Dynamics Of Scalar Field Research Articles

K-inflationary power spectra in the uniform approximation

The advent of explicit Dirac-Born-Infeld inflationary models within string theory has drawn renewed interest to the cosmological role of unusual scalar field dynamics, usually referred to as $k$-inflation. In this situation, the standard method used to determine the behavior of cosmological perturbations breaks down. We present a generic method, based on the uniform approximation, to analytically derive the power spectra of scalar and tensor perturbations. For this purpose, a simple hierarchy of parameters, related to the sound speed of the cosmological fluctuations and its successive derivatives, is introduced in a $k$-inflation analogue of the Hubble flow functions. The scalar spectral index and its running are obtained up to next-to-next-to-leading order for all $k$-inflationary models. This result relies on the existence of a well-motivated initial state, which is not trivial in the present context: having the wavelength of the Fourier mode smaller than the sonic horizon is indeed not enough and some conditions on the dynamics of the sound speed are also required. Our method is then applied to various models encountered in the literature. After deriving a generic slow-roll trajectory valid for any Dirac-Born-Infeld model, simple formulae for the cosmological observables are obtained. In particular, the running, as the spectral index, for the so-called UV and IR brane inflationary models is found to be uniquely determined by the 't Hooft coupling. Finally, the accuracy of these cosmological predictions is assessed by comparing the analytical approximations with exact numerical integrations.

Heavy Fermion Quantum Criticality

During the last few years, investigations of rare-earth materials have made clear that heavy fermion quantum criticality exhibits novel physics not fully understood. In this work, we write for the first time the effective action describing the low energy physics of the system. The f fermions are replaced by a dynamical scalar field whose nonzero expected value corresponds to the heavy fermion phase. The effective theory is amenable to numerical studies as it is bosonic, circumventing the fermion sign problem. Via effective action techniques, renormalization group studies, and Callan-Symanzik resummations, we describe the heavy fermion criticality and predict the heavy fermion critical dynamical susceptibility and critical specific heat. The specific heat coefficient exponent we obtain (0.39) is in excellent agreement with the experimental result at low temperatures (0.4).

Langevin simulations with colored noise and non-Markovian dissipation

The nonequilibrium dynamics of an homogeneous scalar field is studied using Langevin equations. Microscopic derivations based on quantum field theory methods can lead to complicated nonlocal equations of motion. Here we study, numerically, the results obtained by appropriately approximating these equations in a local form (the Markovian approximation) and compare with results obtained with suitable prescriptions for accounting for the nonlocal terms, i.e. the non-Markovian form. We use a prescription for the nonlocal equations motivated by the results obtained from previous derivations using nonequilibrium quantum field theory methods.

Neutrino masses from cosmological probes in interacting neutrino dark-energy models

We investigate whether interaction between massive neutrinos and quintessence scalar field is the origin of the late time accelerated expansion of the universe. We present explicit formulas of the cosmological linear perturbation theory in the neutrinos probes of dark-energy model, and calculate cosmic microwave background anisotropies and matter power spectra. In these models, the evolution of the mass of neutrinos is determined by the quintessence scalar field, which is responsible for a varying effective equation of states; ?eff(z) goes down lesser than -1. We consider several types of scalar field potential and put constraints on the coupling parameter between neutrinos and dark energy. By combining data from cosmic microwave background (CMB) experiments including the WMAP 3-year results, large scale structure with 2dFGRS data sets, we constrain the hypothesis of massive neutrinos in the mass-varying neutrino scenario. Assuming the flatness of the universe, the constraint we can derive from the current observation is ?m??<?0.45 eV at 1? (0.87 eV at 2?) confidence level for the sum over three species of neutrinos. The dynamics of scalar field and the impact of scalar field perturbations on cosmic microwave background anisotropies are discussed. We also discuss on the instability issue and confirm that neutrinos are stable against the density fluctuation in our model.

Reconstructing a model of quintessential inflation

We present an explicit cosmological model where inflation and dark energy both could arise from the dynamics of the same scalar field. We present our discussion in the framework where the inflaton field ϕ attains a nearly constant velocity m−1P|dϕ/dN| ≡ α + βexp(βN) (where N ≡ ln a is the e-folding time) during inflation. We show that the model with |α| < 0.25 and β < 0 can easily satisfy inflationary constraints, including the spectral index of scalar fluctuations (ns = 0.96 ± 0.013), tensor-to-scalar ratio (r < 0.28) and also the bound imposed on Ωϕ during the nucleosynthesis epoch (Ωϕ(1 ∼ MeV) < 0.1). In our construction, the scalar field potential always scales proportionally to the square of the Hubble expansion rate. One may thereby account for the two vastly different energy scales associated with the Hubble parameters at early and late epochs. The inflaton energy could also produce an observationally significant effective dark energy at a late epoch without violating local gravity tests.

