Pulsar binary systems in a nonsymmetric theory of gravitation II. Dipole radiation

This paper deals with the emission of gravitational radiation in the context of a previously studied metric nonsymmetric theory of gravitation. The part coming from the symmetric part of the metric coincides with the mass quadrupole moment result of general relativity. The one associated to the antisymmetric part of the metric involves the dipole moment of the fermionic charge of the system. The results are applied to binary star systems and the decrease of the period of the elliptical motion is calculated.

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

Dynamical Chern-Simons gravity is an extension of general relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard general relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.

Quasinormal modes of black holes in anti-de Sitter space: A numerical study of the eikonal limit

Using series solutions and time-domain evolutions, we probe the eikonal limit of the gravitational and scalar-field quasinormal modes of large black holes and black branes in anti-de Sitter backgrounds. These results are particularly relevant for the AdS/CFT correspondence, since the eikonal regime is characterized by the existence of long-lived modes which (presumably) dominate the decay time scale of the perturbations. We confirm all the main qualitative features of these slowly damped modes as predicted by Festuccia and Liu [G. Festuccia and H. Liu, arXiv:0811.1033.] for the scalar-field (tensor-type gravitational) fluctuations. However, quantitatively we find dimensional-dependent correction factors. We also investigate the dependence of the quasinormal mode frequencies on the horizon radius of the black hole (brane) and the angular momentum (wave number) of vector- and scalar-type gravitational perturbations.

Dynamics and constraints of the massive graviton dark matter flat cosmologies

We discuss the dynamics of the Universe within the framework of the massive graviton cold dark matter scenario (MGCDM) in which gravitons are geometrically treated as massive particles. In this modified gravity theory, the main effect of the gravitons is to alter the density evolution of the cold dark matter component in such a way that the Universe evolves to an accelerating expanding regime, as presently observed. Tight constraints on the main cosmological parameters of the MGCDM model are derived by performing a joint likelihood analysis involving the recent supernovae type Ia data, the cosmic microwave background shift parameter, and the baryonic acoustic oscillations as traced by the Sloan Digital Sky Survey red luminous galaxies. The linear evolution of small density fluctuations is also analyzed in detail. It is found that the growth factor of the MGCDM model is slightly different (similar to 1-4%) from the one provided by the conventional flat Lambda CDM cosmology. The growth rate of clustering predicted by MGCDM and Lambda CDM models are confronted to the observations and the corresponding best fit values of the growth index (gamma) are also determined. By using the expectations of realistic future x-ray and Sunyaev-Zeldovich cluster surveys we derive the dark matter halo mass function and the corresponding redshift distribution of cluster-size halos for the MGCDM model. Finally, we also show that the Hubble flow differences between the MGCDM and the Lambda CDM models provide a halo redshift distribution departing significantly from the those predicted by other dark energy models. These results suggest that the MGCDM model can observationally be distinguished from Lambda CDM and also from a large number of dark energy models recently proposed in the literature.

Equation of state for the magnetic-color-flavor-locked phase and its implications for compact star models

Using the solutions of the gap equations of the magnetic-color-flavor-locked (MCFL) phase of paired quark matter in a magnetic field, and taking into consideration the separation between the longitudinal and transverse pressures due to the field-induced breaking of the spatial rotational symmetry, the equation of state of the MCFL phase is self-consistently determined. This result is then used to investigate the possibility of absolute stability, which turns out to require a field-dependent ""bag constant"" to hold. That is, only if the bag constant varies with the magnetic field, there exists a window in the magnetic field vs bag constant plane for absolute stability of strange matter. Implications for stellar models of magnetized (self-bound) strange stars and hybrid (MCFL core) stars are calculated and discussed.

