Late Time Limit Research Articles

Is the effective field theory of dark energy effective?

The effective field theory of cosmic acceleration systematizes possible contributions to the action, accounting for both dark energy and modifications of gravity. Rather than making model dependent assumptions, it includes all terms, subject to the required symmetries, with four (seven) functions of time for the coefficients. These correspond respectively to the Horndeski and general beyond Horndeski class of theories. We address the question of whether this general systematization is actually effective, i.e. useful in revealing the nature of cosmic acceleration when compared with cosmological data. The answer is no and yes: there is no simple time dependence of the free functions—assumed forms in the literature are poor fits, but one can derive some general characteristics in early and late time limits. For example, we prove that the gravitational slip must restore to general relativity in the de Sitter limit of Horndeski theories, and why it doesn't more generally. We also clarify the relation between the tensor and scalar sectors, and its important relation to observations; in a real sense the expansion history H(z) or dark energy equation of state w(z) is 1/5 or less of the functional information! In addition we discuss the de Sitter, Horndeski, and decoupling limits of the theory utilizing Goldstone techniques.

What happens in a measurement?

It is assumed that in a measurement the system under study interacts with a macroscopic measuring apparatus, in such a way that the density matrix of the measured system evolves according to the Lindblad equation. Under an assumption of non-decreasing von Neumann entropy, conditions on the operators appearing in this equation are given that are necessary and sufficient for the late-time limit of the density matrix to take the form appropriate for a measurement. Where these conditions are satisfied, the Lindblad equation can be solved explicitly. The probabilities appearing in the late-time limit of this general solution are found to agree with the Born rule, and are independent of the details of the operators in the Lindblad equation.

Late time behavior of non-conformal plasmas

We determine analytically the dependence of the approach to thermal equilibrium of strongly coupled plasmas on the breaking of scale invariance. The theories we consider are the holographic duals to Einstein gravity coupled to a scalar with an exponential potential. The coefficient in the exponent, $X$, is the parameter that controls the deviation from the conformally invariant case. For these models we obtain analytic solutions for the plasma expansion in the late-time limit, under the assumption of boost-invariance, and we determine the scaling behaviour of the energy density, pressure, and temperature as a function of time. We find that the temperature decays as a function of proper time as $T\sim \tau^{-s/4}$ with $s$ determined in terms of the non-conformality parameter $X$ as $s=4(1-4X^2)/3$. This agrees with the result of Janik and Peschanski, $s=4/3$, for the conformal plasmas and generalizes it to non-conformal plasmas with $X\neq 0$. We also consider more realistic potentials where the exponential is supplemented by power-law terms. Even though in this case we cannot have exact solutions, we are able under certain assumptions to determine the scaling of the energy, that receives logarithmic corrections.

Dynamics of driven flow with exclusion in graphenelike structures.

We present a mean-field theory for the dynamics of driven flow with exclusion in graphenelike structures, and numerically check its predictions. We treat first a specific combination of bond transmissivity rates, where mean field predicts, and numerics to a large extent confirms, that the sublattice structure characteristic of honeycomb networks becomes irrelevant. Dynamics, in the various regions of the phase diagram set by open boundary injection and ejection rates, is then in general identical to that of one-dimensional systems, although some discrepancies remain between mean-field theory and numerical results, in similar ways for both geometries. However, at the critical point for which the characteristic exponent is z=3/2 in one dimension, the mean-field value z=2 is approached for very large systems with constant (finite) aspect ratio. We also treat a second combination of bond (and boundary) rates where, more typically, sublattice distinction persists. For the two rate combinations, in continuum or late-time limits, respectively, the coupled sets of mean-field dynamical equations become tractable with various techniques and give a two-band spectrum, gapless in the critical phase. While for the second rate combination quantitative discrepancies between mean-field theory and simulations increase for most properties and boundary rates investigated, theory still is qualitatively correct in general, and gives a fairly good quantitative account of features such as the late-time evolution of density profile differences from their steady-state values.

