Stephen M. Feeney, Matthew C. Johnson, Daniel J. Mortlock, Hiranya V. Peiris
备注：
Companion to arXiv:1012.3667. 5 pages, 2 figures. v3: replaced with version accepted by PRL. Significant extensions to the Bayesian pipeline to do the full-sky non-Gaussian source detection problem (previously restricted to patches). Note that this has changed the normalization of evidence values reported previously, as full-sky priors are now employed, but the conclusions remain unchanged
The eternal inflation scenario predicts that our observable universe resides inside a single bubble embedded in a vast inflating multiverse. We present the first observational tests of eternal inflation, performing a search for cosmological signatures of collisions with other bubble universes in cosmic microwave background data from the WMAP satellite. We conclude that the WMAP 7-year data do not warrant augmenting LCDM with bubble collisions, constraining the average number of detectable bubble collisions on the full sky to be less than 1.6 at 68% CL. Data from the Planck satellite can be used to more definitively test the bubble collision hypothesis.
We study various probability measures for eternal inflation by applying their regularization prescriptions to models where inflation is not eternal. For simplicity we work with a toy model describing inflation that can interpolate between eternal and non-eternal inflation by continuous variation of a parameter. We investigate whether the predictions of four different measures (proper time, scale factor cutoff, stationary and causal {diamond}) change continuously with the change of this parameter. We will show that {only} for the stationary measure the predictions change continuously. For the p…
I investigate whether eternal inflation is possible when the inflaton originally travels upslope the scalar potential and inevitably reaches a turn-around point where its classical kinetic energy momentarily vanishes. This behaviour occurs regardless of the steepness of the potential slope. Such steep eternal inflation, if achieved, would satisfy the recent swampland conjecture and allow eternal inflation in the string landscape.
We examine various entropic inflation scenarios, under the light of eternality. After describing the inflation realization and the normal condition for inflation to last at the background level, we investigate the conditions for eternal inflation with the effect of thermal fluctuations produced from standard radiation and from the holographic screen. Furthermore, we incorporate stochastic quantum fluctuations through a phenomenological, Langevin analysis, studying whether they can affect the inflation eternality. In single-holographic-screen scenarios eternality can be easily obtained, while i…
We numerically generate the six-dimensional landscape of D3-brane inflation and identify patches of eternal inflation near sufficiently flat inflection points of the potential. We show that reasonable measures that select patches of eternal inflation in the landscape yield sharp predictions for the spectral properties of primordial perturbations on observable scales. These include a scalar tilt of .936, a running of the scalar tilt -.00103, undetectably small tensors and non-Gaussianity, and no observable spatial curvature. Our results explicitly demonstrate that precision cosmology probes the…
In SuperCool Inflation (SCI), a technically natural and thermal effect gives a graceful exit to old inflation. The Universe starts off hot and trapped in a false vacuum. The Universe supercools and inflates solving the horizon and flatness problems. The inflaton couples to a set of QCD like fermions. When the fermions' non-Abelian gauge group freezes, the Yukawa terms generate a tadpole for the inflaton, which removes the barrier. Inflation ends, and the Universe rapidly reheats. The thermal effect is technically natural in the same way that the QCD scale is technically natural. In fact, Witte…
We study if eternal inflation is realized while satisfying the recently proposed string Swampland criteria concerning the range of scalar field excursion, $|Δϕ| < \mathcal{D} \cdot M_{\rm P}$, and the potential gradient, $|\nabla V| > c \cdot V/M_{\rm P}$, where $\mathcal{D}$ and $c$ are constants of order unity, and $M_{\rm P}$ is the reduced Planck mass. We find that only the eternal inflation of chaotic type is possible for $c \sim {\cal O}(0.01)$ and $1/\mathcal{D} \sim {\cal O}(0.01)$, and that the Hubble parameter during the eternal inflation is parametrically close to the Planck scale, …
We study the effects which the back-reaction of long wavelength fluctuations exert on stochastic inflation. In the cases of power-law and Starobinsky inflation these effects are too weak to terminate the stochastic growth of the inflaton field. However, in the case of the cyclic Ekpyrotic scenario, the back-reaction effects prevent the unlimited growth of the scalar field.
