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Raphael Bousso

Publications and source records attributed to Raphael Bousso.

At least 73 records · Page 4Linked to original sources
arXiv2012

Complementarity Is Not Enough

The near-horizon field B of an old black hole is maximally entangled with the early Hawking radiation R, by unitarity of the S-matrix. But B must be maximally entangled with the black hole interior A, by the equivalence principle. Causal patch complementarity fails to reconcile these conflicting requirements. The system B can be probed by a freely falling observer while there is still time to turn around and remain outside the black hole. Therefore, the entangled state of the BR system is dictated by unitarity even in the infalling patch. If, by monogamy of entanglement, B is not entangled with A, the horizon is replaced by a singularity or "firewall". To illustrate the radical nature of the ideas that are needed, I briefly discuss two approaches for avoiding a firewall: the identification of A with a subsystem of R; and a combination of patch complementarity with the Horowitz-Maldacena final-state proposal.

hep-th↗
arXiv2012

Light-sheets and AdS/CFT

One may ask whether the CFT restricted to a subset b of the AdS boundary has a well-defined dual restricted to a subset H(b) of the bulk geometry. The Poincare patch is an example, but more general choices of b can be considered. We propose a geometric construction of H. We argue that H should contain the set C of causal curves with both endpoints on b. Yet H should not reach so far from the boundary that the CFT has insufficient degrees of freedom to describe it. This can be guaranteed by constructing a superset of H from light-sheets off boundary slices and invoking the covariant entropy bound in the bulk. The simplest covariant choice is L, the intersection of L^+ and L^-, where L^+ (L^-) is the union of all future-directed (past-directed) light-sheets. We prove that C=L, so the holographic domain is completely determined by our assumptions: H=C=L. In situations where local bulk operators can be constructed on b, H is closely related to the set of bulk points where this construction remains unambiguous under modifications of the CFT Hamiltonian outside of b. Our construction leads to a covariant geometric RG flow. We comment on the description of black hole interiors and cosmological regions via AdS/CFT.

hep-th↗
arXiv2012

New Local Duals in Eternal Inflation

Global-local duality is the equivalence of seemingly different regulators in eternal inflation. For example, the light-cone time cutoff (a global measure, which regulates time) makes the same predictions as the causal patch (a local measure that cuts off space). We show that global-local duality is far more general. It rests on a redundancy inherent in any global cutoff: at late times, an attractor regime is reached, characterized by the unlimited exponential self-reproduction of a certain fundamental region of spacetime. An equivalent local cutoff can be obtained by restricting to this fundamental region. We derive local duals to several global cutoffs of interest. The New Scale Factor Cutoff is dual to the Short Fat Geodesic, a geodesic of fixed infinitesimal proper width. Vilenkin's CAH Cutoff is equivalent to the Hubbletube, whose width is proportional to the local Hubble volume. The famous youngness problem of the Proper Time Cutoff can be readily understood by considering its local dual, the Incredible Shrinking Geodesic.

hep-th↗
arXiv2012

Vacuum Structure and the Arrow of Time

We find ourselves in an extended era of entropy production. Unlike most other observations, the arrow of time is usually regarded as a constraint on initial conditions. I argue, however, that it primarily constrains the vacuum structure of the theory. I exhibit simple scalar field potentials in which low-entropy initial conditions are not necessary, or not sufficient, for an arrow of time to arise. I argue that the string theory landscape gives rise to an arrow of time independently of the initial entropy, assuming a plausible condition on the lifetime of its metastable vacua. The dynamical resolution of the arrow of time problem arises from the same structural properties of the string landscape that allow it to solve the cosmological constant problem without producing an empty universe, particularly its high dimensionality and the large difference in vacuum energy between neighboring vacua.

hep-th↗
arXiv2012

New Scale Factor Measure

The computation of probabilities in an eternally inflating universe requires a regulator or "measure". The scale factor time measure truncates the universe when a congruence of timelike geodesics has expanded by a fixed volume factor. This definition breaks down if the generating congruence is contracting---a serious limitation that excludes from consideration gravitationally bound regions such as our own. Here we propose a closely related regulator which is well-defined in the entire spacetime. The New Scale Factor Cutoff restricts to events with scale factor below a given value. Since the scale factor vanishes at caustics and crunches, this cutoff always includes an infinite number of disconnected future regions. We show that this does not lead to divergences. The resulting measure combines desirable features of the old scale factor cutoff and of the light-cone time cutoff, while eliminating some of the disadvantages of each.