A theoretical framework for modeling dilution enhancement of non-reactive solutes in heterogeneous porous media

Spatial heterogeneity of the hydraulic properties of geological porous formations leads to erratically shaped solute clouds, thus increasing the edge area of the solute body and augmenting the dilution rate. In this study, we provide a theoretical framework to quantify dilution of a non-reactive solute within a steady state flow as affected by the spatial variability of the hydraulic conductivity. Embracing the Lagrangian concentration framework, we obtain explicit semi-analytical expressions for the dilution index as a function of the structural parameters of the random hydraulic conductivity field, under the assumptions of uniform-in-the-average flow, small injection source and weak-to-mild heterogeneity. Results show how the dilution enhancement of the solute cloud is strongly dependent on both the statistical anisotropy ratio and the heterogeneity level of the porous medium. The explicit semi-analytical solution also captures the temporal evolution of the dilution rate; for the early- and late-time limits, the proposed solution recovers previous results from the literature, while at intermediate times it reflects the increasing interplay between large-scale advection and local-scale dispersion. The performance of the theoretical framework is verified with high resolution numerical results and successfully tested against the Cape Cod field data.

Matter bounce loop quantum cosmology fromF(R)gravity

Using the reconstruction method, we investigate which $F(R)$ theories, with or without the presence of matter fluids, can produce the matter bounce scenario of holonomy corrected Loop Quantum Cosmology. We focus our study in two limits of the cosmic time, the large cosmic time limit and the small cosmic time limit. For the former, we found that, in the presence of non-interacting and non-relativistic matter, the $F(R)$ gravity that reproduces the late time limit of the matter bounce solution is actually the Einstein-Hilbert gravity plus a power law term. In the early time limit, since it corresponds to large spacetime curvatures, assuming that the Jordan frame is described by a general metric that when it is conformally transformed to the Einstein frame, produces an accelerating Friedmann-Robertson-Walker metric, we found explicitly the scalar field dependence on time. After demonstrating that the solution in the Einstein frame is indeed accelerating, we calculate the spectral index derived from the Einstein frame scalar-tensor counterpart theory of the $F(R)$ theory and compare it with the Planck experiment data. In order to implement the resulting picture, we embed the $F(R)$ gravity explicitly in a Loop Quantum Cosmology framework by introducing holonomy corrections to the $F(R)$ gravity. In this way, the resulting inflation picture corresponding to the $F(R)$ gravity can be corrected in order it coincides to some extent with the current experimental data.

Strong washout approximation to resonant leptogenesis

We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit ε=Xsin(2φ)/(X2+sin2φ), where X=8πΔ/(|Y1|2+|Y2|2), Δ=4(M1-M2)/(M1+M2), φ=arg(Y2/Y1), and M1,2, Y1,2 are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where |Y1,2|2≫ Δ, i.e. where the width dominates the mass splitting. We generalise the formula for the effective decay asymmetry to the case of several flavours of active leptons and demonstrate how this quantity can be used to calculate the lepton asymmetry for phenomenological scenarios that are in agreement with the observed neutrino oscillations. We establish analytic criteria for the validity of the late-time approximation for the decay asymmetry and compare these with numerical results that are obtained by solving for the mixing and the oscillations of the sterile neutrinos. For phenomenologically viable models with two sterile neutrinos, we find that the flavoured effective late-time decay asymmetry can be applied throughout parameter space.

Quantum corrected mode function and power spectrum for a scalar field during inflation

We compute the one- and two-loop corrected mode function of a massless minimally coupled scalar endowed with a quartic self-interaction in the locally de Sitter background of an inflating universe for a state which is released in Bunch-Davies vacuum at time $t=0$. We then employ it to correct the scalar's tree-order scale invariant power spectrum $\Delta^2_\varphi$. The corrections are secular, and have scale dependent part that can be expanded in even powers of $k/(Ha)$, where $k$ is the comoving wave number, $H$ is the expansion rate and $a$ is the cosmic scale factor. At one-loop, the scale invariant shift in the power spectrum grows as $(Ht)^2$ in leading order. The $k$-dependent shifts, however, are constants for each mode, in the late time limit. At two-loop order, on the other hand, the scale invariant shift grows as $(Ht)^4$ whereas the $k$-dependent shifts grow as $(Ht)^2$, in leading order. We finally calculate the scalar's spectral index $n_\varphi$ and the running of the spectral index $\alpha_\varphi$. They imply that the spectrum is slightly red-tilted; hence, the amplitudes of fluctuations grow slightly towards the larger scales.

