Alan H. Guth

Could the universe have recovered from a slow first-order phase transition?☆

We investigate the cosmological consequences of a phase transition which is driven primarily by slow nucleation of bubbles of the new phase via the effectively zero temperature quantum tunneling process of Coleman and Callan. These bubbles will asymptotically fill an arbitrarily large fraction of the space, yet they never percolate. Instead they form finite clusters, with each cluster dominated by a single largest bubble. The large scale thermalization required by the original “inflationary universe” scenario does not take place. The Coleman-De Luccia formalism for bubble formation in curved space is reviewed, with minor extensions. We argue that a single uncollided bubble would contain much less total entropy than the observed universe, unless the Higgs field potential involves widely disparate mass scales, as in the new inflationary universe scenario. We also argue that finite clusters are unlikely to yield a homogeneous and isotropic region containing sufficient entropy. Thus, unless the Higgs potential has the special form required by the new inflationary scenario, it appears quite implausible that there was such a phase transition in our past.

Inflationary Spacetimes Are Incomplete in Past Directions

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating -- or just expanding sufficiently fast -- must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.

Inflation and eternal inflation

Abstract The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Vilenkins proposal for avoiding these problems is also discussed.

Inflationary spacetimes are not past-complete

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating -- or just expanding sufficiently fast -- must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.

Eternal inflation and its implications

I summarize the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions, so some physics other than inflation is needed to describe the past boundary of the inflating region.

Is It Possible to Create a Universe in the Laboratory by Quantum Tunneling

Abstract We explore the possibility that a new universe can be created by producing a small bubble of false vacuum. The initial bubble is small enough to be produced without an initial singularity, but classically it could not become a universe — instead it would reach a maximum radius and then collapse. We investigate the possibility that quantum effects allow the bubble to tunnel into a larger bubble, of the same mass, which would then classically evolve to become a new universe. The calculation of the tunneling amplitude is attempted, in lowest order semiclassical approximation (in the thin-wall limit), using both a canonical and a functional integral approach. The canonical approach is found to have flaws, attributable to our method of space-time slicing. The functional integral approach leads to a euclidean interpolating solution that is not a manifold. To describe it, we define an object which we call a “pseudomanifold”, and give a prescription to define its action. We conjecture that the tunneling probability to produce a new universe can be approximated using this action, and we show that this leads to a plausible result.

Supernatural inflation: inflation from supersymmetry with no (very) small parameters

Abstract Most models of inflation have small parameters, either to guarantee sufficient inflation or the correct magnitude of the density perturbations. In this paper we show that, in supersymmetric theories with weak-scale supersymmetry breaking, one can construct viable inflationary models in which the requisite parameters appear naturally in the form of the ratio of mass scales that are already present in the theory. Successful inflationary models can be constructed from the flat-direction fields of a renormalizable supersymmetric potential, and such models can be realized even in the context of a simple GUT extension of the MSSM. We evade naive “naturalness” arguments by allowing for more than one field to be relevant to inflation, as in “hybrid inflation” models, and we argue that this is the most natural possibility if inflaton fields are to be associated with flat direction fields of a supersymmetric theory. Such models predict a very low Hubble constant during inflation, of order 103–104 GeV, a scalar density perturbation index n which is very close to or greater than unity, and negligible tensor perturbations. In addition, these models lead to a large spike in the density perturbation spectrum at short wavelengths.

An obstacle to creating a universe in the laboratory

Abstract We show that any spherically symmetric false vacuum bubble which forms in an asymptotically flat space and grows beyond a certain critical size must have merged from an initial singularity. Our result requires that the energy-momentum tensor obey the condition T μν k μ k ν ⩾0 for all null k μ , a property which holds at the classical level for almost all theories of matter. For the non-spherical case, we state a necessary condition that a false vacuum bubble must meet in order to avoid an initial singularity. We do not know if this condition can ever be met. The requirement of an initial singularity appears to be an insurmountable obstacle to the creation of an inflationary universe in the laboratory.

Inflationary paradigm after Planck 2013

Abstract Models of cosmic inflation posit an early phase of accelerated expansion of the universe, driven by the dynamics of one or more scalar fields in curved spacetime. Though detailed assumptions about fields and couplings vary across models, inflation makes specific, quantitative predictions for several observable quantities, such as the flatness parameter ( Ω k = 1 − Ω ) and the spectral tilt of primordial curvature perturbations ( n s − 1 = d ln ⁡ P R / d ln ⁡ k ), among others—predictions that match the latest observations from the Planck satellite to very good precision. In the light of data from Planck as well as recent theoretical developments in the study of eternal inflation and the multiverse, we address recent criticisms of inflation by Ijjas, Steinhardt, and Loeb. We argue that their conclusions rest on several problematic assumptions, and we conclude that cosmic inflation is on a stronger footing than ever before.

Inflationary cosmology: exploring the universe from the smallest to the largest scales.

Understanding the behavior of the universe at large depends critically on insights about the smallest units of matter and their fundamental interactions. Inflationary cosmology is a highly successful framework for exploring these interconnections between particle physics and gravitation. Inflation makes several predictions about the present state of the universe—such as its overall shape, large-scale smoothness, and smaller scale structure—which are being tested to unprecedented accuracy by a new generation of astronomical measurements. The agreement between these predictions and the latest observations is extremely promising. Meanwhile, physicists are busy trying to understand inflations ultimate implications for the nature of matter, energy, and spacetime.