Origins of the Universe Conference
 Organized by

Gregory Gabadadze, Ph.D.

Eva Silverstein, Ph.D.Stanford University

Paul Steinhardt, Ph.D.Princeton University
The first annual meeting of the Origins of the Universe program will bring together three diverse groups of theoretical cosmologists, each addressing the history of the universe in their own ways. The themes of the presentations and discussions will include inflationary dynamics and its observational probes, bouncing cosmologies, and other proposals for geodesically pastcomplete classical models.

Report
Origins of the Universe 2018 Meeting Writeup
Bouncing Cosmology (Steinhardt)
Anna Ijjas (Harvard), Frans Pretorius (Princeton) and Paul Steinhardt (Princeton), the three PIs of the Bouncing Cosmology component of the Origins of the Universe Initiative, together presented the leading results from the past year of research.
Steinhardt gave an introduction to bouncing cosmology that described the overall theoretical framework being explored: namely, a cosmology in which the big bang is replaced by a big bounce; there is no beginning or end to space and time; the fundamental largescale features of the universe are set during a period of contraction leading up to the bounce; and the entire evolution of the universe is dominantly classical, described by deterministic equations of motion, with quantum physics only contributing small perturbations.
To illustrate the concept, he invoked “wedge diagrams,” a novel way of representing cosmological scenarios first introduced by Ijjas and Steinhardt during the past year as part of the Simons Foundation project. The conclusion was that all the observed largescale features of the universe can potentially be obtained during a long period of slow contraction (also known as an ekpyrotic phase) without requiring special initial conditions or producing a multiverse.
Ijjas followed with a detailed account of the progress that has been made by the collaboration during the past year in constructing classical bounce solutions that carry the conditions generated during the contracting phase into the expanding phase without encountering any period in which quantum effects dominate. The bounce is based on modifications to Einstein gravity that become important for only a few instants during the bounce phase. In particular, Ijjas described how Horndeski theory, a wellknown scalartensor modification of Einstein gravity, produces an effect called “braiding” that makes the bounce possible. She described her own research showing that the background solution is stable under perturbations of the scalar field and the curvature, an important milestone given that this safely circumvents certain wellknown “nogo” theorems that had been claimed in earlier literature. The analysis utilized conventional lines of linear perturbative analysis familiar to cosmologists, though with proper attention to subtleties of gauge invariant variables that had been missed before.
Finally, Ijjas turned to a major new work with Pretorius and Steinhardt that sets the foundations for studying nonperturbative cosmology, a new area of study essential for analyzing theories in which the background solution is nontrivial (like a bounce) and the gravitational sector differs from Einstein gravity (like Horndeski theories). The methodology combines aspects familiar to cosmologists and aspects familiar to mathematical relativists in a way that is novel to both groups. There could very well be many applications as the methods become better known. In the short run, though, Ijjas’ showed the results of applying this approach to classical bounce solutions described by Horndeski theory – namely, an analytic proof that the theories are linearly wellposed at and about homogeneous and isotropic backgrounds. This is a key step since failure would mean that the bounce solutions are inherently badlybehaved classically.
Pretorius’ talk elaborated on this point and spoke about where the project moves next. Pretorius is the leading pioneer in developing numerical methods to analyze fully nonlinear general relativistic problems, such as black hole mergers. In his presentation, Pretorius described the first applications of these methods to cosmology (by Pretorius, Steinhardt and collaborators) beginning in 2007. He used the examples to emphasize the importance of the mathematical analysis that must precede any numerics, especially the critical step of going beyond standard cosmological perturbative analysis to consider the much more challenging problem of wellposedness, as described by Ijjas. With this breakthrough, he argued, it was now clear that the Horndeski theory of bouncing solutions is sufficiently wellbehaved at the linear level to justify the next step of full nonlinear numerical integration. This is the next step in the program plans, and the key to determining the observational predictions of classical bouncing cosmologies.
The team invited scientists and mathematicians who work on diverse aspects of cosmology and mathematical relativity aside from the work described by Ijjas, Pretorius, and Steinhardt. To take advantage of the opportunity, the team organized a satellite meeting at the Flatiron Institute to take place the following day (Saturday). The program was intentionally designed to be eclectic. Stephon Alexander (Brown) spoke about torsion in general relativity and earlier work by him exploring the idea of a torsionmediated bounce. V. (Slava) Mukhanov (LMU Munich) spoke about his research on “mimetic” quantum field theories that can describe dark matter and dark energy. Robert Brandenberger (McGill) discussed the problems encountered in constructing “matter bounce” models and how those problems may be overcome in the ekpyrotic models described by Steinhardt and Ijjas. Mihalis Dafermos, a mathematical relativist at Princeton, described his foundational work on geodesic incompleteness of Kerr black holes in asymptotically flat and certain cosmological problems. Savdeep Sethi (Chicago) closed by discussing the ongoing debate about whether string theory is compatible with cosmology, in particular the cosmic accelerated expansion observed today and the hypothetical accelerated expansion required in inflationary cosmology.
