arXiv subjects

Sergei Winitzki

Publications and source records attributed to Sergei Winitzki.

14 recordsLinked to original sources

arXiv2011

Geometro-thermodynamics of tidal charged black holes

Tidal charged spherically symmetric vacuum brane black holes are characterized by their mass m and tidal charge q, an imprint of the 5-dimensional Weyl curvature. For q>0 they are formally identical to the Reissner-Nordström black hole of general relativity. We study the thermodynamics and thermodynamic geometries of tidal charged black holes and discuss similarities and differences as compared to the Reissner-Nordström black hole. As a similarity, we show that (for q>0) the heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space, nevertheless both the regularity of the Ruppeiner metric and a Poincaré stability analysis shows no phase transition at those points. The thermodynamic state spaces being different indicates that the underlying statistical models could be different. We find that the q<0 parameter range, which enhances the localization of gravity on the brane, is thermodynamically preferred. Finally we constrain for the first time the possible range of the tidal charge from the thermodynamic limit on gravitational radiation efficiency at black hole mergers.

gr-qc↗

arXiv2010

Observability of the total inflationary expansion

I consider the question of possible observability of the total number of e-folds accumulated during the epoch of inflation. The total number of observable e-folds has been previously constrained by the de Sitter entropy after inflation, assuming that the null energy condition (NEC) holds. The NEC is violated by upward fluctuations of the local Hubble rate, which occur with high probability in the fluctuation-dominated regime of inflation. These fluctuations lead at late times to the formation of black holes and thus limit the observability of inflationary evolution. I compute the maximum number of e-folds that can be observed in principle through measurements of the CMB at arbitrarily late times (if the dark energy disappears). The calculation also provides a reasonably precise definition of the boundary of the fluctuation-dominated regime, with an uncertainty of a few percent. In simple models of single-field inflation compatible with current CMB observations, I find of order 10^5. This upper bound on the observable e-folds, although model-dependent, is much smaller than the de Sitter entropy after inflation. The method of calculation can be used in other models of single-field inflation.

gr-qc↗

arXiv2008

Stationary Measure in the Multiverse

We study the recently proposed "stationary measure" in the context of the string landscape scenario. We show that it suffers neither from the "Boltzmann brain" problem nor from the "youngness" paradox that makes some other measures predict a high CMB temperature at present. We also demonstrate a satisfactory performance of this measure in predicting the results of local experiments, such as proton decay.

hep-th↗

arXiv2008

Reheating-volume measure in the landscape

I recently proposed the "reheating-volume" (RV) prescription as a possible solution to the measure problem in "multiverse" cosmology. The goal of this work is to extend the RV measure to scenarios involving bubble nucleation, such as the string theory landscape. In the spirit of the RV prescription, I propose to calculate the distribution of observable quantities in a landscape that is conditioned in probability to nucleate a finite total number of bubbles to the future of an initial bubble. A general formula for the relative number of bubbles of different types can be derived. I show that the RV measure is well-defined and independent of the choice of the initial bubble type, as long as that type supports further bubble nucleation. Applying the RV measure to a generic landscape, I find that the abundance of Boltzmann brains is always negligibly small compared with the abundance of ordinary observers in the bubbles of the same type. As an illustration, I present explicit results for a toy landscape containing four vacuum states and for landscapes with a single high-energy vacuum and a large number of low-energy vacua.

gr-qc↗

arXiv2008

Reheating-volume measure for random-walk inflation

The recently proposed "reheating-volume" (RV) measure promises to solve the long-standing problem of extracting probabilistic predictions from cosmological "multiverse" scenarios involving eternal inflation. I give a detailed description of the new measure and its applications to generic models of eternal inflation of random-walk type. For those models I derive a general formula for RV-regulated probability distributions that is suitable for numerical computations. I show that the results of the RV cutoff in random-walk type models are always gauge-invariant and independent of the initial conditions at the beginning of inflation. In a toy model where equal-time cutoffs lead to the "youngness paradox," the RV cutoff yields unbiased results that are distinct from previously proposed measures.

