Time-dependent Scalar Field Research Articles

Modified Friedmann equations from Maxwell-Weyl gauge theory

This study investigates the possibility of a homogeneous and isotropic cosmological solution within the context of the Maxwell-Weyl gauge theory of gravity. To achieve this, we utilize the Einstein-Yang-Mills theory as an analogy and represent the Maxwell gauge field in terms of two time-dependent scalar fields. We derive the modified Friedmann equations, integrating the contributions from the Maxwell gauge fields and an effective cosmological constant that depends on the Dirac scalar field. Our analysis reveals how these modifications influence various cosmological scenarios, including power-law evolution, de Sitter-like expansion, inflationary phases, non-singular bounce cosmologies, and cyclic cosmologies.

Suggestions of decreasing dark energy from supernova and BAO data

The potential energy from a time-dependent scalar field provides a possible explanation for the observed cosmic acceleration. In this paper, we investigate how data from supernova and bary acoustic oscillation surveys constrain the possible evolution of a single scalar field over the period of time (roughly half the age of the universe) for which these data are available. Taking a linear approximation to the scalar potential V(ϕ) = V 0 + V 1 ϕ around the present value, a likelihood analysis appears to significantly prefer models with a decreasing potential energy at present, with approximately 99.99 % of the exp(-χ 2/2) distribution having V 1 > 0 in a convention where ϕ̇ ≤ 0 at present. The models favoured by the distribution typically have an order one decrease 〈|Range[V(ϕ(t))]/V(t 0)|〉 ≈ 0.36 in the scalar potential energy over the time frame corresponding to z < 2. According to the likelihood analysis, the ΛCDM model with no variation in dark energy appears to be significantly disfavoured in the context of the linear potential model, but this should be interpreted cautiously since model selection criteria that make use of Δχ 2 while ignoring parameter space volumes still favour ΛCDM. Working with a second order approximation to the potential, the supernova data can be fit well for a wide range of possible potentials, including models where the universe has already stopped accelerating.

Black hole no-hair theorem for self-gravitating time-dependent spherically symmetric multiple scalar fields

We prove under certain weak assumptions a black hole no-hair theorem in spherically symmetric spacetimes for self-gravitating time-dependent multiple scalar fields with an arbitrary target space admitting a Killing field with a non-empty axis and arbitrary non-negative potential invariant under the flow of the Killing field. It is shown that for such configurations the only spherically symmetric and asymptotically flat black hole solutions consist of the Schwarzschild metric and a constant multi-scalar map. In due course of the proof we also unveil the intrinsic connection of the time-dependence of the scalar fields with the symmetries of the target space.

Cosmology from the vacuum

We argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the Universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. In particular, while inflation may explain the origin of perturbations in the cosmology picture, the perturbations can be deduced from the dual picture without any knowledge of the inflationary potential.

A new approach to flatness, horizon and late-time accelerating expansion problems on the basis of Mach’s principle

Based on the idea that the components of a cosmological metric may be determined by the total gravitational potential of the universe, the scalar field $\phi=1/G$ in the Jordan-Brans-Dicke (JBD) theory is introduced as evolving with the inverse square of the scale factor. Since the gravitational potential is related to the field $\phi$ resulting from Mach's principle and depends on time due to the expansion of space, the temporal evolution of the field should be in accord with the evolution of time and space intervals in the metric tensor. For the same reason, the time dependence of the field makes these comoving intervals relative for different points on the time axis. Thus, it is shown that introduction of the cosmic gravitational potential as a time dependent scalar field proportional to $1/a^2$ may resolve the flatness, the horizon and the late-time accelerating expansion problems of the standard model of cosmology. The luminosity distance vs redshift data of Type Ia supernovae is in agreement with this approach.

