arXiv subjects

Jaume Garriga

Publications and source records attributed to Jaume Garriga.

At least 37 records · Page 2Linked to original sources

arXiv2013

Rest frame of bubble nucleation

Vacuum bubbles nucleate at rest with a certain critical size and subsequently expand. But what selects the rest frame of nucleation? This question has been recently addressed in [1] in the context of Schwinger pair production in 1+1 dimensions, by using a model detector in order to probe the nucleated pairs. The analysis in [1] showed that, for a constant external electric field, the adiabatic "in" vacuum of charged particles is Lorentz invariant, and in this case pairs tend to nucleate preferentially at rest with respect to the detector. Here, we sharpen this picture by showing that the typical relative velocity between the frame of nucleation and that of the detector is at most of order Δv ~ S_E^{-1/3} << 1. Here, S_E >> 1 is the action of the instanton describing pair creation. The bound Δv coincides with the minimum uncertainty in the velocity of a non-relativistic charged particle embedded in a constant electric field. A velocity of order Δv is reached after a time interval of order Δt ~ S_E^{-1/3} r_0 << r_0 past the turning point in the semiclassical trajectory, where r_0 is the size of the instanton. If the interaction takes place in the vicinity of the turning point, the semiclassical description of collision does not apply. Nonetheless, we find that even in this case there is still a strong asymmetry in the momentum transferred from the nucleated particles to the detector, in the direction of expansion after the turning point. We conclude that the correlation between the rest frame of nucleation and that of the detector is exceedingly sharp.

hep-th↗

arXiv2013

Inflation and deformation of conformal field theory

It has recently been suggested that a strongly coupled phase of inflation may be described holographically in terms of a weakly coupled quantum field theory (QFT). Here, we explore the possibility that the wave function of an inflationary universe may be given by the partition function of a boundary QFT. We consider the case when the field theory is a small deformation of a conformal field theory (CFT), by the addition of a relevant operator O, and calculate the primordial spectrum predicted in the corresponding holographic inflation scenario. Using the Ward-Takahashi identity associated with Weyl rescalings, we derive a simple relation between correlators of the curvature perturbation and correlators of the deformation operator O at the boundary. This is done without specifying the bulk theory of gravitation, so that the result would also apply to cases where the bulk dynamics is strongly coupled. We comment on the validity of the Suyama-Yamaguchi inequality, relating the bi-spectrum and tri-spectrum of the curvature perturbation.

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arXiv2013

Observer dependence of bubble nucleation and Schwinger pair production

Pair production in a constant electric field is closely analogous to bubble nucleation in a false vacuum. The classical trajectories of the pairs are Lorentz invariant, but it appears that this invariance should be broken by the nucleation process. Here, we use a model detector, consisting of other particles interacting with the pairs, to investigate how pair production is seen by different Lorentzian observers. We focus on the idealized situation where a constant external electric field is present for an infinitely long time, and we consider the in-vacuum state for a charged scalar field that describes the nucleating pairs. The in-vacuum is defined in terms of modes which are positive frequency in the remote past. Even though the construction uses a particular reference frame and a gauge where the vector potential is time dependent, we show explicitly that the resulting quantum state is Lorentz invariant. We then introduce a "detector" particle which interacts with the nucleated pairs, and show that all Lorentzian observers will see the particles and antiparticles nucleating preferentially at rest in the detector's rest frame. Similar conclusions are expected to apply to bubble nucleation in a sufficiently long lived vacuum. We also comment on certain unphysical aspects of the Lorentz invariant in-vacuum, associated with the fact that it contains an infinite density of particles. This can be easily remedied by considering Lorentz breaking initial conditions.