Eternal inflation produces pocket universes with all physically allowed vacua and histories. Some of these pocket universes might contain a phase of slow-roll inflation, some might undergo cycles of cosmological evolution and some might look like the galilean genesis or other "emergent" universe scenarios. Which one of these types of universe we are most likely to inhabit depends on the measure we choose in order to regulate the infinities inherent in eternal inflation. We show that the currently leading measure proposals, namely the global light-cone cut-off and its local counterpart, the cau…
As a result of discussions with Bousso and Vilenkin I want to return to the question of whether the multiverse is past-eternal or if there was a beginning. Not surprisingly, given three people, there were three answers. However, the discussions have led to some common ground. The multiverse being past-eternal, or at least extremely old has content and potential phenomenological implications. I will discuss how the oldness of the multiverse is connected with recent speculations of Douglas.
The possibility that the non-minimal coupling inflation could be eternal is investigated. We calculate the quantum fluctuation of the inflaton in a Hubble time and find that it has the same value as in the minimal case in the slow-roll limit. Armed with this result, we have studied some concrete non-minimal inflationary models including the chaotic inflation and the natural inflation while the inflaton is non-minimally coupled to the gravity and we find that these non-minimal inflations could be eternal in some parameter regions.
The usual theory of inflation breaks down in eternal inflation. We derive a dual description of eternal inflation in terms of a deformed Euclidean CFT located at the threshold of eternal inflation. The partition function gives the amplitude of different geometries of the threshold surface in the no-boundary state. Its local and global behavior in dual toy models shows that the amplitude is low for surfaces which are not nearly conformal to the round three-sphere and essentially zero for surfaces with negative curvature. Based on this we conjecture that the exit from eternal inflation does not …
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.
The Wheeler-DeWitt equation provides the probability distribution for the curvature perturbation, the gauge invariant quantum fluctuation of the inflaton. From this, we can find a tower of power spectra which is not found in a perturbative approach. Since the power spectrum for the modes that cross the horizon contributes to the uncertainty in the classical inflaton displacement, we obtain new conditions for eternal inflation. In the presence of the patch in the higher excitations, the bound on the slow-roll parameter allowing eternal inflation is given by at most $ε\lesssim (2n+1)(H/m_{\rm Pl…
We consider eternal inflation in hilltop-type inflation models, favored by current data, in which the scalar field in inflation rolls off of a local maximum of the potential. Unlike chaotic or plateau-type inflation models, in hilltop inflation the region of field space which supports eternal inflation is finite, and the expansion rate $H_{EI}$ during eternal inflation is almost exactly the same as the expansion rate $H_*$ during slow roll inflation. Therefore, in any given Hubble volume, there is a finite and calculable expectation value for the lifetime of the "eternal" inflation phase, duri…
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.
I apply recently proposed "Swampland" conjectures to eternal inflation in single-scalar field theories. Eternal inflation is a phase of infinite self-reproduction of a quasi-de Sitter universe which has been argued to be a generic consequence of cosmological inflation. The originally proposed de Sitter swampland conjectures were shown by Matsui and Takahashi and by Dimopoulos to be generically incompatible with eternal inflation. However, the more recently proposed "refined" swampland conjecture imposes a slightly weaker criterion on the scalar field potential in inflation, and is consistent w…
We review the paradigm of eternal inflation in the light of the recently proposed corpuscular picture of space-time. Comparing the strength of the average fluctuation of the field up its potential with that of quantum depletion, we show that the latter can be dominant. We then study the full respective distributions in order to show that the fraction of the space-time which has an increasing potential is always below the eternal-inflation threshold. We prove that for monomial potentials eternal inflaton is excluded. This is likely to hold for other models as well.