gr-qc↗

arXiv2008

A volume-weighted measure for eternal inflation

I propose a new volume-weighted probability measure for cosmological "multiverse" scenarios involving eternal inflation. The "reheating-volume (RV) cutoff" calculates the distribution of observable quantities on a portion of the reheating hypersurface that is conditioned to be finite. The RV measure is gauge-invariant, does not suffer from the "youngness paradox," and is independent of initial conditions at the beginning of inflation. In slow-roll inflationary models with a scalar inflaton, the RV-regulated probability distributions can be obtained by solving nonlinear diffusion equations. I discuss possible applications of the new measure to "landscape" scenarios with bubble nucleation. As an illustration, I compute the predictions of the RV measure in a simple toy landscape.

gr-qc↗

arXiv2007

Age-dependent decay in the landscape

The picture of the "multiverse" arising in diverse cosmological scenarios involves transitions between metastable vacuum states. It was pointed out by Krauss and Dent that the transition rates decrease at very late times, leading to a dependence of the transition probability between vacua on the age of each vacuum region. I investigate the implications of this non-Markovian, age-dependent decay on the global structure of the spacetime in landscape scenarios. I show that the fractal dimension of the eternally inflating domain is precisely equal to 3, instead of being slightly below 3 in scenarios with purely Markovian, age-independent decay. I develop a complete description of a non-Markovian landscape in terms of a nonlocal master equation. Using this description I demonstrate by an explicit calculation that, under some technical assumptions about the landscape, the probabilistic predictions of our position in the landscape are essentially unchanged, regardless of the measure used to extract these predictions. I briefly discuss the physical plausibility of realizing non-Markovian vacuum decay in cosmology in view of the possible decoherence of the metastable quantum state.

hep-th↗

arXiv2007

Attractor scenarios and superluminal signals in k-essence cosmology

Cosmological scenarios with k-essence are invoked in order to explain the observed late-time acceleration of the universe. These scenarios avoid the need for fine-tuned initial conditions (the "coincidence problem") because of the attractor-like dynamics of the k-essence field ϕ. It was recently shown that all k-essence scenarios with Lagrangians p=L(X)/ϕ^2, necessarily involve an epoch where perturbations of ϕpropagate faster than light (the "no-go theorem"). We carry out a comprehensive study of attractor-like cosmological solutions ("trackers") involving a k-essence scalar field ϕand another matter component. The result of this study is a complete classification of k-essence Lagrangians that admit asymptotically stable tracking solutions, among all Lagrangians of the form p=K(ϕ)L(X) . Using this classification, we select the class of models that describe the late-time acceleration and avoid the coincidence problem through the tracking mechanism. An analogous "no-go theorem" still holds for this class of models, indicating the existence of a superluminal epoch. In the context of k-essence cosmology, the superluminal epoch does not lead to causality violations. We discuss the implications of superluminal signal propagation for possible causality violations in Lorentz-invariant field theories.

gr-qc↗

arXiv2007

Predictions in eternal inflation

In generic models of cosmological inflation, quantum fluctuations strongly influence the spacetime metric and produce infinitely many regions where the end of inflation (reheating) is delayed until arbitrarily late times. The geometry of the resulting spacetime is highly inhomogeneous on scales of many Hubble sizes. The recently developed string-theoretic picture of the "landscape" presents a similar structure, where an infinite number of de Sitter, flat, and anti-de Sitter universes are nucleated via quantum tunneling. Since observers on the Earth have no information about their location within the eternally inflating universe, the main question in this context is to obtain statistical predictions for quantities observed at a random location. I describe the problems arising within this statistical framework, such as the need for a volume cutoff and the dependence of cutoff schemes on time slicing and on the initial conditions. After reviewing different approaches and mathematical techniques developed in the past two decades for studying these issues, I discuss the existing proposals for extracting predictions and give examples of their applications.

