Multiple Scalar Fields Research Articles

Super-geometrodynamics

We present explicit solutions of the time-symmetric initial value constraints, expressed in terms of freely specfiable harmonic functions for examples of supergravity theories, which emerge as effective theories of compactified string theory. These results are a prequisite for the study of the time-evolution of topologically non-trivial initial data for supergravity theories, thus generalising the "Geometrodynamics" program of Einstein-Maxwell theory to that of supergravity theories. Specifically, we focus on examples of multiple electric Maxwell and scalar fields, and analyse the initial data problem for the general Einstein-Maxwell-Dilaton theory both with one and two Maxwell fields, and the STU model. The solutions are given in terms of up to eight arbitrary harmonic functions in the STU model. As a by-product, in order compare our results with known static solutions, the metric in isotropic coordinates and all the sources of the non-extremal black holes are expressed entirely in terms of harmonic functions. We also comment on generalizations to time-nonsymmetric initial data and their relation to cosmological solutions of gauged so-called fake supergravities with positive cosmological constant.

Asymptotically Static Universe Dominated by Phantom Energy

Abstract In this article, we investigated a generalised scalar field cosmology characterised by a time-dependent coupling function, a time-dependent cosmological constant, a chameleonic field, and a time-dependent equation of state parameter. Based on a particular choice of the Hubble parameter as function of the scalar field and its time derivative, we have investigated the dynamics of the Friedmann–Robertson–Walker flat universe. We have observed that for a particular choice of the free parameters in the theory, the universe accelerates with time and asymptotically tends toward a static universe. For specific values of the free parameters, the asymptotically static universe may be dominated by phantom energy or a cosmological constant without the need to implement in the theory multiple scalar fields or additional interactions. It is also pointed out that an asymptotically static universe is as well one special class of solutions for Horndeski and generalised galileons cosmologies. Special properties and features are discussed accordingly.

Theory of self-resonance after inflation. II. Quantum mechanics and particle-antiparticle asymmetry

We further develop a theory of self-resonance after inflation in a large class of models involving multiple scalar fields. We concentrate on inflaton potentials that carry an internal symmetry, but also analyze weak breaking of this symmetry. This is the second part of a two-part series of papers. Here in part 2 we develop an understanding of the resonance structure from the underlying many-particle quantum mechanics. We begin with a small-amplitude analysis, which obtains the central resonant wave numbers, and relate it to perturbative processes. We show that the dominant resonance structure is determined by (i) the nonrelativistic scattering of many quantum particles and (ii) the application of Bose-Einstein statistics to the adiabatic and isocurvature modes, as introduced in part 1 [M. P. Hertzberg et al., Phys. Rev. D 90, 123528 (2014)]. Other resonance structures are understood in terms of annihilations and decays. We set up Bunch-Davies vacuum initial conditions during inflation and track the evolution of modes including Hubble expansion. In the case of a complex inflaton carrying an internal U(1) symmetry, we show that when the isocurvature instability is active, the inflaton fragments into separate regions of $\ensuremath{\phi}$-particles and anti-$\ensuremath{\phi}$-particles. We then introduce a weak breaking of the U(1) symmetry; this can lead to baryogenesis, as shown by some of us recently [M. P. Hertzberg and J. Karouby, Phys. Lett. B 737, 34 (2014); Phys. Rev. D 89, 063523 (2014)]. Then using our results, we compute corrections to the particle-antiparticle asymmetry from this preheating era.