hep-th↗
arXiv2012

The Cosmological Constant Problem, Dark Energy, and the Landscape of String Theory

In this colloquium-level account, I describe the cosmological constant problem: why is the energy of empty space at least 60 orders of magnitude smaller than several known contributions to it from the Standard Model of particle physics? I explain why the "dark energy" responsible for the accelerated expansion of the universe is almost certainly vacuum energy. The second half of the paper explores a more speculative subject. The vacuum landscape of string theory leads to a multiverse in which many different three-dimensional vacua coexist, albeit in widely separated regions. This can explain both the smallness of the observed vacuum energy and the coincidence that its magnitude is comparable to the present matter density.

astro-ph.CO↗
arXiv2011

The Multiverse Interpretation of Quantum Mechanics

We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics. Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment". In fact decoherence is absent in the complete description of any region larger than the future light-cone of a measurement event. However, if one restricts to the causal diamond - the largest region that can be causally probed - then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many-worlds (all possible decoherent causal diamond histories) in a single geometry. We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in "hats" (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.

hep-th↗
arXiv2010

Geometric origin of coincidences and hierarchies in the landscape

We show that the geometry of cutoffs on eternal inflation strongly constrains predictions for the timescales of vacuum domination, curvature domination, and observation. We consider three measure proposals: the causal patch, the fat geodesic, and the apparent horizon cutoff, which is introduced here for the first time. We impose neither anthropic requirements nor restrictions on landscape vacua. For vacua with positive cosmological constant, all three measures predict the double coincidence that most observers live at the onset of vacuum domination and just before the onset of curvature domination. The hierarchy between the Planck scale and the cosmological constant is related to the number of vacua in the landscape. These results require only mild assumptions about the distribution of vacua (somewhat stronger assumptions are required by the fat geodesic measure). At this level of generality, none of the three measures are successful for vacua with negative cosmological constant. Their applicability in this regime is ruled out unless much stronger anthropic requirements are imposed.

hep-th↗
arXiv2010

Eternal inflation predicts that time will end

Present treatments of eternal inflation regulate infinities by imposing a geometric cutoff. We point out that some matter systems reach the cutoff in finite time. This implies a nonzero probability for a novel type of catastrophe. According to the most successful measure proposals, our galaxy is likely to encounter the cutoff within the next 5 billion years.

hep-th↗
arXiv2010

Boundary definition of a multiverse measure

We propose to regulate the infinities of eternal inflation by relating a late time cut-off in the bulk to a short distance cut-off on the future boundary. The light-cone time of an event is defined in terms of the volume of its future light-cone on the boundary. We seek an intrinsic definition of boundary volumes that makes no reference to bulk structures. This requires taming the fractal geometry of the future boundary, and lifting the ambiguity of the conformal factor. We propose to work in the conformal frame in which the boundary Ricci scalar is constant. We explore this proposal in the FRW approximation for bubble universes. Remarkably, we find that the future boundary becomes a round three-sphere, with smooth metric on all scales. Our cut-off yields the same relative probabilities as a previous proposal that defined boundary volumes by projection into the bulk along timelike geodesics. Moreover, it is equivalent to an ensemble of causal patches defined without reference to bulk geodesics. It thus yields a holographically motivated and phenomenologically successful measure for eternal inflation.

hep-th↗
arXiv2010

Saturating the holographic entropy bound

The covariant entropy bound states that the entropy, S, of matter on a light-sheet cannot exceed a quarter of its initial area, A, in Planck units. The gravitational entropy of black holes saturates this inequality. The entropy of matter systems, however, falls short of saturating the bound in known examples. This puzzling gap has led to speculation that a much stronger bound, S< A^{3/4}, may hold true. In this note, we exhibit light-sheets whose entropy exceeds A^{3/4} by arbitrarily large factors. In open FRW universes, such light-sheets contain the entropy visible in the sky; in the limit of early curvature domination, the covariant bound can be saturated but not violated. As a corollary, we find that the maximum observable matter and radiation entropy in universes with positive (negative) cosmological constant is of order Lambda^{-1} (Lambda^{-2}), and not |Lambda|^{-3/4} as had hitherto been believed. Our results strengthen the evidence for the covariant entropy bound, while showing that the stronger bound S< A^{3/4} is not universally valid. We conjecture that the stronger bound does hold for static, weakly gravitating systems.