It has been suggested that low energy effective field theories should satisfy given conditions in order to be successfully embedded into string theory. In the case of a single canonically normalized scalar field this translates into conditions on its potential and the derivatives thereof. In this Letter we revisit stochastic models of small field inflation and study the compatibility of the swampland constraints with entropy considerations. We show that stochastic inflation either violates entropy bounds or the swampland criterium on the slope of the scalar field potential. Furthermore, we ill…
Eternal inflation is studied in the context of warm inflation. We focus on different tools to analyze the effects of dissipation and the presence of a thermal radiation bath on the fluctuation-dominated regime, for which the self-reproduction of Hubble regions can take place. The tools we explore are the threshold inflaton field and threshold number of e-folds necessary to establish a self-reproduction regime and the counting of Hubble regions, using generalized conditions for the occurrence of a fluctuation-dominated regime. We obtain the functional dependence of these quantities on the dissi…
We consider landscape models that admit several regions where the conditions for eternal inflation hold. It is shown that one can use the no-boundary wave function to calculate small departures from homogeneity within our past light cone despite the possibility of much larger fluctuations on super horizon scales. The dominant contribution comes from the history exiting eternal inflation at the lowest value of the potential. In a class of landscape models this predicts a tensor to scalar ratio of about 10%. In this way the no-boundary wave function defines a measure for the prediction of local …
An eternally inflating universe produces an infinite amount of spatial volume, so every possible event happens an infinite number of times, and it is impossible to define probabilities in terms of frequencies. This problem is usually addressed by means of a measure, which regulates the infinities and produces meaningful predictions. I argue that any measure should obey certain general axioms, but then give a simple toy model in which one can prove that no measure obeying the axioms exists. In certain cases of eternal inflation there are measures that obey the axioms, but all such measures appe…
Inflation creates large-scale cosmological density perturbations that are characterized by an isotropic, homogeneous, and Gaussian random distribution about a locally flat background. Even in a flat universe, the spatial curvature measured within one Hubble volume receives contributions from long wavelength perturbations, and will not in general be zero. These same perturbations determine the Cosmic Microwave Background (CMB) temperature fluctuations, which are O(10^-5). Consequently, the low-l multipole moments in the CMB temperature map predict the value of the measured spatial curvature Ω_k…
Simple monomial inflationary scenarios have been ruled out by recent observations. In this work we revisit the next simplest scenario, a single--field model where the scalar potential is a polynomial of degree four which features a concave ``almost'' saddle point. We focus on trans--Planckian field values. We reparametrize the potential, which greatly simplifies the procedure for finding acceptbale model parameters. This allows for the first comprehensive scan of parameter space consistent with recent Planck and BICEP/Keck 2018 measurements. Even for trans--Planckian field values the tensor--t…
We study the details of eternal inflation in the presence of a spectator Higgs field within the framework of the minimal Standard Model. We have recently shown that in the presence of scalar field(s) which allow inflation only within a finite domain of field values, the universe reaches a steady state where the normalized distribution for the field(s) converges to a steady state distribution [1]. In this paper, we analyze this eternal inflation scenario with the renormalized Standard Model Higgs potential, since it also allows inflation in a finite domain, but turns over at high scales due to …
The phenomenon of stochastic eternal inflation is studied for a chaotic inflation potential in a Bianchi Type I spacetime background. After deriving the appropriate stochastic Klein-Gordon equation, we give details on the conditions for eternal inflation. It is shown that for eternal inflation to occur, the amount of anisotropy must be small. In fact, it is shown that eternal inflation will only take place if the shear anisotropy variables take on values within a small region of the interior of the Kasner circle. We then calculate the probability of eternal inflation occurring based on techniq…
In pursuing the intriguing resemblance of the Einstein equations to thermodynamic equations, most sharply seen in systems possessing horizons, we suggest that eternal inflation of the stochastic type may be a fruitful phenomenon to explore. We develop a thermodynamic first law for quasi-de Sitter space, valid on the horizon of a single observer's Hubble patch and explore consistancy with previous proposals for horizons of various types in dynamic and static situations. We use this framework to demonstrate that for the local observer fluctuations of the type necessary for stochastic eternal inf…
Current data from the Planck satellite and the BICEP2 telescope favor, at around the $2 σ$ level, negative running of the spectral index of curvature perturbations from inflation. We show that for negative running $α< 0$, the curvature perturbation amplitude has a maximum on scales larger than our current horizon size. A condition for the absence of eternal inflation is that the curvature perturbation amplitude always remain below unity on superhorizon scales. For current bounds on $n_{\rm S}$ from Planck, this corresponds to an upper bound of the running $α< - 4 \times 10^{-5}$, so that even …
