Assisted Inflation in Bianchi VI0 Cosmologies

We study adiabatic ~curvature! and entropy ~isocurvature! perturbations produced during a period of cosmological inflation that is driven by multiple scalar fields with an arbitrary interaction potential. A local rotation in field space is performed to separate out the adiabatic and entropy modes. The resulting field equations show explicitly how on large scales entropy perturbations can source adiabatic perturbations if the background solution follows a curved trajectory in field space, and how adiabatic perturbations cannot source entropy perturbations in the long-wavelength limit. It is the effective mass of the entropy field that determines the amplitude of entropy perturbations during inflation. We present two applications of the equations. First, we show why one in general expects the adiabatic and entropy perturbations to be correlated at the end of inflation, and calculate the cross correlation in the context of a double inflation model with two non-interacting fields. Second, we consider two-field preheating after inflation, examining conditions under which entropy perturbations can alter the large-scale curvature perturbation and showing how our new formalism has advantages in numerical stability when the background solution follows a non-trivial trajectory in field space.

Long wavelength limit of evolution of cosmological perturbations in the universe where scalar fields and fluids coexist

A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to the domain scientists. It has been shown in recent works that a single scalar field is insufficient to capture many important topological features in the data, instead one needs to consider topological relationships between multiple scalar fields. In the current paper, we propose a novel method of finding similarity between two multifield data by comparing their respective fiber component distributions. Given a time-varying multifield data, the method computes a metric plot for each pair of histograms at consecutive time stamps to understand the topological changes in the data over time. We validate the method using real and synthetic data. The effectiveness of the proposed method is shown by its ability to capture important topological features that are not always possible to detect using the individual component scalar fields.

Non-Gaussian fluctuations for structure formation may arise in inflation from the nonlinear interaction of long wavelength gravitational and scalar fields. Long wavelength fields have spatial gradients a -1∇ small compared to the Hubble radius, and they are described in terms of classical random fields that are fed by short wavelength quantum noise. Lattice Langevin calculations are given for a ‘toy model’ with a scalar field interacting with an exponential potential where one can obtain exact analytic solutions of the Fokker-Planck equation. For single scalar field models that are consistent with current microwave background fluctuations, the fluctuations are Gaussian. However, for scales much larger than our observable Universe, one expects large metric fluctuations that are non-Gaussian. This example illuminates non-Gaussian models involving multiple scalar fields which are consistent with current microwave background limits.KeywordsScalar FieldHubble ParameterLapse FunctionExponential PotentialMomentum ConstraintThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The relative values of a single 2D scalar field can be effectively perceived when the field is represented by height and rendered as a surface in three dimensions. When multiple scalar fields are simultaneously rendered on the same domain, control of additional rendering attributes such as color, transparency, texturing, and lighting is needed for effective perception. However, the transition from foreground to background due to surface intersections can confound accurate surface perception, even for techniques that work well for overlapping non-intersecting surfaces. We propose a general method for decomposing and stratifying multiple intersecting surfaces into layered components to permit complete rendering control of each surface component. We explore different rendering schemes based on stratification values and report initial results from experimentation.

Low energy effective field theories motivated by string theory will likely contain several scalar moduli fields which will be relevant to early Universe cosmology. Some of these fields are expected to couple with non-standard kinetic terms to gravity. In this paper, we study the splitting into adiabatic and isocurvature perturbations for a model with two scalar fields, one of which has a non-standard kinetic term in the Einstein-frame action. Such actions can arise, e.g., in the Pre-Big-Bang and Ekpyrotic scenarios. The presence of a non-standard kinetic term induces a new coupling between adiabatic and isocurvature perturbations which is non-vanishing when the potential for the matter fields is nonzero. This coupling is un-suppressed in the long wavelength limit and thus can lead to an important transfer of power from the entropy to the adiabatic mode on super-Hubble scales. We apply the formalism to the case of a previously found exact solution with an exponential potential and study the resulting mixing of adiabatic and isocurvature fluctuations in this example. We also discuss the possible relevance of the extra coupling in the perturbation equations for the process of generating an adiabatic component of the fluctuations spectrum from isocurvature perturbations without considering a later decay of the isocurvature component.