Theory of self-resonance after inflation. I. Adiabatic and isocurvature Goldstone modes

We develop a theory of self-resonance after inflation. We study a large class of models involving multiple scalar fields with an internal symmetry. For illustration, we often specialize to dimension 4 potentials, but we derive results for general potentials. This is the first part of a two part series of papers. Here in Part 1 we especially focus on the behavior of long wavelengths modes, which are found to govern most of the important physics. Since the inflaton background spontaneously breaks the time translation symmetry and the internal symmetry, we obtain Goldstone modes; these are the adiabatic and isocurvature modes. We find general conditions on the potential for when a large instability band exists for these modes at long wavelengths. For the adiabatic mode, this is determined by a sound speed derived from the time averaged potential. While for the isocurvature mode, this is determined by a speed derived from a time averaged auxiliary potential. Interestingly, we find that this instability band usually exists for one of these classes of modes, rather than both simultaneously. We focus on backgrounds that evolve radially in field space, as setup by inflation, and also mention circular orbits, as relevant to Q-balls. In Part 2 [1] we derive the central behavior from the underlying description of many particle quantum mechanics, and introduce a weak breaking of the symmetry to study corrections to particle-antiparticle production from preheating.

Multiscale renormalization group methods for effective potentials with multiple scalar fields

Multi-scale renormalization group (RG) methods are reviewed and applied to the analysis of the effective potential for radiative symmetry breaking with multiple scalar fields, allowing an extension of the Gildener & Weinberg (GW) method beyond the weak coupling limit. A model containing two interacting real scalar fields is used to illustrate multi-scale RG methods and the multi-scale RG functions of this model are calculated to one-loop order for the $\beta$ function and two-loop order for the anomalous mass dimension. The introduction of an extra renormalization scale allows the mapping of the effective potential in this model onto an RG-equivalent form with an O(2) symmetric structure along a particular trajectory in the multiple renormalization-scale space, leading to a simplified form of the effective potential. It is demonstrated that the physical content of the effective potential in the original model, referenced to a single conventional renormalization scale, can be extracted from a particular RG-trajectory that connects to this multi-scale O(2)-symmetric form of the effective potential. Extensions of these multi-scale methods for effective potentials in models containing multiple scalars with $O(M)\times O(N)$ symmetry are also discussed.

Cosmology in generalized Horndeski theories with second-order equations of motion

We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) background. In addition to a dark energy field $\chi$ associated with the gravitational sector, we take into account multiple scalar fields $\phi_I$ ($I=1,2\cdots,N-1$) characterized by the Lagrangians $P^{(I)}(X_I)$ with $X_I=\partial_{\mu}\phi_I\partial^{\mu}\phi_I$. These additional scalar fields can model the perfect fluids of radiation and non-relativistic matter. We derive propagation speeds of scalar and tensor perturbations as well as conditions for the absence of ghosts. The theories beyond Horndeski induce non-trivial modifications to all the propagation speeds of $N$ scalar fields, but the modifications to those for the matter fields $\phi_I$ are generally suppressed relative to that for the dark energy field $\chi$. We apply our results to the covariantized Galileon with an Einstein-Hilbert term in which partial derivatives of the Minkowski Galileon are replaced by covariant derivatives. Unlike the covariant Galileon with second-order equations of motion in general space-time, the scalar propagation speed square $c_{s1}^2$ associated with the field $\chi$ becomes negative during the matter era for late-time tracking solutions, so the two Galileon theories can be clearly distinguished at the level of linear cosmological perturbations.

Covariant and gauge-invariant linear scalar perturbations in multiple scalar field cosmologies

We derive a set of equations monitoring the evolution of covariant and gauge-invariant linear scalar perturbations of Friedman-Lema\^itre-Robertson-Walker models with multiple interacting non-linear scalar fields. We use a dynamical systems' approach in order to perform a stability analysis for some classes of scalar field potentials. In particular, using a recent approximation for the inflationary dynamics of the background solution, we derive conditions under which homogenization occurs for chaotic (quadratic and quartic potentials) and new inflation. We also prove a cosmic no-hair result for power-law inflation and its generalisation for two scalar fields with independent exponential potentials (assisted power-law inflation).