In this Letter, we briefly review the multi-stream inflation scenario, and discuss its implications in the string theory landscape and the inflationary multiverse. In multi-stream inflation, the inflation trajectory encounters bifurcations. If these bifurcations are in the observable stage of inflation, then interesting observational effects can take place, such as domain fences, non-Gaussianities, features and asymmetries in the CMB. On the other hand, if the bifurcation takes place in the eternal stage of inflation, it provides an alternative creation mechanism of bubbles universes in eterna…
It has recently been shown that in single field slow-roll inflation the total volume cannot grow by a factor larger than e^(S_dS/2) without becoming infinite. The bound is saturated exactly at the phase transition to eternal inflation where the probability to produce infinite volume becomes non zero. We show that the bound holds sharply also in any space-time dimensions, when arbitrary higher-dimensional operators are included and in the multi-field inflationary case. The relation with the entropy of de Sitter and the universality of the bound strengthen the case for a deeper holographic inter…
In the picture of eternal inflation, our observable universe resides inside a single bubble nucleated from an inflating false vacuum. Many of the theories giving rise to eternal inflation predict that we have causal access to collisions with other bubble universes, providing an opportunity to confront these theories with observation. We present the results from the first observational search for the effects of bubble collisions, using cosmic microwave background data from the WMAP satellite. Our search targets a generic set of properties associated with a bubble collision spacetime, which we d…
We investigate the Higgs potential beyond the Planck scale in the superstring theory, under the assumption that the supersymmetry is broken at the string scale. We identify the Higgs field as a massless state of the string, which is indicated by the fact that the bare Higgs mass can be zero around the string scale. We find that, in the large field region, the Higgs potential is connected to a runaway vacuum with vanishing energy, which corresponds to opening up an extra dimension. We verify that such universal behavior indeed follows from the toroidal compactification of the non-supersymmetric…
Eternal inflation is a seemingly generic consequence of theories that give rise to accelerated expansion of the universe and possess multiple vacuum states. Making predictions in an eternally inflating universe is notoriously difficult because one must compare infinite quantities, and a wide variety of regulating procedures yield radically different results. This is the measure problem of eternal inflation. In this paper, we analyze models of eternal inflation which allow for the possibility of cyclic bubble universes: in each bubble, standard cosmological evolution is re-played over and over …
The no-boundary wave function (NBWF) specifies a measure for prediction in cosmology that selects inflationary histories and remains well behaved for spatially large or infinite universes. This paper explores the predictions of the NBWF for linear scalar fluctuations about homogeneous and isotropic backgrounds in models with a single scalar field moving in a quadratic potential. We treat both the space-time geometry of the universe and the observers inhabiting it quantum mechanically. We evaluate top-down probabilities for local observations that are conditioned on the NBWF and on part of our …
The work is an attempt to model a scenario of inflation in the framework of Anti de Sit- ter/Conformal Field theory (AdS/CFT) duality, a potentially complete nonperturbative description of quantum gravity via string theory. We look at bubble geometries with de Sitter interiors within an ambient Schwarzschild anti-de Sitter black hole spacetime and obtain a characterization for the states in the dual CFT on boundary of the asymptotic AdS which code the expanding dS bubble. These can then in turn be used to specify initial conditions for cosmology. Our scenario naturally interprets the entropy o…
We propose a 3 + 1 dimensional model of gravity which results in inflation at early times, followed by radiation- and matter-dominated epochs and a subsequent acceleration at late times. Both the inflation and late time acceleration are nearly de Sitter with a large hierarchy between the effective cosmological constants. There is no scalar field agent of inflation, and the transition from the inflation to the radiation-dominated period is smooth. This model is designed so that it yields, at the cost of giving up on Lorentz invariance in the gravitational sector, the Dirac-Born-Infeld type conf…
We compute the distribution of sizes of inflating and non-inflating regions in an eternally inflating Universe. As a first illustrative problem, we study a simple scenario of an eternally inflating Universe in the presence of a massless scalar field $φ$ whose field values lie within some finite domain $φ\in(-φ_{cr},φ_{cr})$, with $\pmφ_{cr}$ marking the onset of thermalization/crunching. We compute many important quantities, including the fractal dimension, distribution of field values among inflating regions, and the number of inflating and non-inflating Hubble regions. With the aid of simula…
We analyze the cosmological role of terminal vacua in the string theory landscape, and point out that existing work on this topic makes very strong assumptions about the properties of the terminal vacua. We explore the implications of relaxing these assumptions (by including "arrival" as well as "departure" terminals) and demonstrate that the results in earlier work are highly sensitive to their assumption of no arrival terminals. We use our discussion to make some general points about tuning and initial conditions in cosmology.