Cosmological application of the Maxwell gravity

In this study, we consider a cosmological model for the Maxwell gravity which is constructed by gauging the semi-simple extended Poincaré algebra. Inspired by the Einstein–Yang–Mills theory, we describe the Maxwell gauge field in terms of two additional time-dependent scalar fields. Within the context of a homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker universe, we derive the Friedmann equations together with new contributions. Additionally, we examine the modified Friedmann equation to demonstrate how diverse cosmological scenarios can be achieved within this framework. Moreover, we investigate the gauge theory of gravity based on the Maxwell algebra and show that this model leads to the (anti)-de Sitter universe as well as a non-accelerated universe model.

Accelerating cosmology from Λ < 0 gravitational effective field theory

A large class of Λ < 0 cosmologies have big-bang/big crunch spacetimes with time-symmetric backgrounds and asymptotically AdS Euclidean continuations suggesting a possible holographic realization. We argue that these models generically have time-dependent scalar fields, and these can lead to realistic cosmologies at the level of the homogeneous background geometry, with an accelerating phase prior to the turnaround and crunch. We first demonstrate via explicit effective field theory examples that models with an asymptotically AdS Euclidean continuation can also exhibit a period of accelerated expansion without fine tuning. We then show that certain significantly more tuned examples can give predictions arbitrarily close to a ΛCDM model. Finally, we demonstrate via an explicit construction that the potentials of interest can arise from a superpotential, thus suggesting that these solutions may be compatible with an underlying supersymmetric theory.

Conformally coupled scalar in Lovelock theory

In arbitrary higher dimension, we consider the combination of Lovelock gravity alongside a scalar-tensor action built out of higher order operators and Euler densities. The latter action is constructed in such a way as to ensure conformal invariance for the scalar field. For the combined version of these theories, we show the existence of black hole solutions interpreted as stealth configurations within Lovelock gravity theory. The scalar field solutions are endowed with an integration constant that may be identified as a scalar charge. In particular, we show that these stealth solutions can be extended to include a time-dependent scalar field despite the underlying theory being non shift symmetric. Finally, we present a procedure to obtain a nonconformally invariant action in even dimensions from the considered theory. For the target theory, the scalar field is not conformally coupled to gravity although the scalar field equation itself is conformally invariant. By means of this procedure, the black hole stealth configurations are converted into nonstealth black hole solutions, as discovered recently in four dimensions.

Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields

In time-independent quantum systems, entanglement entropy possesses an inherent scaling symmetry that the energy of the system does not have. The symmetry also assures that entropy divergence can be associated with the zero modes. We generalize this symmetry to time-dependent systems all the way from a coupled harmonic oscillator with a time-dependent frequency, to quantum scalar fields with time-dependent mass. We show that such systems have dynamical scaling symmetry that leaves the evolution of various measures of quantum correlations invariant; entanglement entropy, GS fidelity, the Loschmidt echo, and circuit complexity. Using this symmetry, we show that several quantum correlations are related at late times when the system develops instabilities. We then quantify such instabilities in terms of scrambling time and Lyapunov exponents. The delayed onset of exponential decay of the Loschmidt echo is found to be determined by the largest inverted mode in the system. On the other hand, a zero mode retains information about the system for a considerably longer time, finally resulting in a power-law decay of the Loschmidt echo. We extend the analysis to time-dependent massive scalar fields in ($1+1$)-dimensions and discuss the implications of zero modes and inverted modes occurring in the system at late times. We explicitly show the entropy scaling oscillates between the area-law and volume-law for a scalar field with stable modes or zero modes. We then provide a qualitative discussion of the above effects for scalar fields in cosmological and black hole spacetimes.

Black hole sensitivities in Einstein-scalar-Gauss-Bonnet gravity

The post-Newtonian dynamics of black hole binaries in Einstein-scalar-Gauss-Bonnet theories of gravity depends on the so-called "sensitivities", quantities which characterize a black hole's adiabatic response to the time-dependent scalar field environment sourced by its companion. In this work, we calculate numerically the sensitivities of nonrotating black holes, including spontaneously scalarized ones, in three classes of Einstein-scalar-Gauss-Bonnet gravity: the shift-symmetric, dilatonic and Gaussian theories. When possible, we compare our results against perturbative analytical results, finding excellent agreement. Unlike their general relativistic counterparts, black holes in Einstein-scalar-Gauss-Bonnet gravity only exist in a restricted parameter space controlled by the theory's coupling constant. A preliminary study of the role played by the sensitivities in black hole binaries suggests that, in principle, black holes can be driven outside of their domain of existence during the inspiral, for binary parameters which we determine.