Modern Inflation (Silverstein)
At the Origins of the Universe meeting in September 2018, the talks and discussions of the Modern Inflation group covered topics ranging from theoretical structures to large scale structure data analysis. Results that were reported included the genericity of the onset of inflation (using mean curvature flow techniques along with numerics), a new primordial black hole production mechanism and an analysis of strong nonGaussian tails during inflation and in (p)reheating, as well as a careful analysis of the origin of stochastic methods from the full quantum field theory in de Sitter spacetime. The more theoretical topics included the derivation of the GibbonsHawking entropy as entanglement entropy in a holographic dual framework, and a careful analysis of multifield axion spectra within a class of string theory compactifications, in the context of a broader overview of largefield inflation. Finally, the talks reported progress on the characterization of largescale structure and its use as a probe of cosmological parameters, including neutrino physics as well as tests of new physics such as nonGaussianity and oscillatory features motivated by string theory.The participant list consisted of a broad and very interesting set of people; intense discussions were frequently interrupted by the interesting talks; as such the meeting went very well both informally and formally. I recall fruitful cross talk among the groups on the question of alternative (beyond GR) gravity theories vis a vis black hole thermodynamics, the initial value problem in mean curvature flow and beyondGR physics, and the issue of theoretical control of spacelike singularities as a few examples.
Following the New York meeting, the group had an extremely full and productive workshop at IAS. We would like to thank the Simons Foundation for the support of both meetings and the arrangements in between which all went very smoothly.
Beyond Einstein Cosmology (Gabadadze)
There were three talks presented by the “Beyond Einstein Cosmology” group. Claudia de Rham summarized recent developments on various strongly coupled theories and their possible applications in astrophysics and cosmology. Notably the question of gravitational wave production in such theories goes hand in hand with the understanding of the time dependent Vainshtein mechanism that she investigated and showed to be qualitatively similar but quantitatively differed from the static Vainshtein mechanism. Claudia also summarized the present and possible future observational bounds on graviton mass giving an exhaustive list of the constraints.
David Pirtskhalava’s talk addressed two questions of a tremendous magnitude: (1) whether one can come up with meaningful theories that would, unlike inflation, be geodesically past complete, and (2) whether such theories can be used to solve the old cosmological constant (CC) problem. In the direction (1) David reviewed the null energy violating theories that seem to provide a natural framework for geodesically past complete early universe and discussed perturbative stability of such theories in various contexts. In the direction (2) David presented an existence proof model in which the CC is be adjusted before the universe enters the FRW phase.
Greg Gabadadze talked about a proposal to embed massive gravity and bigravity in a five dimensional braneworld theory to address the strong coupling issue of these theories. He presented an embedding that raises the strong scale by many orders of magnitude, and also proposed a theory in which the strong scale could be raised all the way up to the 5D Planck scale. Greg outlined how this theory can be used for geodesically complete cosmology in the early universe, as well as for the description of the late time accelerated expansion of the universe.
Talks
Paul Steinhardt
Introduction to Bouncing Cosmology
This talk will explain how models that replace the big bang with a classical, nonsingular transition from contraction to expansion can address many of the fundamental problems of cosmology.
Anna Ijjas
Recent Advances in Constructing Smooth Cosmological Bounces
In this talk, I will describe newly discovered, smooth, nonsingular bounce solutions. In particular, I will focus on how adapting insights and tools from mathematical relativity has been crucial for these constructions and why it will also be a central focus looking ahead.
Frans Pretorius
Numerical Approaches to Bouncing Cosmologies
In this talk, I will give an introduction to numerical solutions of the Einstein equations, focusing on their application to bouncing cosmologies. I will review some work that has been done and discuss some of the challenges going forward that will need to be overcome to fully investigate generic, nonperturbative regimes in nonsingular bounce models.