In this paper we provide a new expression for the variation of the inflaton field $Δϕ$ during the horizon crossing epoch in the context of single field slow roll inflationary models. Such an expression represents a generalization of the well-know Lyth bound. We also explore the consequences of a detection of permille order of the tensor-to-scalar ratio amplitude, $r$, as well as an improvement on the estimation of the scalar spectral index, $n_s$ and its running $α_s$, by the upcoming CMB polarization experiments that will provide plausible constraints on the quantity $Δϕ$ during the horizon e…
We consider the eternal inflation scenario of the slow-roll/chaotic type with the additional element of an objective collapse of the wave function. The incorporation of this new agent to the traditional inflationary setting might represent a possible solution to the quantum measurement problem during inflation, a subject that has not reached a consensus among the community. Specifically, it could provide an explanation for the generation of the primordial anisotropies and inhomogeneities, starting from a perfectly symmetric background and invoking symmetric dynamics. We adopt the continuous sp…
Slow-roll inflation can become eternal if the quantum variance of the inflaton field around its slowly rolling classical trajectory is converted into a distribution of classical spacetimes inflating at different rates, and if the variance is large enough compared to the rate of classical rolling that the probability of an increased rate of expansion is sufficiently high. Both of these criteria depend sensitively on whether and how perturbation modes of the inflaton interact and decohere. Decoherence is inevitable as a result of gravitationally-sourced interactions whose strength are proportion…
We present a framework in which well-defined predictions are obtained in an eternally inflating multiverse, based on the principles of quantum mechanics. We show that the entire multiverse is described purely from the viewpoint of a single "observer," who describes the world as a quantum state defined on his/her past light cones bounded by the (stretched) apparent horizons. We find that quantum mechanics plays an essential role in regulating infinities. The framework is "gauge invariant," i.e. predictions do not depend on how spacetime is parametrized, as it should be in a theory of quantum gr…
We propose a new measure for eternal inflation, based on search optimization and first-passage statistics. This work builds on the dynamical selection mechanism for vacua based on search optimization proposed recently by the author and Parrikar. The approach is motivated by the possibility that eternal inflation has unfolded for a finite time much shorter than the exponentially long mixing time for the landscape. The proposed accessibility measure assigns greater weight to vacua that are accessed efficiently under time evolution. It is the analogue of the closeness centrality index widely used…
The definition of probabilities in eternally inflating universes requires a measure to regulate the infinite spacetime volume, and much of the current literature uses a global time cutoff for this purpose. Such measures have been found to lead to paradoxical behavior, and recently Bousso, Freivogel, Leichenauer, and Rosenhaus have argued that, under reasonable assumptions, the only consistent interpretation for such measures is that time must end at the cutoff. Here we argue that there is an alternative, consistent formulation of such measures, in which time extends to infinity. Our formulatio…
We argue that the total number of distinguishable locally Friedmann universes generated by eternal inflation is proportional to the exponent of the entropy of inflationary perturbations and is limited by e^{e^{3 N}}, where N is the number of e-folds of slow-roll post-eternal inflation. For simplest models of chaotic inflation, N is approximately equal to de Sitter entropy at the end of eternal inflation; it can be exponentially large. However, not all of these universes can be observed by a local observer. In the presence of a cosmological constant Λthe number of distinguishable universes is b…
The swampland conjectures from string theory have had some really interesting implications on cosmology, in particular on inflationary models. Some models of inflation have been shown to be incompatible with these criterion while some have been shown to be severely fine tuned, with most of these problems arising in single field inflationary models in a General relativistic cosmology. Recent works have although optimistically shown that single field models in more general cosmologies can be consistent with these conjectures and hence there is an optimism that not all such models lie in the swam…