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arXiv2013

Living with ghosts in Lorentz invariant theories

We argue that theories with ghosts may have a long lived vacuum state even if all interactions are Lorentz preserving. In space-time dimension D = 2, we consider the tree level decay rate of the vacuum into ghosts and ordinary particles mediated by non-derivative interactions, showing that this is finite and logarithmically growing in time. For D > 2, the decay rate is divergent unless we assume that the interaction between ordinary matter and the ghost sector is soft in the UV, so that it can be described in terms of non-local form factors rather than point-like vertices. We provide an example of a nonlocal gravitational-strength interaction between the two sectors, which appears to satisfy all observational constraints.

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arXiv2013

Watchers of the multiverse

An unresolved question in inflationary cosmology is the assignment of probabilities to different types of events that can occur in the eternally inflating multiverse. We explore the possibility that the resolution of this "measure problem" may rely on non-standard dynamics in regions of high curvature. In particular, "big crunch" singularities at the future boundary of bubbles with negative vacuum energy density may lead to bounces, where contraction is replaced by inflationary expansion driven by different vacua in the landscape. Similarly, singularities inside of black holes might be gateways to other inflating vacua. This would drastically affect the global structure of the inflating multiverse. We consider a measure based on a probe geodesic which undergoes an infinite number of passages through crunches. This can be thought of as the world-line of an eternal "watcher", collecting data in an orderly fashion. We compare this to previous approaches to the measure problem. The watcher's measure is independent of initial conditions and does not suffer from ambiguities associated with the choice of a cut-off surface. Another potential benefit from passing through crunches is that the observations collected by the watcher may easily depart from ergodicity, in very generic landscapes. This may significantly alleviate the problem of Boltzmann Brain dominance.

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arXiv2011

Minkowski vacua can be metastable

We investigate the recent suggestion that a Minkowski vacuum is either absolutely stable, or it has a divergent decay rate and thus fails to have a locally Minkowski description. The divergence comes from boost integration over momenta of the vacuum bubbles. We point out that a prototypical example of false-vacuum decay is pair production in a uniform electric field, so if the argument leading to the divergence is correct, it should apply to this case as well. We provide evidence that no catastrophic vacuum instability occurs in a constant electric field, indicating that the argument cannot be right. Instead, we argue that the boost integration that leads to the divergence is unnecessary: when all possible fluctuations of the vacuum bubble are included, the quantum state of the bubble is invariant under Lorentz boosts.

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arXiv2011

Holographic description of vacuum bubbles

We discuss a holographic description of vacuum bubbles, with possible implications for a consistent description of the multiverse. In particular, we elaborate on the recent observation by Maldacena, that the interior of AdS bubbles can be described in terms of CFT degrees of freedom living on the worldsheet of the bubble wall. We consider the scattering of bulk gravitons in the ambient parent vacuum, off the bubble wall. In the dual description, the transmission coefficient is interpreted as the probability that a graviton is absorbed by the worldsheet CFT degrees of freedom. The result is in agreement with intuitive expectations. Conformal invariance is not exact in this setup, and the leading corrections due to the IR and UV cut-offs are displayed. Aside from bulk scattering states, we find that when a bubble nucleates within a parent dS vacuum, there is a zero mode of the graviton which describes lower dimensional gravity with a finite Newton's constant. This massless graviton lives within one Hubble radius away from the bubble wall. Possible implications for a fully holographic description of the inflating multiverse are briefly discussed.

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arXiv2010

Semiclassical Unimodular Gravity

Classically, unimodular gravity is known to be equivalent to General Relativity (GR), except for the fact that the effective cosmological constant $Λ$ has the status of an integration constant. Here, we explore various formulations of unimodular gravity beyond the classical limit. We first consider the non-generally covariant action formulation in which the determinant of the metric is held fixed to unity. We argue that the corresponding quantum theory is also equivalent to General Relativity for localized perturbative processes which take place in generic backgrounds of infinite volume (such as asymptotically flat spacetimes). Next, using the same action, we calculate semiclassical non-perturbative quantities, which we expect will be dominated by Euclidean instanton solutions. We derive the entropy/area ratio for cosmological and black hole horizons, finding agreement with GR for solutions in backgrounds of infinite volume, but disagreement for backgrounds with finite volume. In deriving the above results, the path integral is taken over histories with fixed 4-volume. We point out that the results are different if we allow the 4-volume of the different histories to vary over a continuum range. In this "generalized" version of unimodular gravity, one recovers the full set of Einstein's equations in the classical limit, including the trace, so $Λ$ is no longer an integration constant. Finally, we consider the generally covariant theory due to Henneaux and Teitelboim, which is classically equivalent to unimodular gravity. In this case, the standard semiclassical GR results are recovered provided that the boundary term in the Euclidean action is chosen appropriately.

