Showing papers on "Scalar field published in 2009"

Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors

Abstract: We extend to curved backgrounds all flat-space scalar field models that obey purely second-order equations, while maintaining their second-order dependence on both field and metric. This extension simultaneously restores to second order the, originally higher derivative, stress tensors as well. The process is transparent and uniform for all dimensions.

Zero temperature limit of holographic superconductors

Abstract: We consider holographic superconductors whose bulk description consists of gravity minimally coupled to a Maxwell field and charged scalar field with general potential. We give an analytic argument that there is no ``hard gap'': the real part of the conductivity at low frequency remains nonzero (although typically exponentially small) even at zero temperature. We also numerically construct the gravitational dual of the ground state of some holographic superconductors. Depending on the charge and dimension of the condensate, the infrared theory can have emergent conformal or just Poincare symmetry. In all cases studied, the area of the horizon of the dual black hole goes to zero in the extremal limit, consistent with a nondegenerate ground state.

Surface feature detection and description with applications to mesh matching

Abstract: In this paper we revisit local feature detectors/descriptors developed for 2D images and extend them to the more general framework of scalar fields defined on 2D manifolds. We provide methods and tools to detect and describe features on surfaces equiped with scalar functions, such as photometric information. This is motivated by the growing need for matching and tracking photometric surfaces over temporal sequences, due to recent advancements in multiple camera 3D reconstruction. We propose a 3D feature detector (MeshDOG) and a 3D feature descriptor (MeshHOG) for uniformly triangulated meshes, invariant to changes in rotation, translation, and scale. The descriptor is able to capture the local geometric and/or photometric properties in a succinct fashion. Moreover, the method is defined generically for any scalar function, e.g., local curvature. Results with matching rigid and non-rigid meshes demonstrate the interest of the proposed framework.

Zero Temperature Limit of Holographic Superconductors

Abstract: We consider holographic superconductors whose bulk description consists of gravity minimally coupled to a Maxwell field and charged scalar field with general potential. We give an analytic argument that there is no "hard gap": the real part of the conductivity at low frequency remains nonzero (although typically exponentially small) even at zero temperature. We also numerically construct the gravitational dual of the ground state of some holographic superconductors. Depending on the charge and dimension of the condensate, the infrared theory can have emergent conformal or just Poincare symmetry. In all cases studied, the area of the horizon of the dual black hole goes to zero in the extremal limit, consistent with a nondegenerate ground state.

Cosmology of the Lifshitz universe

Abstract: We study the ultraviolet complete non-relativistic theory recently proposed by Hořava. After introducing a Lifshitz scalar for a general background, we analyze the cosmology of the model in Lorentzian and Euclidean signature. Vacuum solutions are found and it is argued the existence of non-singular bouncing profiles. We find a general qualitative agreement with both the picture of Causal Dynamical Triangulations and Quantum Einstein Gravity. However, inflation driven by a Lifshitz scalar field on a classical background might not produce a scale-invariant spectrum when the principle of detailed balance is assumed.

Cosmology of the Lifshitz universe

Abstract: We study the ultraviolet complete non-relativistic theory recently proposed by Horava. After introducing a Lifshitz scalar for a general background, we analyze the cosmology of the model in Lorentzian and Euclidean signature. Vacuum solutions are found and it is argued the existence of non-singular bouncing profiles. We find a general qualitative agreement with both the picture of Causal Dynamical Triangulations and Quantum Einstein Gravity. However, inflation driven by a Lifshitz scalar field on a classical background might not produce a scale-invariant spectrum when the principle of detailed balance is assumed.

Dynamical Chern-Simons modified gravity: Spinning black holes in the slow-rotation approximation