Constraints on cold dark matter accelerating cosmologies and cluster formation

We discuss the properties of homogeneous and isotropic flat cosmologies in which the present accelerating stage is powered only by the gravitationally induced creation of cold dark matter (CCDM) particles (Omega(m) = 1). For some matter creation rates proposed in the literature, we show that the main cosmological functions such as the scale factor of the universe, the Hubble expansion rate, the growth factor, and the cluster formation rate are analytically defined. The best CCDM scenario has only one free parameter and our joint analysis involving baryonic acoustic oscillations + cosmic microwave background (CMB) + SNe Ia data yields (Omega) over tilde = 0.28 +/- 0.01 (1 sigma), where (Omega) over tilde (m) is the observed matter density parameter. In particular, this implies that the model has no dark energy but the part of the matter that is effectively clustering is in good agreement with the latest determinations from the large- scale structure. The growth of perturbation and the formation of galaxy clusters in such scenarios are also investigated. Despite the fact that both scenarios may share the same Hubble expansion, we find that matter creation cosmologies predict stronger small scale dynamics which implies a faster growth rate of perturbations with respect to the usual Lambda CDM cosmology. Such results point to the possibility of a crucial observational test confronting CCDM with Lambda CDM scenarios through a more detailed analysis involving CMB, weak lensing, as well as the large-scale structure.

Kinematic constraints to the transition redshift from supernovae type Ia union data

The kinematic approach to cosmological tests provides direct evidence to the present accelerating stage of the Universe that does not depend on the validity of general relativity, as well as on the matter-energy content of the Universe. In this context, we consider here a linear two-parameter expansion for the decelerating parameter, q(z)=q(0)+q(1)z, where q(0) and q(1) are arbitrary constants to be constrained by the union supernovae data. By assuming a flat Universe we find that the best fit to the pair of free parameters is (q(0),q(1))=(-0.73,1.5) whereas the transition redshift is z(t)=0.49(-0.07)(+0.14)(1 sigma) +0.54-0.12(2 sigma). This kinematic result is in agreement with some independent analyses and more easily accommodates many dynamical flat models (like Lambda CDM).

Nonsingular bounce in modified gravity

We investigate bouncing solutions in the framework of the nonsingular gravity model of Brandenberger, Mukhanov and Sornborger. We show that a spatially flat universe filled with ordinary matter undergoing a phase of contraction reaches a stage of minimal expansion factor before bouncing in a regular way to reach the expanding phase. The expansion can be connected to the usual radiation-and matter-dominated epochs before reaching a final expanding de Sitter phase. In general relativity (GR), a bounce can only take place provided that the spatial sections are positively curved, a fact that has been shown to translate into a constraint on the characteristic duration of the bounce. In our model, on the other hand, a bounce can occur also in the absence of spatial curvature, which means that the time scale for the bounce can be made arbitrarily short or long. The implication is that constraints on the bounce characteristic time obtained in GR rely heavily on the assumed theory of gravity. Although the model we investigate is fourth order in the derivatives of the metric (and therefore unstable vis-a-vis the perturbations), this generic bounce dynamics should extend to string-motivated nonsingular models which can accommodate a spatially flat bounce.

Physical approximations for the nonlinear evolution of perturbations in inhomogeneous dark energy scenarios

The abundance and distribution of collapsed objects such as galaxy clusters will become an important tool to investigate the nature of dark energy and dark matter. Number counts of very massive objects are sensitive not only to the equation of state of dark energy, which parametrizes the smooth component of its pressure, but also to the sound speed of dark energy, which determines the amount of pressure in inhomogeneous and collapsed structures. Since the evolution of these structures must be followed well into the nonlinear regime, and a fully relativistic framework for this regime does not exist yet, we compare two approximate schemes: the widely used spherical collapse model and the pseudo-Newtonian approach. We show that both approximation schemes convey identical equations for the density contrast, when the pressure perturbation of dark energy is parametrized in terms of an effective sound speed. We also make a comparison of these approximate approaches to general relativity in the linearized regime, which lends some support to the approximations.

Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to nonreflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the nonlinear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the nonaxisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.