hep-th↗
arXiv2010

The Entropic Landscape

We initiate a quantitative exploration of the entire landscape. Predictions thus far have focused on subsets of landscape vacua that share most properties with our own. Using the entropic principle (the assumption that entropy production traces the formation of complex structures such as observers), we derive six predictions that apply to the whole landscape. Typical observers find themselves in a flat universe, at the onset of vacuum domination, surrounded by a recently produced bath of relativistic quanta. These quanta are neither very dilute nor condensed, and thus appear as a roughly thermal background. Their characteristic wavelength is of order the inverse fourth root of the vacuum energy. These predictions hold for completely arbitrary observers, in arbitrary vacua with potentially exotic particle physics and cosmology. They agree with observation: We live in a flat universe at the onset of vacuum domination, whose dominant entropy production process (the glow of galactic dust) has recently produced a radiation bath (the cosmic infrared background). This radiation is marginally dilute, relativistic, and has a wavelength of order 100 microns, as predicted.

hep-th↗
arXiv2009

Global-Local Duality in Eternal Inflation

We prove that the light-cone time cut-off on the multiverse defines the same probabilities as a causal patch with initial conditions in the longest-lived metastable vacuum. This establishes the complete equivalence of two measures of eternal inflation which naively appear very different (though both are motivated by holography). The duality can be traced to an underlying geometric relation which we identify.

hep-th↗
arXiv2009

Multiverse Understanding of Cosmological Coincidences

There is a deep cosmological mystery: although dependent on very different underlying physics, the timescales of structure formation, of galaxy cooling (both radiatively and against the CMB), and of vacuum domination do not differ by many orders of magnitude, but are all comparable to the present age of the universe. By scanning four landscape parameters simultaneously, we show that this quadruple coincidence is resolved. We assume only that the statistical distribution of parameter values in the multiverse grows towards certain catastrophic boundaries we identify, across which there are drastic regime changes. We find order-of-magnitude predictions for the cosmological constant, the primordial density contrast, the temperature at matter-radiation equality, the typical galaxy mass, and the age of the universe, in terms of the fine structure constant and the electron, proton and Planck masses. Our approach permits a systematic evaluation of measure proposals; with the causal patch measure, we find no runaway of the primordial density contrast and the cosmological constant to large values.

hep-th↗
arXiv2009

Predictions from Star Formation in the Multiverse

We compute trivariate probability distributions in the landscape, scanning simultaneously over the cosmological constant, the primordial density contrast, and spatial curvature. We consider two different measures for regulating the divergences of eternal inflation, and three different models for observers. In one model, observers are assumed to arise in proportion to the entropy produced by stars; in the others, they arise at a fixed time (5 or 10 billion years) after star formation. The star formation rate, which underlies all our observer models, depends sensitively on the three scanning parameters. We employ a recently developed model of star formation in the multiverse, a considerable refinement over previous treatments of the astrophysical and cosmological properties of different pocket universes. For each combination of observer model and measure, we display all single and bivariate probability distributions, both with the remaining parameter(s) held fixed, and marginalized. Our results depend only weakly on the observer model but more strongly on the measure. Using the causal diamond measure, the observed parameter values (or bounds) lie within the central $2σ$ of nearly all probability distributions we compute, and always within $3σ$. This success is encouraging and rather nontrivial, considering the large size and dimension of the parameter space. The causal patch measure gives similar results as long as curvature is negligible. If curvature dominates, the causal patch leads to a novel runaway: it prefers a negative value of the cosmological constant, with the smallest magnitude available in the landscape.

hep-th↗
arXiv2009

Complementarity in the Multiverse

In the multiverse, as in AdS, light-cones relate bulk points to boundary scales. This holographic UV-IR connection defines a preferred global time cut-off that regulates the divergences of eternal inflation. An entirely different cut-off, the causal patch, arises in the holographic description of black holes. Remarkably, I find evidence that these two regulators define the same probability measure in the multiverse. Initial conditions for the causal patch are controlled by the late-time attractor regime of the global description.

hep-th↗
arXiv2009

Properties of the scale factor measure

We show that in expanding regions, the scale factor measure can be reformulated as a local measure: Observations are weighted by integrating their physical density along a geodesic that starts in the longest-lived metastable vacuum. This explains why some of its properties are similar to those of the causal diamond measure. In particular, both measures are free of Boltzmann brains, subject to nearly the same conditions on vacuum stability. However, the scale factor measure assigns a much smaller probability to the observed value of the cosmological constant. The probability decreases further, like the inverse sixth power of the primordial density contrast, if the latter is allowed to vary.

hep-th↗