Abstract: The low-energy limit of string theory contains an anomaly-canceling correction to the Einstein-Hilbert action, which defines an effective theory: Chern-Simons (CS) modified gravity. The CS correction consists of the product of a scalar field with the Pontryagin density, where the former can be treated as a background field (nondynamical formulation) or as an evolving field (dynamical formulation). Many solutions of general relativity persist in the modified theory; a notable exception is the Kerr metric, which has sparked a search for rotating black hole solutions. Here, for the first time, we find a solution describing a rotating black hole within the dynamical framework, and in the small-coupling/slow-rotation limit. The solution is axisymmetric and stationary, constituting a deformation of the Kerr metric with dipole scalar ``hair,'' whose effect on geodesic motion is to weaken the frame-dragging effect and shift the location of the innermost stable circular orbit outwards (inwards) relative to Kerr for corotating (counterrotating) geodesics. We further show that the correction to the metric scales inversely with the fourth power of the radial distance to the black hole, suggesting it will escape any meaningful bounds from weak-field experiments. For example, using binary pulsar data we can only place an initial bound on the magnitude of the dynamical coupling constant of ${\ensuremath{\xi}}^{1/4}\ensuremath{\lesssim}{10}^{4}\text{ }\text{ }\mathrm{km}$. More stringent bounds will require observations of inherently strong-field phenomena.

Scale-invariant cosmological perturbations from Horava-Lifshitz gravity without inflation

Abstract: Based on the renormalizable theory of gravitation recently proposed by Horava, we present a simple scenario to generate almost scale-invariant, super-horizon curvature perturbations. The anisotropic scaling with dynamical critical exponent z=3 implies that the amplitude of quantum fluctuations of a free scalar field generated in the early epoch of the expanding universe is insensitive to the Hubble expansion rate and, thus, scale-invariant. Those fluctuations are later converted to curvature perturbations by the curvaton mechanism or/and the modulated decay of heavy particles/oscillating fields. This scenario works, for example, for power law expansion a\propto t^p with p>1/3 and, thus, does not require inflation. Also, this scenario does not rely on any additional assumptions such as the detailed balance condition.

An analytic Lifshitz black hole

Abstract: A Lifshitz point is described by a quantum field theory with anisotropic scale invariance (but not Galilean invariance). In [8], gravity duals were conjectured for such theories. We construct analytically a black hole that asymptotes to a vacuum Lifshitz solution; this black hole solves the equations of motion of some simple (but somewhat strange) extensions of the models of [8]. We study its thermodynamics and scalar response functions. The scalar wave equation turns out to be exactly solvable. Interestingly, the Green's functions do not exhibit the ultralocal behavior seen previously in the free Lifshitz scalar theory.

Horava-Lifshitz Dark Energy

Abstract: We formulate Horava-Lifshitz cosmology with an additional scalar field that leads to an effective dark energy sector. We find that, due to the inherited features from the gravitational background, Horava-Lifshitz dark energy naturally presents very interesting behaviors, possessing a varying equation-of-state parameter, exhibiting phantom behavior and allowing for a realization of the phantom divide crossing. In addition, Horava-Lifshitz dark energy guarantees for a bounce at small scale factors and it may trigger the turnaround at large scale factors, leading naturally to cyclic cosmology.

Scalar Dissipation Rate Modeling and its Validation

Abstract: A simple algebraic model for the Favre averaged scalar dissipation rate, c, in high Damkohler number premixed flames is obtained from its transport equation by balancing the leading order terms Recently proposed models for the dominant terms in the transport equation are revisited and revised The algebraic model incorporates essential physics of turbulent premixed flames, namely, dilatation rate, its influence on turbulence-scalar interaction, chemical reactions, and dissipation processes A realizability analysis is carried out to show that the algebraic model is always unconditionally realizable The model predictions of dissipation rate are compared with the DNS results, and the agreement is good over a range of flame conditions Application of the Kolmogorov-Petrovski-Piskunov (KPP) theorem along with the above algebraic model gives an expression for the turbulent flame speed Its prediction compares well with a range of experimental data with no modifications to the model constants

Kerr-CFT and gravitational perturbations

Abstract: Motivated by the Kerr-CFT conjecture, we investigate perturbations of the near-horizon extreme Kerr spacetime. The Teukolsky equation for a massless field of arbitrary spin is solved. Solutions fall into two classes: normal modes and traveling waves. Imposing suitable (outgoing) boundary conditions, we find that there are no unstable modes. The explicit form of metric perturbations is obtained using the Hertz potential formalism, and compared with the Kerr-CFT boundary conditions. The energy and angular momentum associated with scalar field and gravitational normal modes are calculated. The energy is positive in all cases. The behaviour of second order perturbations is discussed.