gr-qc↗

arXiv2006

Self-reproduction in k-inflation

We study cosmological self-reproduction in models of inflation driven by a scalar field $ϕ$ with a noncanonical kinetic term ($k$-inflation). We develop a general criterion for the existence of attractors and establish conditions selecting a class of $k$-inflation models that admit a unique attractor solution. We then consider quantum fluctuations on the attractor background. We show that the correlation length of the fluctuations is of order $c_{s}H^{-1}$, where $c_{s}$ is the speed of sound. By computing the magnitude of field fluctuations, we determine the coefficients of Fokker-Planck equations describing the probability distribution of the spatially averaged field $ϕ$. The field fluctuations are generally large in the inflationary attractor regime; hence, eternal self-reproduction is a generic feature of $k$-inflation. This is established more formally by demonstrating the existence of stationary solutions of the relevant FP equations. We also show that there exists a (model-dependent) range $ϕ_{R}<ϕ<ϕ_{\max}$ within which large fluctuations are likely to drive the field towards the upper boundary $ϕ=ϕ_{\max}$, where the semiclassical consideration breaks down. An exit from inflation into reheating without reaching $ϕ_{\max}$ will occur almost surely (with probability 1) only if the initial value of $ϕ$ is below $ϕ_{R}$. In this way, strong self-reproduction effects constrain models of $k$-inflation.

gr-qc↗

arXiv2005

Probabilities in the inflationary multiverse

Inflationary cosmology leads to the picture of a "multiverse," involving an infinite number of (spatially infinite) post-inflationary thermalized regions, called pocket universes. In the context of theories with many vacua, such as the landscape of string theory, the effective constants of Nature are randomized by quantum processes during inflation. We discuss an analytic estimate for the volume distribution of the constants within each pocket universe. This is based on the conjecture that the field distribution is approximately ergodic in the diffusion regime, when the dynamics of the fields is dominated by quantum fluctuations (rather than by the classical drift). We then propose a method for determining the relative abundances of different types of pocket universes. Both ingredients are combined into an expression for the distribution of the constants in pocket universes of all types.

hep-th↗

arXiv2005

Cosmological particle production and the precision of the WKB approximation

Particle production by slow-changing gravitational fields is usually described using quantum field theory in curved spacetime. Calculations require a definition of the vacuum state, which can be given using the adiabatic (WKB) approximation. I investigate the best attainable precision of the resulting approximate definition of the particle number. The standard WKB ansatz yields a divergent asymptotic series in the adiabatic parameter. I derive a novel formula for the optimal number of terms in that series and demonstrate that the error of the optimally truncated WKB series is exponentially small. This precision is still insufficient to describe particle production from vacuum, which is typically also exponentially small. An adequately precise approximation can be found by improving the WKB ansatz through perturbation theory. I show quantitatively that the fundamentally unavoidable imprecision in the definition of particle number in a time-dependent background is equal to the particle production expected to occur during that epoch. The results are illustrated by analytic and numerical examples.

gr-qc↗

arXiv2005

Time-reparametrization invariance in eternal inflation

I address some recently raised issues regarding the time-parametrization dependence in stochastic descriptions of eternal inflation. To clarify the role of the choice of the time gauge, I show examples of gauge-dependent as well as gauge-independent statements about physical observables in eternally inflating spacetimes. In particular, the relative abundance of thermalized and inflating regions is highly gauge-dependent. The unbounded growth of the 3-volume of the inflating regions is found in certain time gauges, such as the proper time or the scale factor gauge. Yet in the same spacetimes there exist time foliations with a finite and monotonically decreasing 3-volume, which I demonstrate by an explicit construction. I also show that there exists no "correct" choice of the time gauge that would yield an unbiased stationary probability distribution for observables in thermalized regions.

gr-qc↗

arXiv2005

Drawing conformal diagrams for a fractal landscape

Generic models of cosmological inflation and the recently proposed scenarios of a recycling universe and the string theory landscape predict spacetimes whose global geometry is a stochastic, self-similar fractal. To visualize the complicated causal structure of such a universe, one usually draws a conformal (Carter-Penrose) diagram. I develop a new method for drawing conformal diagrams, applicable to arbitrary 1+1-dimensional spacetimes. This method is based on a qualitative analysis of intersecting lightrays and thus avoids the need for explicit transformations of the spacetime metric. To demonstrate the power and simplicity of this method, I present derivations of diagrams for spacetimes of varying complication. I then apply the lightray method to three different models of an eternally inflating universe (scalar-field inflation, recycling universe, and string theory landscape) involving the nucleation of nested asymptotically flat, de Sitter and/or anti-de Sitter bubbles. I show that the resulting diagrams contain a characteristic fractal arrangement of lines.

gr-qc↗