Resource Letter DEAU-1: Dark energy and the accelerating universe

This Resource Letter provides a guide to the literature on dark energy and the accelerating universe. It is intended to be of use to researchers, teachers, and students at several levels. Journal articles, books, and websites are cited for the following topics: Einstein’s cosmological constant, quintessence or dynamical scalar fields, modified cosmic gravity, relations to high-energy physics, cosmological probes and observations, terrestrial probes, calculational tools and parameter estimation, teaching strategies and educational resources, and the fate of the universe.

Inflation and the semiclassical dynamics of a conformal scalar field

We derive the semiclassical evolution of massless conformally coupled scalar matter in the de Sitter space-time from the Born-Oppenheimer reduction of the Wheeler-DeWitt equation. We find a remarkable difference with respect to the minimally coupled case: the effect of the quantum gravitational corrections does not depend on the momentum of the scalar mode up to second order in the Planck length and, therefore, there are no relevant corrections to the dispersion relation.

Exact results for two-dimensional coarsening

We consider the statistics of the areas enclosed by domain boundaries (‘hulls’) during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area, n h (A, t)dA, with enclosed area in the range (A,A + dA), is described, for large time t, by the scaling form n h (A, t) = 2c h /(A + λ h t)2, demonstrating the validity of dynamical scaling in this system. Here $$ c_h = {1 \mathord{\left/ {\vphantom {1 8}} \right. \kern-\nulldelimiterspace} 8}\pi \sqrt 3 $$ is a universal constant associated with the enclosed area distribution of percolation hulls at the percolation threshold, and λ h is a material parameter. The distribution of domain areas, n d (A, t), is apparently very similar to that of hull areas up to very large values of A/λ h t. Identical forms are obtained for coarsening from a critical initial state, but with c h replaced by c h /2. The similarity of the two distributions (of areas enclosed by hulls, and of domain areas) is accounted for by the smallness of c h . By applying a ‘mean-field’ type of approximation we obtain the form n d (A, t) ≃ 2c d [λ d (t+t 0)] τ−2/[A+λ d (t+t 0)] τ , where t 0 is a microscopic timescale and τ = 187/91 ≃ 2.055, for a disordered initial state, and a similar result for a critical initial state but with c d → c d /2 and τ → τ c = 379/187 ≃ 2.027. We also find that c d = c h + O(c 2 ) and λ d = λ h (1 + O(c h )). These predictions are checked by extensive numerical simulations and found to be in good agreement with the data.

Greybody Factor and Hawking Radiation of Charged Dilatonic Black Holes

The greybody factor and the Hawking temperature for a class of asymptotically flat charged dilatonic black holes are computed by using the low-energy dynamics of scalar fields in the black hole background. In the semi-classical approximation, the Hawking temperature has a good agreement with the one computed from the surface gravity, which is independent of the magnetic (or electric) charges of dilatonic black holes.

Domain and hull-enclosed area distributions in two-dimensional coarsening

We obtain the exact distribution of the areas enclosed by domain boundaries (“hulls”) during the coarsening dynamics of a two-dimensional nonconserved scalar field. We prove that the number of hulls per unit area that enclose an area greater than A has the form N h ( A , t ) = 2 c / ( A + λ t ) , where c = 1 8 π 3 . This result is also a demonstration of the validity of the dynamical scaling hypothesis in this system. We also show that domain areas (regions of aligned spins) have a similar distribution.

De-Sitter Space and Some Exact Matter Solutions: D=3 Scalar Field Dynamics

De-Sitter Space and Some Exact Matter Solutions: D=3 Scalar Field Dynamics

Dynamical behavior of generic quintessence potentials: Constraints on key dark energy observables

We perform a comprehensive study of a class of dark energy models---scalar field models where the effective potential can be described by a polynomial series---exploring their dynamical behavior using the method of flow equations that has previously been applied to inflationary models. Using supernova, baryon oscillation, cosmic microwave background (CMB) and Hubble constant data, and an implicit theoretical prior imposed by the scalar field dynamics, we find that the $\ensuremath{\Lambda}\mathrm{CDM}$ model provides an excellent fit to the data. Constraints on the generic scalar field potential parameters are presented, along with the reconstructed $w(z)$ histories consistent with the data and the theoretical prior. We propose and pursue computationally feasible algorithms to obtain estimates of the principal components of the equation of state, as well as parameters ${w}_{0}$ and ${w}_{a}$. Further, we use the Monte Carlo Markov chain machinery to simulate future data based on the Joint Dark Energy Mission, Planck, and baryon acoustic oscillation surveys and find that the inverse area figure of merit improves nearly by an order of magnitude. Therefore, most scalar field models that are currently consistent with data can be potentially ruled out by future experiments. We also comment on the classification of dark energy models into thawing and freezing in light of the more diverse evolution histories allowed by this general class of potentials.

Exact Results for Curvature-Driven Coarsening in Two Dimensions

We consider the statistics of the areas enclosed by domain boundaries ("hulls") during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than A has, for large time t, the scaling form Nh(A,t)=2c/(A+lambdat), demonstrating the validity of dynamical scaling in this system, where c=1/8pisquare root 3 is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of A/lambdat. Identical forms are obtained for coarsening from a critical initial state, but with c replaced by c/2.