Scale-invariant cosmological perturbations from Hořava-Lifshitz gravity without inflation

Abstract: Based on the renormalizable theory of gravitation recently proposed by Ho?ava, we present a simple scenario to generate almost scale-invariant, super-horizon curvature perturbations. The anisotropic scaling with dynamical critical exponent z = 3 implies that the amplitude of quantum fluctuations of a free scalar field generated in the early epoch of the expanding universe is insensitive to the Hubble expansion rate and, thus, scale-invariant. Those fluctuations are later converted to curvature perturbations by the curvaton mechanism or/and the modulated decay of heavy particles/oscillating fields. This scenario works, for example, for power law expansion at p with 1/3$> p>1/3 and, thus, does not require inflation. Also, this scenario does not rely on any additional assumptions such as the detailed balance condition.

Generation of fluctuations during inflation: Comparison of stochastic and field-theoretic approaches

Abstract: We prove that the stochastic and standard field-theoretical approaches produce exactly the same results for the amount of light massive scalar field fluctuations generated during inflation in the leading order of the slow-roll approximation. This is true both in the case for which this field is a test one and inflation is driven by another field, and the case for which the field plays the role of inflaton itself. In the latter case, in order to calculate the mean square of the gauge-invariant inflaton fluctuations, the logarithm of the scale factor $a$ has to be used as the time variable in the Fokker-Planck equation in the stochastic approach. The implications of particle production during inflation for the second stage of inflation and for the moduli problem are also discussed. The case of a massless self-interacting test scalar field in de Sitter background with a zero initial renormalized mean square is also considered in order to show how the stochastic approach can easily produce results corresponding to diagrams with an arbitrary number of scalar field loops in the field-theoretical approach (explicit results up to four loops included are presented).

Holographic Superconductor/Insulator Transition at Zero Temperature

Abstract: We analyze the five-dimensional AdS gravity coupled to a gauge field and a charged scalar field. Under a Scherk-Schwarz compactification, we show that the system undergoes a superconductor/insulator transition at zero temperature in 2+1 dimensions as we change the chemical potential. By taking into account a confinement/deconfinement transition, the phase diagram turns out to have a rich structure. We will observe that it has a similarity with the RVB (resonating valence bond) approach to high-Tc superconductors via an emergent gauge symmetry.

Trapped Inflation

Abstract: We analyze a distinctive mechanism for inflation in which particle production slows down a scalar field on a steep potential, and show how it descends from angular moduli in string compactifications The analysis of density perturbations -- taking into account the integrated effect of the produced particles and their quantum fluctuations -- requires somewhat new techniques that we develop We then determine the conditions for this effect to produce sixty e-foldings of inflation with the correct amplitude of density perturbations at the Gaussian level, and show that these requirements can be straightforwardly satisfied Finally, we estimate the amplitude of the non-Gaussianity in the power spectrum and find a significant equilateral contribution

Instability of wormholes supported by a ghost scalar field. I. Linear stability analysis

Abstract: We examine the linear stability of static, spherically symmetric wormhole solutions of Einstein's field equations coupled to a massless ghost scalar field. These solutions are parametrized by the areal radius of their throat and the product of the masses at their asymptotically flat ends. We prove that all these solutions are unstable with respect to linear fluctuations and possess precisely one unstable, exponentially in time growing mode. The associated time scale is shown to be of the order of the wormhole throat divided by the speed of light. The nonlinear evolution is analyzed in a subsequent article.

Crossing of the phantom divide in modified gravity

Abstract: We reconstruct an explicit model of modified gravity in which a crossing of the phantom divide can be realized It is shown that the (finite-time) Big Rip singularity appears in the model of modified gravity (ie, in the so-called Jordan-frame), whereas that in the corresponding scalar field theory obtained through the conformal transformation (ie, in the so-called Einstein frame) the singularity becomes the infinite-time one Furthermore, we investigate the relations between the scalar field theories with realizing a crossing of the phantom divide and the corresponding modified gravitational theories by using the inverse conformal transformation It is demonstrated that the scalar field theories describing the nonphantom phase (phantom one with the Big Rip) can be represented as the theories of real (complex) F(R) gravity through the inverse (complex) conformal transformation We also study a viable model of modified gravity in which the transition from the de Sitter universe to the phantom phase can occur In addition, we explore the stability for the obtained solutions of the crossing of the phantom divide under a quantum correction coming from conformal anomaly