We study integrability by quadrature of a spatially flat Friedmann model containing both a perfect fluid with barotropic equation of state p = (1− h)ρ and a minimally coupled scalar field φ with either a single exponential potential V(φ) ~ exp[−√6σκφ], \(K = \sqrt {8\pi {G_N}}\), of arbitrary sign or a simplest multiple exponential potential V(φ) = W 0 − V 0 sinh (√6σκφ), where the parameters W 0 and V 0 are arbitrary. From the mathematical view point the model is pseudo-Euclidean Toda-like system with 2 degrees of freedom. We apply the methods developed in our previous papers, based on the Minkowsky-like geometry for 2 characteristic vectors depending on the parameters σ and h. For the single exponential potential we present 4 classes of general solutions with the parameters obeying the following relations: A. σ is arbitrary, h = 0; B. σ = 1− h/2, 0 < h < 2; C1. σ =1−h/4, 0 < h ≤ 2; C2. σ = |1−h|, 0 < h ≤ 2, h ≠ 1, 4/3. The properties of the exact solutions near the initial singularity and at the final stage of evolution are analyzed. For the multiple exponential potential the model is integrated with h = 1 and σ = 1/2 and all exact solutions describe the recollapsing universe. We single out the exact solution describing the evolution within the time approximately equal to 2H 0 −1 with the present-day values of the acceleration parameter q 0 = 0.5 and the density parameter Ω ρ 0 = 0.3.

We derive a new regular dynamical system on a three-dimensional compact state space describing linear scalar perturbations of spatially flat Robertson–Walker geometries for relativistic models with a minimally coupled scalar field with an exponential potential. This enables us to construct the global solution space, illustrated with figures, where known solutions are shown to reside on special invariant sets. We also use our dynamical systems approach to obtain new results about the comoving and uniform density curvature perturbations. Finally we show how to extend our approach to more general scalar field potentials. This leads to state spaces where the state space of the models with an exponential potential appears as invariant boundary sets, thereby illustrating their role as building blocks in a hierarchy of increasingly complex cosmological models.

Pseudo-Nambu-Goldstone (pNG) Higgs Inflation is a novel approach to relate the Higgs boson and its interaction with Electroweak gauge bosons with cosmic inflation, with the potential of solving both the fine-tuning issues in the Higgs mass and inflationary potentials. In this work, we present a linear perturbation analysis of the minimal implementation of pNG Higgs inflation using the symmetry coset SU(5)/SO(5). Similar to Chromo-natural inflation, this model exhibits a period of instability in the tensor modes that exponentially enhance left-handed gravitational waves. Thus, large Chern-Simons couplings β ≳ 6 × 108 and decay constants f ≳ 1 × 1018 GeV are required to suppress the tensor-to-scalar ratio r to be compatible with the cosmic microwave background (CMB) measurement. These large couplings also cause an overproduction of the scalar modes, making the minimal construction of pNG Higgs inflation disfavored by CMB observations. However, this tension could potentially be relieved by considering multi-field inflation. The pNG Higgs construction naturally contains multiple scalar fields via the interplay of spontaneously broken global and gauge symmetries. The rich structure enables a broad range of multi-field inflation, and we conclude by briefly discussing this possibility and future work.

We study Dirac-Born-Infeld inflation models with multiple scalar fields. We show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at the sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We show that this could strongly affect the observable curvature power spectrum as well as the amplitude of non-Gaussianities, although their shape remains as in the single-field Dirac-Born-Infeld case.

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).

We investigate primordial magnetogenesis within a quantum bouncing model driven by a scalar field, focusing on various non-minimal couplings between the electromagnetic field and the scalar field. We test three cases: no coupling, a Cauchy coupling with gradual decay, and a Gaussian coupling with rapid fall-off. By exploring these scenarios, we assess a wide range of coupling strengths across different scales. The scalar field, with an exponential potential, behaves as pressureless matter in the asymptotic past of the contracting phase, as stiff matter around the bounce, and as dark energy during the expanding phase. Our findings reveal that, among the tested cases, only the Gaussian coupling can explain the generation of primordial magnetic fields on cosmological scales.