Nonlocal scalar fields in static spacetimes via heat kernels

We solve the non-local equation ${-e^{-\ell^2\square}\square{\phi}=J}$ for i) static scalar fields in static spacetimes and ii) time-dependent scalar fields in ultrastatic spacetimes. Corresponding equations are rewritten as non-local Poisson/inhomogeneous Helmholtz equations in compact and non-compact weighted/Riemannian manifolds using static/frequency-domain Green's functions, which can be computed from the heat kernels in the respective manifolds. With the help of the heat kernel estimates, we derive the static Green's function estimates and use them to discuss the regularity. We also present several examples of exact and estimated static/frequency-domain Green's functions.

The exact WKB and the Landau-Zener transition for asymmetry in cosmological particle production

Cosmological particle production by a time-dependent scalar field is common in cosmology. We focus on the mechanism of asymmetry production when interaction explicitly violates symmetry and its motion is rapid enough to create particles by itself. Combining the exact WKB analysis and the Landau-Zener transition, we point out that perturbation before the non-perturbative analysis may drastically change the structure of the Stokes lines of the theory. The Exact WKB can play an important role in avoiding such discrepancies.

Temporal Merge Tree Maps: A Topology-Based Static Visualization for Temporal Scalar Data.

Creating a static visualization for a time-dependent scalar field is a non-trivial task, yet very insightful as it shows the dynamics in one picture. Existing approaches are based on a linearization of the domain or on feature tracking. Domain linearizations use space-filling curves to place all sample points into a 1D domain, thereby breaking up individual features. Feature tracking methods explicitly respect feature continuity in space and time, but generally neglect the data context in which those features live. We present a feature-based linearization of the spatial domain that keeps features together and preserves their context by involving all data samples. We use augmented merge trees to linearize the domain and show that our linearized function has the same merge tree as the original data. A greedy optimization scheme aligns the trees over time providing temporal continuity. This leads to a static 2D visualization with one temporal dimension, and all spatial dimensions compressed into one. We compare our method against other domain linearizations as well as feature-tracking approaches, and apply it to several real-world data sets.

Equatorial orbits and imaging of hairy cubic Galileon black holes

Null and timelike equatorial orbits are investigated in a family of hairy black holes in the cubic Galileon theory. These include rotating generalizations of static black hole metrics supporting a time-dependent scalar field. Depending on the coupling and rotation, the properties of the geodesics expectedly deviate from general relativity. In particular, it is found that stable circular geodesics only exist below a critical coupling, which is related to the existence of an outermost stable circular orbit. Focusing on the strong-field region, images of an accretion disk are also produced to highlight tendencies that would constrain the model given further accurate observations of supermassive black holes.

Skyscraper visualization of multiple time-dependent scalar fields on surfaces

We present a system to visualize multiple time-dependent scalar fields defined on 3D surfaces as they arise from numerical simulations. Domain experts want to understand correlations between multiple scalar fields to verify underlying processes. However, existing visualization techniques require high exploration effort to perceive temporal changes and relations of multiple fields on 3D surfaces. This makes analysis time-consuming and carries a high risk of overlooking regions with specific correlations.Therefore, we introduce a novel concept to facilitate exploration of multiple time-dependent scalar fields simultaneously. The basic idea is to use a novel glyph-based depiction, called skyline visualization, which is inspired by the skyscraper metaphor from information visualization. The skyscrapers are represented by 2D and 3D bar charts, where their floors show the temporal behavior of scalar fields of the corresponding surface region. The user can interact with the skyline visualization to see at which surface areas the scalar fields take on striking values or whether correlations exist between them. Furthermore, the user can immediately see in which regions scalar fields change strongly over time or show strongly inverted behavior. We evaluated our system with several CFD engineers, radiologists and visualization experts. Compared to existing systems, they were able to find regions of interest quickly and with high accuracy.