Counterterms in cosmological perturbation theory

Cosmological perturbation theory is the theory of fluctuations (scalar as well as tensor) around the inflationary cosmological background solution. It is important to understand the details of the process of renormalization in this theory. In more familiar applications of quantum field theory, the dependence on the external momenta of the dimensionally regulated expression of the one-loop contribution to a correlator determines the number of counterterms (and their forms) required to renormalize it. In this work, it is pointed out that in cosmological perturbation theory, though this still happens, it happens in a completely different way such that in the late time limit, the information about the number and forms of counterterms required gets erased. This is to be compared with what happens in spontaneous symmetry breaking where the use of fluctuation fields around a chosen vacuum seems to suggest that more counterterms are needed to renormalize the theory than are actually required. We also comment on how the field strength of curvature perturbation, $\ensuremath{\zeta}$, could get renormalized.

Outgoing gravitational shock wave at the inner horizon: The late-time limit of black hole interiors

We investigate the interiors of 3+1 dimensional asymptotically flat charged and rotating black holes as described by observers who fall into the black holes at late times, long after any perturbations of the exterior region have decayed. In the strict limit of late infall times, the initial experiences of such observers are precisely described by the region of the limiting stationary geometry to the past of its inner horizon. However, we argue that late infall-time observers encounter a null shockwave at the location of the would-be outgoing inner horizon. In particular, for spherically symmetric black hole spacetimes we demonstrate that freely-falling observers experience a metric discontinuity across this shock, that is, a gravitational shock-wave. Furthermore, the magnitude of this shock is at least of order unity. A similar phenomenon of metric discontinuity appears to take place at the inner horizon of a generically-perturbed spinning black hole. We compare the properties of this null shockwave singularity with those of the null weak singularity that forms at the Cauchy horizon.

G-Essence as the cosmic speed-up

In the present work we analyze the g-essence model for the particular Lagrangian: \(L=R+2[\alpha X^{n}+\epsilon Y-V(\psi,\bar{\psi})]\). The g-essence models were proposed recently as an alternative and a generalization of the scalar k-essence models. We have presented the three types of the solutions for the g-essence model. We reconstructed the corresponding potentials and the dynamics of the scalar and fermionic fields according the evolution of the scale factor. The results show that the g-essence model predicts that our universe can be in both of the decelerated and accelerated expansion phases. In late time limit, we show that there is a family of exact solutions in which the free parameter may be remains in the range of m>−1. Further we discuss the existence of the de Sitter solutions in such a model.

Unruh–DeWitt Detectors in Spherically Symmetric Dynamical Space-Times

In the present paper, Unruh–DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh–DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW space-time interpolating de Sitter space with the Einstein–de Sitter universe (that is a more realistic situation in the frame of ΛCDM cosmologies), we show that the detector response splits into a de Sitter contribution plus a fluctuating term containing no trace of Boltzmann-like factors, but rather describing the way thermal equilibrium is reached in the late time limit. As a consequence, and unlike the case of black holes, the identification of the dynamical surface gravity of a cosmological trapping horizon as an effective temperature parameter seems lost, at least for our co-moving simplified detectors. The possibility remains that a detector performing a proper motion along a Kodama trajectory may register something more, in which case the horizon surface gravity would be associated more likely to vacuum correlations than to particle creation.

NUMERICAL TEST OF IMPROVED NONLINEAR GUIDING CENTER THEORIES

Previous diffusion theories make diverse predictions concerning the ability of slab modes to scatter charged particles across the mean magnetic field. Whereas the original nonlinear guiding center theory provides a strong contribution of slab modes if a two-component model is employed, improved nonlinear guiding center theories describe cross-field transport due to slab modes as a subdiffusive process. Therefore, the slab fluctuations do not explicitly contribute to the perpendicular spatial diffusion coefficient in the late time limit. In the present article, numerical simulations are used to explore the validity of the different predictions. Only a very weak contribution is found due to slab modes. The numerical results confirm improved nonlinear guiding center theories. This conclusion has also implications for cross-field diffusion in three-dimensional turbulence.

Exact Friedmann solutions in higher-order gravity theories

We find the general behaviour of homogeneous and isotropic cosmological models in some fourth-order theories of gravity. Explicit, exact, general solutions are given for both empty universes and those filled with a perfect fluid. For the vacuum case, solutions are found with closed, open and flat geometries, whilst the perfect fluid solutions are all spatially flat. Both early- and late-time limits are studied, and attractor behaviour towards simple power-law expansion is identified. Multiple solutions to the same theories, with the same matter content and topology are found. It is shown that these solutions exhibit a great variety in their evolution.