We study a class of minisuperspace models consisting of a homogenous isotropic universe with a minimally coupled homogenous scalar field with a potential alpha cosh(2-phi) + beta sinh(2-phi), where alpha and beta are arbitrary parameters. This includes the case of a pure exponential potential exp(2-phi), which arises in the dimensional reduction to four dimensions of five-dimensional Kaluza-Klein theory. We study the classical Lorentzian solutions for the model and find that they exhibit exponential or power-law inflation. We show that the Wheeler-DeWitt equation for this model is exactly soluble. Concentrating on the two particular cases of potentials cosh(2-phi) and exp(2-phi), we consider the Euclidean minisuperspace path integral for a propagation amplitude between fixed scale factors and scalar-field configurations. In the gauge N = 0 (where N is the rescaled lapse function), the path integral reduces, after some essentially trivial functional integrations, to a single nontrivial ordinary integral over N. Because the Euclidean action is unbounded from below, N must be integrated along a complex contour for convergence. We find all possible complex contours which lead to solutions of the Wheeler-DeWitt equation or Green's functions of the Wheeler-DeWitt operator, and we give an approximate evaluation of the integral along these contours, using the method of steepest descents. The steepest-descent contours may be dominated by saddle points corresponding to exact solutions to the full Einstein-scalar equations which may be real Euclidean, real Lorentzian, or complex. We elucidate the conditions under which each of these different types of solution arise. For the exp(2-phi) potential, we evaluate the path integral exactly. Although we cannot evaluate the path integral in closed form for the cosh(2-phi) potential, we show that for particular N contours the amplitude may be written as a given superposition of exact solutions to the Wheeler-DeWitt equation. By choosing certain initial data for the path-integral amplitude we obtain the amplitude specified by the proposal of Hartle and Hawking. We discuss the nature of the geometries corresponding to the saddle points of the no-boundary amplitude. We identify the set of classical solutions this proposal picks out in the classical limit.

The problem of the cosmic coincidence is a longstanding puzzle. This conundrum may be solved by introducing a coupling between the two dark sectors. In this Letter, we study two cases of the coupled quintessence scenario. (a) Assume that the mass of dark matter particles depends exponentially on the scalar field associated to dark energy and meanwhile the scalar field evolves in an exponential potential; (b) Assume that the mass of dark matter particles depends on a power law function of the scalar field and meanwhile the scalar field evolves in a power law potential. Since the dynamics of this system is dominated by an attractor solution, the mass of dark matter particles is forced to change with time as to ensure that the ratio between the energy densities of dark matter and dark energy becomes a constant at late times, and one thus solve the cosmic coincidence problem naturally. We perform a statefinder diagnostic to both cases of this coupled quintessence scenario. It is shown that the evolving trajectory of this scenario in the s–r diagram is quite different from those of other dark energy models.

Gravitational theories with multiple scalar fields coupled to the metric and each other—a natural extension of the well studied single-scalar-tensor theories—are interesting phenomenological frameworks to describe deviations from general relativity in the strong-field regime. In these theories, the N-tuple of scalar fields takes values in a coordinate patch of an N-dimensional Riemannian target-space manifold whose properties are poorly constrained by weak-field observations. Here we introduce for simplicity a non-trivial model with two scalar fields and a maximally symmetric target-space manifold. Within this model we present a preliminary investigation of spontaneous scalarization for relativistic, perfect fluid stellar models in spherical symmetry. We find that the scalarization threshold is determined by the eigenvalues of a symmetric scalar-matter coupling matrix, and that the properties of strongly scalarized stellar configurations additionally depend on the target-space curvature radius. In preparation for numerical relativity simulations, we also write down the 3 + 1 decomposition of the field equations for generic tensor-multi-scalar theories.