Cosmological scaling solutions for multiple scalar fields

The general k-essence Lagrangian for the existence of cosmological scaling solutions is derived in the presence of multiple scalar fields coupled to a barotropic perfect fluid. In addition to the scaling fixed point associated with the dynamics during the radiation and matter eras, we also obtain a scalar-field dominated solution relevant to dark energy and discuss the stability of them in the two-field set-up. We apply our general results to a model of two canonical fields with coupled exponential potentials arising in string theory. Depending on model parameters and initial conditions, we show that the scaling matter-dominated epochs followed by an attractor with cosmic acceleration can be realized with/without the couplings to scalar fields. The different types of scaling solutions can be distinguished from each other by the evolution of the dark energy equation of state from high-redshifts to today.

Non-Gaussian signatures arising from warm inflation driven by geometric tachyon

In a warm inflationary scenario, the initial seeds of density perturbation arise from thermal fluctuations of the inflaton field. These fluctuations in principle have Gaussian distribution. In a Gaussian distribution the density perturbation can be expressed as the two point correlation function. Thus if in an inflationary model the density perturbation is expressed as correlation function of order higher than two, these fluctuations are non-Gaussian in nature. A simple inflationary model containing single scalar field, slow roll, canonical kinetic term and vacuum initial state can produce a tiny amount of non-Gaussianity which are very small to be detected by any experiment. Non-Gaussianity can also arise in inflationary models containing multiple scalar fields. For an inflationary scenario with single scalar field, non-Gaussianity can be expressed in terms of bi-spectrum however for multi field Inflation, it is expressed in terms of trispectrum etc. In this piece of work, the warm inflationary scenario, driven by a D3 brane due to the presence of a stack of k coincident NS 5 branes is considered and the non-Gaussian effects in such an inflationary scenario has been analysed by measuring the bispectrum of the gravitational field fluctuations generated during the warm inflation in strong dissipative regime. The bi-spectrum of the Inflation is expressed in terms of the parameter fNL and it is seen that the value of fNL parameter lies well within the limit observed by WMAP7.

Tumbling through a landscape: Evidence of instabilities in high-dimensional moduli spaces

We argue that a generic instability afflicts vacua that arise in theories whose moduli space has large dimension. Specifically, by studying theories with multiple scalar fields we provide numerical evidence that for a generic local minimum of the potential the usual semiclassical bubble nucleation rate, Gamma = A e^{-B}, increases rapidly as function of the number of fields in the theory. As a consequence, the fraction of vacua with tunneling rates low enough to maintain metastability appears to fall exponentially as a function of the moduli space dimension. We discuss possible implications for the landscape of string theory. Notably, if our results prove applicable to string theory, the landscape of metastable vacua may not contain sufficient diversity to offer a natural explanation of dark energy.

Primordial bispectrum from multifield inflation with nonminimal couplings

Realistic models of high-energy physics include multiple scalar fields. Renormalization requires that the fields have nonminimal couplings to the spacetime Ricci curvature scalar, and the couplings can be large at the energy scales of early-universe inflation. The nonminimal couplings induce a nontrivial field-space manifold in the Einstein frame, and they also yield an effective potential in the Einstein frame with nontrivial curvature. The ridges or bumps in the Einstein-frame potential can lead to primordial non-Gaussianities of observable magnitude. We develop a covariant formalism to study perturbations in such models and calculate the primordial bispectrum. As in previous studies of non-Gaussianities in multifield models, our results for the bispectrum depend sensitively on the fields' initial conditions.

DBI inflation inN=1supergravity

It was recently demonstrated that, when coupled to N=1 supergravity, the Dirac-Born-Infeld (DBI) action constructed from a single chiral superfield has the property that when the higher-derivative terms become important, the potential becomes negative. Thus, DBI inflation cannot occur in its most interesting, relativistic regime. In this paper, it is shown how to overcome this problem by coupling the model to one or more additional chiral supermultiplets. In this way, one obtains effective single real scalar field DBI models with arbitrary positive potentials, as well as multiple real scalar field DBI inflation models with hybrid potentials.

