocity, respectively. Therefore, the obtained results open the possibility of testing the hybrid metric-Palatini gravitational models at the galactic or extra-galactic scale by using direct astronomical and astrophysical observations.

gr-qc↗

arXiv2013

Hybrid modified gravity unifying local tests, galactic dynamics and late-time cosmic acceleration

The non-equivalence between the metric and Palatini formalisms of $f(R)$ gravity is an intriguing feature of these theories. However, in the recently proposed hybrid metric-Palatini gravity, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed à la Palatini, the "true" gravitational field is described by the interpolation of these two non-equivalent approaches. The theory predicts the existence of a light long-range scalar field, which passes the local constraints and affects the galactic and cosmological dynamics. Thus, the theory opens new possibilities for a unified approach, in the same theoretical framework, to the problems of dark energy and dark matter, without distinguishing a priori matter and geometric sources, but taking their dynamics into account under the same standard.

gr-qc↗

arXiv2013

Further matters in space-time geometry: $f(R,T,R_{μν}T^{μν})$ gravity

We consider a gravitational model in which matter is non-minimally coupled to geometry, with the effective Lagrangian of the gravitational field being given by an arbitrary function of the Ricci scalar, the trace of the matter energy-momentum tensor, and the contraction of the Ricci tensor with the matter energy-momentum tensor. The field equations of the model are obtained in the metric formalism, and the equation of motion of a massive test particle is derived. In this type of models the matter energy-momentum tensor is generally not conserved, and this non-conservation determines the appearance of an extra-force acting on the particles in motion in the gravitational field. The Newtonian limit of the model is also considered, and an explicit expression for the extra-acceleration which depends on the matter density is obtained in the small velocity limit for dust particles. We also analyze in detail the so-called Dolgov-Kawasaki instability, and obtain the stability conditions of the model with respect to local perturbations. A particular class of gravitational field equations can be obtained by imposing the conservation of the energy-momentum tensor. We derive the corresponding field equations for the conservative case by using a Lagrange multiplier method, from a gravitational action that explicitly contains an independent parameter multiplying the divergence of the energy-momentum tensor. The cosmological implications of the model are investigated for both the conservative and non-conservative cases, and several classes of analytical solutions are obtained.

gr-qc↗

arXiv2013

Wormhole geometries in Eddington-inspired Born-Infeld gravity

Eddington-inspired Born-Infeld gravity (EiBI) gravity is a recently proposed modified theory of gravity, based on the classic work of Eddington and on Born-Infeld nonlinear electrodynamics. In this paper, we consider the possibility that wormhole geometries are sustained in EiBI gravity. We present the gravitational field equations for an anisotropic stress-energy tensor and consider the generic conditions, for the auxiliary metric, at the wormhole throat. In addition to this, we obtain an exact solution for an asymptotically flat wormhole.

gr-qc↗

arXiv2013

Cosmological anisotropy from non-comoving dark matter and dark energy

We consider a cosmological model in which the two major fluid components of the Universe, dark energy and dark matter, flow with distinct four-velocities. This cosmological configuration is equivalent to a single anisotropic fluid, expanding with a four-velocity that is an appropriate combination of the two fluid four-velocities. The energy density of the single cosmological fluid is larger than the sum of the energy densities of the two perfect fluids, i.e., dark energy and dark matter, respectively, and contains a correction term due to the anisotropy generated by the differences in the four-velocities. Furthermore, the gravitational field equations of the two-fluid anisotropic cosmological model are obtained for a Bianchi type I geometry. By assuming that the non-comoving motion of the dark energy and dark matter induces small perturbations in the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker type cosmological background, and that the anisotropy parameter is small, the equations of the cosmological perturbations due to the non-comoving nature of the two major components are obtained. The time evolution of the metric perturbations is explicitly obtained for the cases of the exponential and power law background cosmological expansion. Therefore, if there is a slight difference between the four-velocities of the dark energy and dark matter, the Universe would acquire some anisotropic characteristics, and its geometry will deviate from the standard FLRW one. In fact, the recent Planck results show that the presence of an intrinsic large scale anisotropy in the Universe cannot be excluded {\it a priori}, so that the model presented in this work can be considered as a plausible and viable working hypothesis.

gr-qc↗

arXiv2013

The virial theorem and the dark matter problem in hybrid metric-Palatini gravity

Hybrid metric-Palatini gravity is a recently proposed theory, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed à la Palatini. The theory predicts the existence of a long-range scalar field, which passes the Solar System observational constraints, even if the scalar field is very light, and modifies the cosmological and galactic dynamics. Thus, the theory opens new possibilities to approach, in the same theoretical framework, the problems of both dark energy and dark matter. In this work, we consider the generalized virial theorem in the scalar-tensor representation of the hybrid metric-Palatini gravity. More specifically, taking into account the relativistic collisionless Boltzmann equation, we show that the supplementary geometric terms in the gravitational field equations provide an effective contribution to the gravitational potential energy. We show that the total virial mass is proportional to the effective mass associated with the new terms generated by the effective scalar field, and the baryonic mass. This shows that the geometric origin in the generalized virial theorem may account for the well-known virial theorem mass discrepancy in clusters of galaxies. In addition to this, we also consider astrophysical applications of the model and show that the model predicts that the mass associated to the scalar field and its effects extend beyond the virial radius of the clusters of galaxies. In the context of the galaxy cluster velocity dispersion profiles predicted by the hybrid metric-Palatini model, the generalized virial theorem can be an efficient tool in observationally testing the viability of this class of generalized gravity models.

physics.gen-ph↗

arXiv2013

Semiclassical geons as solitonic black hole remnants

We find that the end state of black hole evaporation could be represented by non-singular and without event horizon stable solitonic remnants with masses of the order the Planck scale and up to 16 units of charge. Though these objects are locally indistinguishable from spherically symmetric, massive electric (or magnetic) charges, they turn out to be sourceless geons containing a wormhole generated by the electromagnetic field. Our results are obtained by interpreting semiclassical corrections to Einstein's theory in the first-order (Palatini) formalism, which yields second-order equations and avoids the instabilities of the usual (metric) formulation of quadratic gravity. We also discuss the potential relevance of these solutions for primordial black holes and the dark matter problem.

hep-th↗