Efficient spectral IP-modelling in the time domain

We show that the modelling of time-domain spectral induced polarization (SIP) data can be carried out using a DC resistivity code. The intrinsic resistivity at each point in space is calculated by Fourier transforming the complex, frequency-dependent resistivity, and a separate DC problem is solved for each time channel. This procedure constitutes an approximation, because the exact formulation involves a convolution of the time-dependent conductivities with the electric field. The approximation dramatically simplifies numerical modelling of time-domain SIP data. Implicitly, it is already in use in inversion routines where data are inverted independently for separate time channels. However, the accuracy has not been investigated in detail. We first formulate the underlying equations in terms of a maximum chargeability M. We expand the exact and the approximate solutions with respect to the maximum chargeability and show that the differences are at least second order in M. Next, we investigate the reflection factor for a simple two-layer model, where the second layer resistivity is assumed to exhibit Cole–Cole behaviour. We calculate exact and approximate solutions analytically and show that the early- and late-time limits are identical. In the intermediate time range the error of the approximation is limited to a few percent. Finally, we calculate approximate and exact apparent resistivities for dipole–dipole configurations over a layered and a full 3-D model and show that the differences are far below the typical measurement noise level. The conclusion is that the approximation is excellent and will work in all practical situations.

Tachyon driven quantum cosmology in string theory

The quantum mechanical analysis of the canonical hamiltonian description of the effective action of a SDp-brane in bosonic ten dimensional Type II supergravity in a homogeneous background is given. We find exact solutions for the corresponding quantum theory by solving the Wheeler-deWitt equation in the late-time limit of the rolling tachyon. The probability densities for several values of p are shown and their possible interpretation is discussed. In the process the effects of electromagnetic fields are also incorporated and it is shown that in this case the interpretation of tachyon regarded as ``matter clock'' is modified.

Quantum cosmology of tachyons in string theory

The Hamiltonian formulation of the effective bosonic action of the SDp-brane in Type II superstring theory is given. This effective description involves the Tachyon driven matter coupled to bosonic ten dimensional Type II supergravity. An exact solution to the corresponding Wheeler-deWitt equation in the late-time limit of the rolling tachyon is found. Finally some comments about the incorporation of electromagnetic fluxes are given.

Brane-Cosmology Dynamics with Induced Gravity

The Friedmann equations for a brane with induced gravity are analyzed and compared with the standard general relativity and Randall-Sundrum cases. Randall-Sundrum gravity modifies the early universe dynamics, whereas induced gravity changes the late universe evolution. The early and late time limits are investigated. Induced gravity effects can contribute to late-universe acceleration. The conditions for this are found. Qualitative analysis is given for a range of scalar field potentials.

ANISOTROPIC BRANE COSMOLOGIES WITH EXPONENTIAL POTENTIALS

We study Bianchi I type brane cosmologies with scalar matter self-interacting through combinations of exponential potentials. Such models correspond in some cases to inflationary universes. We discuss in detail the conditions for accelerated expansion to occur: in particular, we show that the condition which is necessary and sufficient for inflation in the relativistic version of the models is not sufficient in the brane case. Another peculiar feature of the models is that the relationship between the value of the scale factor at the beginning of inflation and the equation of state is very different from what one finds in the relativistic framework. We also analyze the influence of the value of the anisotropy and the brane tension, and show that the associated effects become negligible in the late time limit, those related to the anisotropy disappearing earlier. This study focuses mainly on single field models, but we also consider a generalization yielding models with multiple non-interacting fields and examine their features briefly. We conclude that, in the brane scenario, an increase in the number of fields assists inflation, as happened in general relativity.

Nonexponential decay at late times and a different Zeno paradox

The decay profile of a metastable quantum state decaying in isolation is predicted to depart from exponential behaviour after many lifetimes, and in typical cases to adopt algebraic behaviour as the late-time limit. The effect of environmental interactions, including measurement, is quite different from that of the familiar Zeno (and anti-Zeno) effects that have been observed at very early times. Instead of arresting the decay (or hastening it), the late-time interactions tend to enforce the exponential decay law, without substantially changing the decay constant intrinsic to the isolated system. The experimental challenge is to prevent these interactions and observe the crossover to the nonexponential regime.