Unitarity-violation in generalized Higgs inflation models

Unitarity-violation presents a challenge for non-minimally coupled models of inflation based on weak-scale particle physics. We examine the energy scale of tree-level unitarity-violation in scattering processes for generalized models with multiple scalar fields where the inflaton is either a singlet scalar or the Higgs. In the limit that the non-minimal couplings are all equal (e.g. in the case of Higgs or other complex inflaton), the scale of tree-level unitarity-violation matches the existing result. However if the inflaton is a singlet, and if it has a larger non-minimal coupling than other scalars in the model, then this hierarchy increases the scale of tree-level unitarity-violation. A sufficiently strong hierarchy pushes the scale of tree-level unitarity-violation above the Planck scale. We also discuss models which attempt to resolve the issue of unitarity-violation in Higgs Inflation.

Cosmological perturbations in SFT inspired non-local scalar field models

We study cosmological perturbations in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field and explicitly prove that for the free field it is identical to a system of local cosmological perturbation equations in a particular model with multiple (maybe infinitely many) local free scalar fields.

Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests

We review different dark energy cosmologies. In particular, we present the ΛCDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes. In the first part, we explain the ΛCDM model and well-established observational tests which constrain the current cosmic acceleration. After that, we investigate the dark fluid universe where a fluid has quite general equation of state (EoS) [including inhomogeneous or imperfect EoS]. All the above dark energy cosmologies for different fluids are explicitly realized, and their properties are also explored. It is shown that all the above dark energy universes may mimic the ΛCDM model currently, consistent with the recent observational data. Furthermore, special attention is paid to the equivalence of different dark energy models. We consider single and multiple scalar field theories, tachyon scalar theory and holographic dark energy as models for current acceleration with the features of quintessence/phantom cosmology, and demonstrate their equivalence to the corresponding fluid descriptions. In the second part, we study another equivalent class of dark energy models which includes F(R) gravity as well as F(R) Hořava-Lifshitz gravity and the teleparallel f(T) gravity. The cosmology of such models representing the ΛCDM-like universe or the accelerating expansion with the quintessence/phantom nature is described. Finally, we approach the problem of testing dark energy and alternative gravity models to general relativity by cosmography. We show that degeneration among parameters can be removed by accurate data analysis of large data samples and also present the examples.

Dynamics of Multiple Scalar Fields Model of Dark Energy with Spatial Curvature

The dynamical system of multiple scalar fields in FRW universe with different spatial curvature have been analyzed in this paper. In the radiation-dominated phase, the constant curvature factor k does not work on the cosmic dynamical behaviors, including the scaling solution, energy density parameter and equation-of-state parameter. These aspects are affected by curvature factor k in the matter-dominated phase. In the special scalar field-dominated phase, the energy density parameter normalization restricts the Universe is spatial flat and the curvature factor k is not present in the dynamics. In this paper, the Universe is closed in the matter-dominated phase, and flat in the scalar field-dominated phase. The spatial flatness and the wϕ=−1 in the third phase are coincide with the current observations.

Cosmology of axions and moduli: A dynamical systems approach

This paper is concerned with string cosmology and the dynamics of multiple scalar fields in potentials that can become negative, and their features as (early) dark energy models. Our point of departure is the ``string axiverse,'' a scenario that motivates the existence of cosmologically light axion fields as a generic consequence of string theory. We couple such an axion to its corresponding modulus. We give a detailed presentation of the rich cosmology of such a model, ranging from the setting of initial conditions on the fields during inflation, to the asymptotic future. We present some simplifying assumptions based on the fixing of the axion decay constant ${f}_{a}$, and on the effective field theory when the modulus trajectory is adiabatic, and find the conditions under which these assumptions break down. As a by-product of our analysis, we find that relaxing the assumption of fixed ${f}_{a}$ leads to the appearance of a new metastable de Sitter region for the modulus without the need for uplifting by an additional constant. A dynamical systems analysis reveals the existence of many fixed point attractors, repellers and saddle points, which we analyze in detail. We also provide geometric interpretations of the phase space. The fixed points can be used to bound the couplings in the model. A systematic scan of certain regions of parameter space reveals that the future evolution of the Universe in this model can be rich, containing multiple epochs of accelerated expansion.