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arXiv2010

Primordial Perturbations in Einstein-Aether and BPSH Theories

We study the primordial perturbations generated during a stage of single-field inflation in Einstein-aether theories. Quantum fluctuations of the inflaton and aether fields seed long wavelength adiabatic and isocurvature scalar perturbations, as well as transverse vector perturbations. Geometrically, the isocurvature mode is the potential for the velocity field of the aether with respect to matter. For a certain range of parameters, this mode may lead to a sizable random velocity of the aether within the observable universe. The adiabatic mode corresponds to curvature perturbations of co-moving slices (where matter is at rest). In contrast with the standard case, it has a non-vanishing anisotropic stress on large scales. Scalar and vector perturbations may leave significant imprints on the cosmic microwave background. We calculate their primordial spectra, analyze their contributions to the temperature anisotropies, and formulate some of the phenomenological constraints that follow from observations. These may be used to further tighten the existing limits on the parameters for this class of theories. The results for the scalar sector also apply to the extension of Horava gravity recently proposed by Blas, Pujolas and Sibiriakov.

astro-ph.CO↗

arXiv2009

Holographic multiverse and conformal invariance

We consider a holographic description of the inflationary multiverse, according to which the wave function of the universe is interpreted as the generating functional for a lower dimensional Euclidean theory. We analyze a simple model where transitions between inflationary vacua occur through bubble nucleation, and the inflating part of spacetime consists of de Sitter regions separated by thin bubble walls. In this model, we present some evidence that the dual theory is conformally invariant in the UV.

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arXiv2008

Prediction and explanation in the multiverse

Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical? There is a widespread belief that this question is inherently vague, and that there are various possible choices for the types of reference objects which should be counted in. Here we argue that the ``ideal'' reference class (for the purpose of making predictions) can be defined unambiguously in a rather precise way, as the set of all observers with identical information content. When the observers in a given class perform an experiment, the class branches into subclasses who learn different information from the outcome of that experiment. The probabilities for the different outcomes are defined as the relative numbers of observers in each subclass. For practical purposes, wider reference classes can be used, where we trace over all information which is uncorrelated to the outcome of the experiment, or whose correlation with it is beyond our current understanding. We argue that, once we have gathered all practically available evidence, the optimal strategy for making predictions is to consider ourselves typical in any reference class we belong to, unless we have evidence to the contrary. In the latter case, the class must be correspondingly narrowed.

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arXiv2007

Can infrared gravitons screen $Λ$?

It has been suggested that infrared gravitons in de Sitter space may lead to a secular screening of the effective cosmological constant. This seems to clash with the naive expectation that the curvature scalar should stay constant due to the Heisenberg equation of motion. Here, we show that the tadpole correction to the local expansion rate, which has been used in earlier analyses as an indicator of a decaying effective $Λ$, is not gauge invariant. On the other hand, we construct a gauge invariant operator which measures the renormalized curvature scalar smeared over an arbitrary window function, and we find that there is no secular screening of this quantity (to any given order in perturbation theory).