Noncommutative effects in the black hole evaporation in two dimensions

We discuss some possible implications of a two-dimensional toy model for black hole evaporation in noncommutative field theory. While the noncommutativity we consider does not affect gravity, it can play an important role in the dynamics of massless and Hermitian scalar fields in the event horizon of a Schwarzschild black hole. We find that noncommutativity will affect the flux of outgoing particles and the nature of its UV/IR divergences. Moreover, we show that the noncommutative interaction does not affect Leahy's and Unruh's interpretation of thermal ingoing and outgoing fluxes in the black hole evaporation process. Thus, the noncommutative interaction still destroys the thermal nature of fluxes. In the process, some nonlocal implications of the noncommutativity are discussed.

A vielbein formulation of unified Einstein–Maxwell theory

In the framework of -bundles a vielbein formulation of unified Einstein–Maxwell theory is proposed. In the resulting scheme, field equations matching the gravitational and electromagnetic fields are derived by constraining a five-dimensional variational principle. No dynamical scalar field is involved.

Interacting quintessence, the coincidence problem, and cosmic acceleration

Faced by recent evidence for a flat universe dominated by dark energy, cosmologists grapple with deep cosmic enigmas such as the cosmological constant problem, extreme fine-tuning and the cosmic coincidence problem. The extent to which we observe the dimming of distant supernovae suggests that the cosmic acceleration is as least as severe as in cosmological constant models. Extrapolating this to our cosmic future implies terrifying visions of either a cold and empty universe or an explosive demise in a ``Big Rip.'' We construct a class of dynamical scalar field models of dark energy and dark matter. Within this class we can explain why supernovae imply a cosmic equation of state $w\ensuremath{\lesssim}\ensuremath{-}1$, address fine-tuning issues, protect the universe from premature acceleration and predict a constant fraction of dark energy to dark matter in the future (thus solving the coincidence problem), satisfy the dominant energy condition, and ensure that gravitationally bound objects remain so forever (avoid a Big Rip). This is achieved with a string theory inspired Lagrangian containing standard kinetic terms, exponential potentials and couplings, and parameters of order unity.

Dynamics of generalized assisted inflation

We study the dynamics of multiple scalar fields and barotropic fluid in an FLRW-universe. The scalar potential is a sum of exponentials. All critical points are constructed and these include scaling and de Sitter solutions. A stability analysis of the critical points is performed for generalized assisted inflation, which is an extension of assisted inflation where the fields mutually interact. Effects in generalized assisted inflation which differ from assisted inflation are emphasized. One such difference is that an (inflationary) attractor can exist if some of the exponential terms in the potential are negative.

Comparison of Boltzmann equations with quantum dynamics for scalar fields

Boltzmann equations are often used to study the thermal evolution of particle reaction networks. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after relativistic heavy ion collisions. However, Boltzmann equations are only a classical approximation of the quantum thermalization process which is described by the so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the full Kadanoff-Baym equations. Therefore, we present in this paper a detailed comparison between the Kadanoff-Baym and Boltzmann equations in the framework of a scalar ${\ensuremath{\Phi}}^{4}$ quantum field theory in $3+1$ space-time dimensions. The obtained numerical solutions reveal significant discrepancies in the results predicted by both types of equations. Apart from quantitative discrepancies, on a qualitative level the universality respected by the Kadanoff-Baym equations is severely restricted in the case of Boltzmann equations. Furthermore, the Kadanoff-Baym equations strongly separate the time scales between kinetic and chemical equilibration. This separation of time scales is absent for the Boltzmann equation.

Non-gravitating scalars and spacetime compactification

Abstract We discuss role of partially gravitating scalar fields, scalar fields whose energy–momentum tensors vanish for a subset of dimensions, in dynamical compactification of a given set of dimensions. We show that the resulting spacetime exhibits a factorizable geometry consisting of usual four-dimensional spacetime with full Poincare invariance times a manifold of extra dimensions whose size and shape are determined by the scalar field dynamics. Depending on the strength of its coupling to the curvature scalar, the vacuum expectation value (VEV) of the scalar field may or may not vanish. When its VEV is zero the higher-dimensional spacetime is completely flat and there is no compactification effect at all. On the other hand, when its VEV is nonzero the extra dimensions get spontaneously compactified. The compactification process is such that a bulk cosmological constant is utilized for curving the extra dimensions.

Cosmological tachyon from cubic string field theory

The classical dynamics of the tachyon scalar field of cubic string field theory is considered on a cosmological background. Starting from a nonlocal action with arbitrary tachyon potential, which encodes the bosonic and several supersymmetric cases, we study the equations of motion in the Hamilton-Jacobi formalism and with a generalized Friedmann equation, appliable in braneworld or modified gravity models. The cases of cubic (bosonic) and quartic (supersymmetric) tachyon potential in general relativity are automatically included. We comment the validity of the slow-roll approximation, the stability of the cosmological perturbations, and the relation between this tachyon and the Dirac-Born-Infeld one.