TASI Lectures on Inflation

Abstract: This series of lectures gives a pedagogical review of the subject of cosmological inflation I discuss Friedmann-Robertson-Walker cosmology and the horizon and flatness problems of the standard hot Big Bang, and introduce inflation as a solution to those problems, focusing on the simple scenario of inflation from a single scalar field I discuss quantum modes in inflation and the generation of primordial tensor and scalar fluctuations Finally, I provide comparison of inflationary models to the WMAP satellite measurement of the Cosmic Microwave Background, and briefly discuss future directions for inflationary physics The majority of the lectures should be accessible to advanced undergraduates or beginning graduate students with only a background in Special Relativity, although familiarity with General Relativity and quantum field theory will be helpful for the more technical sections

Extreme- and intermediate-mass ratio inspirals in dynamical Chern-Simons modified gravity

Abstract: Chern-Simons modified gravity is a four-dimensional, effective theory that descends both from string theory and loop quantum gravity, and that corrects the Einstein-Hilbert action by adding the product of a scalar field and the parity-violating, Pontryagin density. The Chern-Simons modification deforms the gravitational field of spinning black holes, which is now described by a modified Kerr geometry whose multipole moments deviate from the Kerr ones only at the fourth multipole $\ensuremath{\ell}=4$. This paper investigates possible signatures of this theory in the gravitational-wave emission produced in the inspiral of stellar compact objects into massive black holes, both for intermediate- and extreme-mass ratios. We use the semirelativistic approximation, where the trajectory of the small compact object is modeled via geodesics of the massive black hole geometry, while the gravitational waveforms are obtained from a multipolar decomposition of the radiative field. The main Chern-Simons corrections to the waveforms arise from modifications to the geodesic trajectories, which in turn are due to changes to the massive black hole geometry, and manifest themselves as an accumulating dephasing relative to the general relativistic case. We also explore the propagation and the stress-energy tensor of gravitational waves in this theory, using the short-wavelength approximation. We find that, although this tensor has the same form as in general relativity, the energy and angular momentum balance laws are indeed modified through the stress-energy tensor of the Chern-Simons scalar field. These balance laws could be used to describe the inspiral through adiabatic changes in the orbital parameters, which in turn would enhance the dephasing effect. Gravitational-wave observations of intermediate- or extreme-mass-ratio inspirals with advanced ground detectors or with the Laser Interferometer Space Antenna could use such dephasing to test the dynamical theory to unprecedented levels, thus beginning the era of gravitational-wave tests of effective quantum gravity theories.

Renormalization group in Lifshitz-type theories

Abstract: We study the one-loop renormalization and evolution of the couplings in scalar field theories of the Lifshitz type, i.e. with different scaling in space and time. These theories are unitary and renormalizable, thanks to higher spatial derivative terms that modify the particle propagator at high energies, but at the expense of explicitly breaking Lorentz symmetry. We study if and under what conditions the Lorentz symmetry can be considered as emergent at low energies by studying the RG evolution of the ``speed of light'' coupling c2 and, for more than one field, of δc2≡c21−c22 in simple models. We find that in the UV both c2 and δc2 generally flow logarithmically with the energy scale. A logarithmic running of c2 persists also at low-energies, if δc2≠0 in the UV. As a result, Lorentz symmetry is not recovered at low energies with the accuracy needed to withstand basic experimental constraints, unless all the Lorentz breaking terms, including δc2, are unnaturally fine-tuned to extremely small values in the UV. We expect that the considerations of this paper will apply to any generic theory of Lifshitz type, including a recently proposed quantum theory of gravity by Hořava.