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arXiv2006

Eternal inflation, bubble collisions, and the persistence of memory

A ``bubble universe'' nucleating in an eternally inflating false vacuum will experience, in the course of its expansion, collisions with an infinite number of other bubbles. In an idealized model, we calculate the rate of collisions around an observer inside a given reference bubble. We show that the collision rate violates both the homogeneity and the isotropy of the bubble universe. Each bubble has a center which can be related to ``the beginning of inflation'' in the parent false vacuum, and any observer not at the center will see an anisotropic bubble collision rate that peaks in the outward direction. Surprisingly, this memory of the onset of inflation persists no matter how much time elapses before the nucleation of the reference bubble.

hep-th↗

arXiv2006

Non-perturbative materialization of ghosts

In theories with a hidden ghost sector that couples to visible matter through gravity only, empty space can decay into ghosts and ordinary matter by graviton exchange. Perturbatively, such processes can be very slow provided that the gravity sector violates Lorentz invariance above some cut-off scale. Here, we investigate non-perturbative decay processes involving ghosts, such as the spontaneous creation of self-gravitating lumps of ghost matter, as well as pairs of Bondi dipoles (i.e., lumps of ghost matter chasing after positive energy objects). We find the corresponding instantons and calculate their Euclidean action. In some cases, the instantons induce topology change or have negative Euclidean action. To shed some light on the meaning of such peculiarities, we also consider the nucleation of concentrical domain walls of ordinary and ghost matter, where the Euclidean calculation can be compared with the canonical (Lorentzian) description of tunneling. We conclude that non-perturbative ghost nucleation processes can be safely suppressed in phenomenological scenarios.

hep-th↗

arXiv2006

Global structure of bigravity solutions

We discuss the causal diagrams of static and spherically symmetric bigravity vacuum solutions, with interacting metrics $f$ and $g$. Such solutions can be classified into type I (or "non-diagonal") and type II (or "diagonal"). The general solution of type I is known, and leads to metrics $f$ and $g$ in the Schwarzschild-(Anti)de Sitter family. The two metrics are not always diagonalizable in the same coordinate system, and the light-cone structure of both metrics can be quite different. In spite of this, we find that causality is preserved, in the sense that closed time-like curves cannot be pieced together from geodesics of both metrics. We propose maximal extensions of Type I bigravity solutions, where geodesics of both metrics do not stop unless a curvature singularity is encountered. Such maximal extensions can contain several copies (or even an infinite number of them) of the maximally extended "individual" geometries associated to $f$ and $g$ separately. Generically, we find that the maximal extensions of bigravity solutions are not globally hyperbolic, even in cases when the individual geometries are. The general solution of type II has not been given in closed form. We discuss a subclass where $g$ is an arbitrary solution of Einstein's equations with a cosmological constant, and we find that in this case the only solutions are such that $f\propto g$ (with trivial causal structure).

hep-th↗

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

Anthropic prediction for Lambda and the Q catastrophe

We discuss probability distributions for the cosmological constant Lambda and the amplitude of primordial density fluctuations Q in models where they both are anthropic variables. With mild assumptions about the prior probabilities, the distribution P(Lambda,Q) factorizes into two independent distributions for the variables Q and $y \propto Λ/Q^3$. The distribution for y is largely model-independent and is in a good agreement with the observed value of y. The form of P(Q) depends on the origin of density perturbations. If the perturbations are due to quantum fluctuations of the inflaton, then P(Q) tends to have an exponential dependence on Q, due to the fact that in such models Q is correlated with the amount of inflationary expansion. For simple models with a power-law potential, P(Q) is peaked at very small values of Q, far smaller than the observed value of 10^{-5}. This problem does not arise in curvaton-type models, where the inflationary expansion factor is not correlated with Q.

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arXiv2004

Football Shaped Extra Dimensions and the Absence of Self-Tuning

There have been some recent claims that brane-worlds of co-dimension two in a 6D bulk with compact extra dimensions may lead to self-tuning of the effective 4D cosmological constant. Here we show that if a phase transition occurs on a flat brane, so as to change its tension, then the brane will not remain flat. In other words, there is really no self-tuning in such models, which can in fact be understood in four-dimensional terms and are therefore subject to Weinberg's no-go theorem.

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