Leonardo Senatore
Field Theory, Geometry and Data in Cosmology
I will discuss several applications of geometry and field theory to cosmology and how they can affect our understanding of the cosmological data. In the context of geometry, I will show how Thurston’s geometrization classification and mean curvature flow, together with advanced numerical techniques in general relativity, are used to shed light on how inflation starts out of completely inhomogenous initial conditions. I will also discuss a rigorous formalism that allows us to compute correlation functions of fields that are light during inflation and that are endowed with a nontrivial potential, for which naïve perturbation theory is IR divergent. In a multifield landscape of scalar fields, we derive a strongly nonGaussian tail of the distribution of primordial perturbations, exhibiting factorial growth of N point correlators. I will then show how these results allow us to identify novel inflationary signatures and connect to some cosmological data, exploring CMB and primordial black hole signals.
Benjamin Wallisch
Signatures of the Early Universe in the BAO Spectrum
Many aspects of the early universe are currently probed through the cosmic microwave background. Due to theoretical developments and an increase in survey sensitivity, these measurements can now be complemented by largescale structure observations. In this talk, I will advocate the spectrum of baryon acoustic oscillations (BAO) as a new observable for early universe cosmology beyond its use as a standard ruler. I will present the first measurement of the cosmic neutrino background as imprinted in the BAO spectrum of galaxy clustering obtained by BOSS. As a second example, I will discuss a new search for oscillatory features of the primordial power spectrum in the same observable.
Jonathan Braden
Curvature Perturbations from Entropy Generation on Ballistic Trajectories
Inflation provides a dynamical mechanism to produce the primordial density perturbations that seed the formation of structure in the Universe through gravitational collapse. However, during the inflationary phase, the Universe is in a nearly homogeneous and lowentropy state, which must eventually give rise to the dense thermal plasma of the standard hot big bang. This transition, known as (p)reheating, is a necessary ingredient in inflationary theory. Microscopic models of this transition typically lead to strong instabilities and the eventual onset of highly complex, nonlinear modemode coupled behavior.
I will introduce a novel viewpoint on preheating dynamics — the ballistic approximation — where the derivatives coupling nearby points in spacetime (separated by less than Hubble scales) are ignored and individual points in spacetime evolve independently. Remarkably, this approximation captures the relevant dynamics obtained in full lattice simulations. We define a nonlinear generalization of the comoving curvature perturbation that applies on subhorizon as well as superhorizon scales, allowing it be monitored at the level of individual lattice sites in a nonlinear lattice simulation. Absent couplings between trajectories, this quantity is conserved, and the production of curvature fluctuations can be identified with entropy generation. Using this viewpoint, I will argue that the production of curvature perturbations from endofinflation dynamics is ubiquitous, rather than occurring in only a few highly specialized models. Furthermore, our formalism can be extended to study the effects of particle production and evolution on nontrivial potential surfaces during inflation, thus providing a unifying description of both the inflationary and early postinflationary Universe.
Liam McAllister
Inflationary Theory and Quantum Gravity
Important conceptual and technical issues in inflationary theory depend on the details of the ultraviolet completion of gravity. String theory provides a concrete framework for attacking these problems and has inspired new approaches to understanding inflation and de Sitter space. Conjectured properties of quantum gravity and features of known solutions of string theory have led to novel inflationary models and signatures. The structure of the string landscape, along with holographic duality, also feeds into ongoing research on de Sitter quantum gravity. After summarizing the status of this subject, I will describe several developments over the past year. These may include analyses of inflationary scenarios building from the geometry of string compactifications, the kinetic sector of supergravity and the largeflavor limit of string theory; careful assessments of the weak gravity conjecture and its interplay with largefield inflation; and basic quantum information theoretic properties of de Sitter space.
Claudia de Rham
Physics under the Gravitational Rainbow
The recent direct detection of gravitational waves marks the beginning of a new era for physics and astronomy with an opportunity to probe gravity at its most fundamental level. I will discuss how the behavior of gravity on large scales may differ from general relativity and its implications for early and latetime cosmology as well as the potential signatures on the spectrum of gravitational waves observable at LIGO and LISA.
David Pirtskhalava
Violation of the Null Energy Condition and the Early Universe Cosmology
I will review recent progress in understanding lowenergy effective field theories that can consistently violate the null energy condition of general relativity. The implications of these theories for alternatives to cosmic inflation as well as the nonanthropic approaches to the cosmological constant problem will be discussed.
David Pirtskhalava
NEC and the Physics of the Early Universe
I will review recent progress in understanding lowenergy effective field theories that can consistently violate the null energy condition of general relativity. The implications of these theories for alternatives to cosmic inflation as well as the nonanthropic approaches to the cosmological constant problem will be discussed.
Greg Gabadadze
Strong Coupling and Early Universe in Beyond Einstein Theories
Certain cosmologically interesting field theories that, at the classical level, exhibit strongly coupled behavior can be embedded in broader theories that help the strong coupling issue. I will discuss recent developments on these theories and their possible cosmological implications.
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