Trace anomaly and massless scalar degrees of freedom in gravity

Abstract: The trace anomaly of quantum fields in electromagnetic or gravitational backgrounds implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. Considering first the axial anomaly and using QED as an example, we compute the full one-loop triangle amplitude of the fermionic stress tensor with two current vertices, $⟨{T}^{\ensuremath{\mu}\ensuremath{ u}}{J}^{\ensuremath{\alpha}}{J}^{\ensuremath{\beta}}⟩$, and exhibit the scalar pole in this amplitude associated with the trace anomaly, in the limit of zero electron mass $m\ensuremath{\rightarrow}0$. To emphasize the infrared aspect of the anomaly, we use a dispersive approach and show that this amplitude and the existence of the massless scalar pole is determined completely by its ultraviolet finite terms, together with the requirements of Poincar\'e invariance of the vacuum, Bose symmetry under interchange of ${J}^{\ensuremath{\alpha}}$ and ${J}^{\ensuremath{\beta}}$, and vector current and stress-tensor conservation. We derive a sum rule for the appropriate positive spectral function corresponding to the discontinuity of the triangle amplitude, showing that it becomes proportional to $\ensuremath{\delta}({k}^{2})$ and therefore contains a massless scalar intermediate state in the conformal limit of zero electron mass. The effective action corresponding to the trace of the triangle amplitude can be expressed in local form by the introduction of two scalar auxiliary fields which satisfy massless wave equations. These massless scalar degrees of freedom couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects.

k-Mouflage gravity

Abstract: We introduce a large class of scalar-tensor theories where gravity becomes stronger at large distances via the exchange of a scalar that mixes with the graviton. At small distances, i.e. large curvature, the scalar is screened via an analog of the Vainshtein mechanism of massive gravity. The crossover distance between the two regimes can be made cosmological by an appropriate choice of the parameters.

Vortex and droplet engineering in a holographic superconductor

Abstract: We give a detailed account of the construction of nontrivial localized solutions in a $2+1$ dimensional model of superconductors using a $3+1$ dimensional gravitational dual theory of a black hole coupled to a scalar field The solutions are found in the presence of a background magnetic field We use numerical and analytic techniques to solve the full Maxwell-scalar equations of motion in the background geometry, finding condensate droplet solutions, and vortex solutions possessing a conserved winding number These solutions and their properties, which we uncover, help shed light on key features of the $(B,T)$ phase diagram

Super-Hubble de Sitter Fluctuations and the Dynamical RG

Abstract: Perturbative corrections to correlation functions for interacting theories in de Sitter spacetime often grow secularly with time, due to the properties of fluctuations on super-Hubble scales This growth can lead to a breakdown of perturbation theory at late times We argue that Dynamical Renormalization Group (DRG) techniques provide a convenient framework for interpreting and resumming these secularly growing terms In the case of a massless scalar field in de Sitter with quartic self-interaction, the resummed result is also less singular in the infrared, in precisely the manner expected if a dynamical mass is generated We compare this improved infrared behavior with large-N expansions when applicable

Full trispectrum in single field DBI inflation

Abstract: We compute the tree-level connected four-point function of the primordial curvature perturbation for a fairly general minimally coupled single field inflationary model, where the inflaton's Lagrangian is a general function of the scalar field and its first derivatives. This model includes K inflation and DBI inflation as particular cases. We show that, at the leading order in the slow-roll expansion and in the small sound speed limit, there are two important tree-level diagrams for the trispectrum. One is a diagram where a scalar mode is exchanged and the other is a diagram where the interaction occurs at a point, i.e. a contact interaction diagram. The scalar exchange contribution is comparable to the contact interaction contribution. For the DBI-inflation model, in the so-called equilateral configuration, the scalar exchange trispectrum is maximized when the angles between the four momentum vectors are equal and in this case the amplitude of the trispectrum from the scalar exchange is 1 order of magnitude higher than the contact interaction trispectrum.

Constraint on coupled dark energy models from observations

Abstract: The coupled dark energy models, in which the quintessence scalar field nontrivially couples to the cold dark matter, have been proposed to explain the coincidence problem. In this paper we study the perturbations of coupled dark energy models and the effects of this interaction on the current observations. Here, we pay particular attention to its imprint on the late-time integrated Sachs-Wolfe effect. We perform a global analysis of the constraints on this interaction from the current observational data. Considering the typical exponential form as the interaction form, we obtain that the strength of interaction between dark sectors is constrained as {beta}<0.085 at 95% confidence level. Furthermore, we find that future measurements with smaller error bars could improve the constraint on the strength of coupling by a factor of 2, when compared to the present constraints.