Gravitational quasinormal modes of AdS black branes in d spacetime dimensions

The AdS/CFT duality has established a mapping between quantities in the bulk AdS black-hole physics and observables in a boundary finite-temperature field theory. Such a relationship appears to be valid for an arbitrary number of spacetime dimensions, extrapolating the original formulations of Maldacena`s correspondence. In the same sense properties like the hydrodynamic behavior of AdS black-hole fluctuations have been proved to be universal. We investigate in this work the complete quasinormal spectra of gravitational perturbations of d-dimensional plane-symmetric AdS black holes (black branes). Holographically the frequencies of the quasinormal modes correspond to the poles of two-point correlation functions of the field-theory stress-energy tensor. The important issue of the correct boundary condition to be imposed on the gauge-invariant perturbation fields at the AdS boundary is studied and elucidated in a fully d-dimensional context. We obtain the dispersion relations of the first few modes in the low-, intermediate- and high-wavenumber regimes. The sound-wave (shear-mode) behavior of scalar (vector)-type low- frequency quasinormal mode is analytically and numerically confirmed. These results are found employing both a power series method and a direct numerical integration scheme.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Expansió accelerada de l’univers i teories de gravetat modificada a grans escales

Estudi realitzat a partir d’una estada al Physics Department de la New York University, United States, Estats Units, entre 2006 i 2008. Una de les observacions de més impacte en la cosmologia moderna ha estat la determinació empírica que l’Univers es troba actualment en una fase d’Expansió Accelerada (EA). Aquest fenòmen implica que o bé l’Univers està dominat per un nou sector de matèria/energia, o bé la Relativitat General deixa de tenir validesa a escales cosmològiques. La primera possibilitat comprèn els models d’Energia Fosca (EF), i el seu principal problema és que l’EF ha de tenir propietats tan especials que es fan difícils de justificar teòricament. La segona possibilitat requereix la construcció de teories consistents de Gravetat Modificada a Grans Distàncies (GMGD), que són una generalització dels models de gravetat massiva. L’interès fenomenològic per aquestes teories també va resorgir amb l’aparició dels primers exemples de models de GMGD, com ara el model de Dvali, Gabadadze i Porrati (DGP), que consisteix en un tipus de brana en una dimensió extra. Malauradament, però, aquest model no permet explicar de forma consistent l’EA de l’Univers. Un dels objectius d’aquest projecte ha estat establir la viabilitat interna i fenomenològica dels models de GMGD. Des del punt de vista fenomenològic, ens hem centrat en la questió més important a la pràctica: trobar signatures observacionals que permetin distingir els models de GMGD dels d’EF. A nivell més teòric, també hem investigat el significat de les inestabilitats del model DGP.L’altre gran objectiu que ens vam proposar va ser la construcció de noves teories de GMGD. En la segona part d’aquest projecte, hem elaborat i mostrat la consistència del model “DGP en Cascada”, que generalitza el model DGP a més dimensions extra, i representa el segon model consistent i invariant-Lorentz a l’espai pla conegut. L’existència d’altres models de GMGD més enllà de DGP és de gran interès atès que podria permetre obtenir l’EA de l’Univers de forma purament geomètrica.

Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.

Dimensional reduction and gauge group reduction in Bianchi-type cosmology

In this paper we examine in detail the implementation, with its associated difficulties, of the Killing conditions and gauge fixing into the variational principle formulation of Bianchi-type cosmologies. We address problems raised in the literature concerning the Lagrangian and the Hamiltonian formulations: We prove their equivalence, make clear the role of the homogeneity preserving diffeomorphisms in the phase space approach, and show that the number of physical degrees of freedom is the same in the Hamiltonian and Lagrangian formulations. Residual gauge transformations play an important role in our approach, and we suggest that Poincaré transformations for special relativistic systems can be understood as residual gauge transformations. In the Appendixes, we give the general computation of the equations of motion and the Lagrangian for any Bianchi-type vacuum metric and for spatially homogeneous Maxwell fields in a nondynamical background (with zero currents). We also illustrate our counting of degrees of freedom in an appendix.