Stationary spacetimes with time-dependent real scalar fields

In 1981 Wyman classified the solutions of the Einstein–Klein–Gordon equations with static spherically symmetric spacetime metric and vanishing scalar potential. For one of these classes, the scalar field linearly grows with time. We generalize this symmetry noninheriting solution, perturbatively, to a rotating one and extend the static solution exactly to arbitrary spacetime dimensions. Furthermore, we investigate the existence of nonminimally coupled, time-dependent real scalar fields on top of static black holes, and prove a no-hair theorem for stealth scalar fields on the Schwarzschild background.

Boson and neutron stars with increased density

We discuss boson stars and neutron stars, respectively, in a scalar-tensor gravity model with an explicitly time-dependent real scalar field. While the boson stars in our model – in contrast to the neutron stars – do not possess a hard core, we find that the qualitative effects of the formation of scalar hair are similar in both cases: the presence of the gravity scalar allows both type of stars to exist for larger central density as well as larger mass at given radius than their General Relativity counterparts. In particular, we find new types of neutron stars with scalar hair which have radii very close to the corresponding Schwarzschild radius and hence are comparable in density to black holes. This new branch of solutions is stable with respect to the decay into individual baryons.

Towards rotating noncircular black holes in string-inspired gravity

We study stationary slowly rotating black holes, up to quadratic order in the spin angular momentum, in dynamical Chern-Simons gravity and shift symmetric Einstein scalar Gauss-Bonnet gravity, as models of string-inspired gravities. These gravity theories modify general relativity by introducing dynamical scalar fields coupled with curvature invariants. We show that the linear time dependence of the scalar fields is allowed from the stationarity of the effective stress energy tensors. However, these time dependent scalar fields yield singular behavior of the metric functions at the black hole horizons, or they are incompatible with the stationarity of the spacetimes. Thus, these gravity theories admit only known solutions as regular stationary solutions. Our results suggest the non-existence of rotating non-circular black holes in these gravity theories.

Equivalence principle on cosmological backgrounds in scalar–tensor theories

We study the extent up to which the equivalence principle is obeyed in models of modified gravity and dark energy involving a single scalar degree of freedom. We focus on the effective field theories of dark energy describing the late time acceleration in the presence of ordinary matter species. In their covariant form these coincide with the Horndeski theories on a cosmological background with a slowly varying Hubble rate and a time-dependent scalar field. We show that in the case of an exactly de Sitter universe both the weak and strong equivalence principles hold. This occurs due to the combination of the shift symmetry of the scalar and the time translational invariance of de Sitter space. When generalized to Friedmann–Robertson–Walker cosmologies (FRW) we show that the weak equivalence principle is obeyed for test particles and extended objects in the quasi-static subhorizon limit. We do this by studying the field created by an extended object moving in an FRW background as well as its equation of motion in an external gravitational field. We also estimate the corrections to the geodesic equation of the extended object due to the approximations made.

Black hole solutions in shift-symmetric degenerate higher-order scalar-tensor theories

We show that most classes of shift-symmetric degenerate higher-order scalar-tensor (DHOST) theories which satisfy certain degeneracy conditions are not compatible with the conditions for the existence of exact black hole solutions with a linearly time-dependent scalar field whose canonical kinetic term take a constant value. Combined with constraints from the propagation speed of gravitational waves, our results imply that cubic DHOST theories are strongly disfavored and that pure quadratic theories are likely to be the most viable class of DHOST theories. We find exact static and spherically symmetric (Schwarzschild and Schwarzschild-(anti-)de Sitter) black hole solutions in all shift-symmetric higher-derivative scalar-tensor theories which contain up to cubic order terms of the second-order derivatives of the scalar field, especially the full class of Horndeski and Gleyzes-Langlois-Piazza-Vernizzi theories. After deriving the conditions for the coupling functions in the DHOST Lagrangian that allow the exact solutions, we clarify their compatibility with the degeneracy conditions.