We forecast the ability of cosmic microwave background (CMB) temperature and polarization datasets to constrain theories of eternal inflation using cosmic bubble collisions. Using the Fisher matrix formalism, we determine both the overall detectability of bubble collisions and the constraints achievable on the fundamental parameters describing the underlying theory. The CMB signatures considered are based on state-of-the-art numerical relativistic simulations of the bubble collision spacetime, evolved using the full temperature and polarization transfer functions. Comparing a theoretical cosmi…
In some well-known scenarios of open-universe eternal inflation, developed by Vilenkin and co-workers, a large number of universes nucleate and thermalize within the eternally inflating mega-universe. According to the proposal, each universe nucleates at a point, and therefore the boundary of the nucleated universe is a space-like surface nearly coincident with the future light cone emanating from the point of nucleation, all points of which have the same proper-time. This leads the authors to conclude that at the proper-time t = t_{nuc} at which any such nucleation occurs, an infinite open un…
Cosmological models in 1+1 dimensions are an ideal setting for investigating the quantum structure of inflationary dynamics -- gravity is renormalizable, while there is room for spatial structure not present in the minisuperspace approximation. We use this fortuitous convergence to investigate the mechanism of slow-roll eternal inflation. A variant of 1+1 Liouville gravity coupled to matter is shown to model precisely the scalar sector of cosmological perturbations in 3+1 dimensions. A particular example of quintessence in 1+1d is argued on the one hand to exhibit slow-roll eternal inflation a…
Breaking Eternal Inflation: Empirical Viability of a Spontaneous Collapse Scenario
Universidad Nacional de La Plata（拉普拉塔国立大学）；CONICET（阿根廷国家科学研究委员会）；Università di Padova（帕多瓦大学）；INFN Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Universidad de Barcelona（巴塞罗那大学）
In the context of eternal inflation, cosmological predictions depend on the choice of measure to regulate the diverging spacetime volume. The spectrum of inflationary perturbations is no exception, as we demonstrate by comparing the predictions of the fat geodesic and causal patch measures. To highlight the effect of the measure---as opposed to any effects related to a possible landscape of vacua---we take the cosmological model, including the model of inflation, to be fixed. We also condition on the average CMB temperature accompanying the measurement. Both measures predict a 1-point expectat…
We compute the probability distribution for bubble collisions in an inflating false vacuum which decays by bubble nucleation. Our analysis generalizes previous work of Guth, Garriga, and Vilenkin to the case of general cosmological evolution inside the bubble, and takes into account the dynamics of the domain walls that form between the colliding bubbles. We find that incorporating these effects changes the results dramatically: the total expected number of bubble collisions in the past lightcone of a typical observer is N ~ γV_f / V_i, where γis the fastest decay rate of the false vacuum, V_f…
Perhaps the most controversial idea in modern cosmology is that our observable universe is contained within one bubble among many, all inhabiting the eternally inflating multiverse. One of the few way to test this idea is to look for evidence of the relic inhomogeneities left by the collisions between other bubbles and our own. Such relic inhomogeneities induces a coherent bulk flow over gigaparsec scales. Therefore, bubble collisions leave unique imprints in the cosmic microwave background (CMB) through the kinetic Sunyaev Zel'dovich (kSZ) effect, temperature anisotropies induced by the scatt…
We propose a novel scenario to explain the small cosmological constant (CC) by a finely tuned inflaton potential. The tuned shape is stable under radiative corrections, and our setup is technically natural. The peculiar po- tential approximately satisfies the following conditions: the inflation is eternal if CC is positive, and not eternal if CC is negative. By introducing a slowly varying CC from a positive value to a negative value, the dominant volume of the Universe after the inflation turns out to have a vanishingly small CC. The scenario does not require eternal inflation but the e-foldi…