Nonsingular power-law and assisted inflation in loop quantum cosmology

We investigate the dynamics of single and multiple scalar fields with exponential potentials, leading to power-law and assisted inflation, in loop quantum cosmology. Unlike in the classical theory, dynamical trajectories in loop quantum cosmology are generically nonsingular, with a big bounce replacing classical big bang in the Planck regime. Post-bounce, after a phase of superinflation, dynamical trajectories evolve towards the classical attractor in the inflationary scenarios. Depending on the initial conditions, bounce is shown to occur in kinetic as well as potential dominated regimes. We analyze the number of e-foldings resulting from the phase of superinflation and find the dependence of the maximum possible number of e-foldings on the equation of state at the bounce and on the steepness of the potential. We find that if the potential is not steep, this phase can lead to a large number of e-foldings in power-law inflation. For the assisted inflation scenario, an increase in the number of fields can yield a significant increase in the number of e-foldings during superinflation.

Effective theories of single field inflation when heavy fields matter

We compute the low energy effective field theory (EFT) expansion for single-field inflationary models that descend from a parent theory containing multiple other scalar fields. By assuming that all other degrees of freedom in the parent theory are sufficiently massive relative to the inflaton, it is possible to derive an EFT valid to arbitrary order in perturbations, provided certain generalized adiabaticity conditions are respected. These conditions permit a consistent low energy EFT description even when the inflaton deviates off its adiabatic minimum along its slowly rolling trajectory. By generalizing the formalism that identifies the adiabatic mode with the Goldstone boson of this spontaneously broken time translational symmetry prior to the integration of the heavy fields, we show that this invariance of the parent theory dictates the entire non-perturbative structure of the descendent EFT. The couplings of this theory can be written entirely in terms of the reduced speed of sound of adiabatic perturbations. The resulting operator expansion is distinguishable from that of other scenarios, such as standard single inflation or DBI inflation. In particular, we re-derive how certain operators can become transiently strongly coupled along the inflaton trajectory, consistent with slow-roll and the validity of the EFT expansion, imprinting features in the primordial power spectrum, and we deduce the relevant cubic operators that imply distinct signatures in the primordial bispectrum which may soon be constrained by observations.

CosmoTransitions: Computing cosmological phase transition temperatures and bubble profiles with multiple fields

I present a numerical package (CosmoTransitions) for analyzing finite-temperature cosmological phase transitions driven by single or multiple scalar fields. The package analyzes the different vacua of a theory to determine their critical temperatures (where the vacuum energy levels are degenerate), their supercooling temperatures, and the bubble wall profiles which separate the phases and describe their tunneling dynamics. I introduce a new method of path deformation to find the profiles of both thin- and thick-walled bubbles. CosmoTransitions is freely available for public use.Program summaryProgram Title: CosmoTransitionsCatalogue identifier: AEML_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEML_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 8775No. of bytes in distributed program, including test data, etc.: 621096Distribution format: tar.gzProgramming language: Python.Computer: Developed on a 2009 MacBook Pro. No computer-specific optimization was performed.Operating system: Designed and tested on Mac OS X 10.6.8. Compatible with any OS with Python installed.RAM: Approximately 50 MB, mostly for loading plotting packages.Classification: 1.9, 11.1.External routines: SciPy, NumPy, matplotLibNature of problem: I describe a program to analyze early-Universe finite-temperature phase transitions with multiple scalar fields. The goal is to analyze the phase structure of an input theory, determine the amount of supercooling at each phase transition, and find the bubble-wall profiles of the nucleated bubbles that drive the transitions.Solution method: To find the bubble-wall profile, the program assumes that tunneling happens along a fixed path in field space. This reduces the equations of motion to one dimension, which can then be solved using the overshoot/undershoot method. The path iteratively deforms in the direction opposite the forces perpendicular to the path until the perpendicular forces vanish (or become very small). To find the phase structure, the program finds and integrates the change in a phase’s minimum with respect to temperature.Running time: Approximately 1 minute for full analysis of the two-scalar-field test model on a 2.5 GHz CPU.