The two-point correlation function of a massive field ⟨χ(τ)χ(0)⟩, measured along an observer’s worldline in de Sitter (dS), decays exponentially as τ → ∞. Meanwhile, every dS observer is surrounded by a horizon and the holographic interpretation of the horizon entropy S dS suggests that the correlation function should stop decaying, and start behaving erratically at late times. We find evidence for this expectation in Jackiw-Teitelboim gravity by finding a topologically nontrivial saddle, which is suppressed by   <math> <msup> <mi>e</mi> <mrow> <mo>−</mo> <msub> <mi>S</mi> <mi>dS</mi> </msub> </mrow> </msup> </math>  $$ {e}^{-{S}_{\textrm{dS}}} $$ , and which gives a constant contribution to | ⟨χ(τ)χ(0)⟩ |2. This constant might have the interpretation of the late-time average of | ⟨χ(τ)χ(0)⟩ |2 over all microscopic theories that have the same low-energy effective description.

Italy

Mehrdad Mirbabayi

An observer’s measure of de Sitter entropy

We argue that there is a lower bound of order <math><msup><mn>10</mn><mrow><mo>−</mo><mn>19</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>eV</mi></math> on dark matter mass if it is produced after inflation via a process with finite correlation length. We rely on nondetection of free-streaming suppression and white-noise enhancement of density perturbations as the observational inputs.

United States

Mustafa A. Amin

A Lower Bound on Dark Matter Mass

In a QFT on de Sitter background, one can study correlators between fields pushed to the future and past horizons of a comoving observer. This is a neat probe of the physics in the observer’s causal diamond (known as the static patch). We use this observable to give a generalization of the quasinormal spectrum in interacting theories, and to connect it to the spectral density that appears in the Källén-Lehmann expansion of dS correlators. We also introduce a finite-temperature effective field theory consisting of free bulk fields coupled to a boundary. In matching it to the low frequency expansion of correlators, we find positivity constraints on the EFT parameters following from unitarity.

Flavio Riccardi

Probing de Sitter from the horizon

If a bulk gravitational path integral can be identified with an average of partition functions over an ensemble of boundary quantum theories, then a corresponding moment problem can be solved. We review existence and uniqueness criteria for the Stieltjes moment problem, which include an infinite set of positivity conditions. The existence criteria are useful to rule out an ensemble interpretation of a theory of gravity, or to indicate incompleteness of the gravitational data. We illustrate this in a particular class of 2D gravities including variants of the CGHS model and JT supergravity. The uniqueness criterion is relevant for an unambiguous determination of quantities such as   <math> <mover> <mrow> <mo>log</mo> <mi>Z</mi> <mfenced> <mi>β</mi> </mfenced> </mrow> <mo>¯</mo> </mover> </math>  $$ \overline{\log Z\left(\beta \right)} $$  or the quenched free energy. We prove in JT gravity that perturbation theory, both in the coupling which suppresses higher-genus surfaces and in the temperature, fails when the number of boundaries is taken to infinity. Since this asymptotic data is necessary for the uniqueness problem, the question cannot be settled without a nonperturbative completion of the theory.

Oliver Janssen

Russia

Peter Zograf

Gravity as an ensemble and the moment problem

For ensembles of Hamiltonians that fall under the Dyson classification of random matrices with β ∈ {1, 2, 4}, the low-temperature mean entropy can be shown to vanish as 〈S(T)〉 ∼ κT β + 1. A similar relation holds for Altland-Zirnbauer ensembles. JT gravity has been shown to be dual to the double-scaling limit of a β = 2 ensemble, with a classical eigenvalue density   <math> <mo>∝</mo> <msup> <mi>e</mi> <msub> <mi>S</mi> <mn>0</mn> </msub> </msup> <msqrt> <mi>E</mi> </msqrt> </math>  $$ \propto {e}^{S_0}\sqrt{E} $$  when 0 &lt; E ≪ 1. We use universal results about the distribution of the smallest eigenvalues in such ensembles to calculate κ up to corrections that we argue are doubly exponentially small in S 0.

Low-temperature entropy in JT gravity

We propose a Euclidean preparation of an asymptotically AdS2 spacetime that contains an inflating dS2 bubble. The setup can be embedded in a four dimensional theory with a Minkowski vacuum and a false vacuum. AdS2 approximates the near horizon geometry of a two-sided near-extremal Reissner-Nordström black hole, and the two sides can connect to the same Minkowski asymptotics to form a topologically nontrivial worm- hole geometry. Likewise, in the false vacuum the near-horizon geometry of near-extremal black holes is approximately dS2 times 2-sphere. We interpret the Euclidean solution as describing the decay of an excitation inside the wormhole to a false vacuum bubble. The result is an inflating region inside a non-traversable asymptotically Minkowski wormhole.

Uptunneling to de Sitter

We present the exact solution for the scattering problem in the flat space Jackiw-Teitelboim (JT) gravity coupled to an arbitrary quantum field theory. JT gravity results in a gravitational dressing of field theoretical scattering amplitudes. The exact expression for the dressed S -matrix was previously known as a solvable example of a novel UV asymptotic behavior, dubbed asymptotic fragility. This dressing is equivalent to the T T ¯ $$ T\overline{T} $$ deformation of the initial quantum field theory. JT gravity coupled to a single mass-less boson provides a promising action formulation for an integrable approximation to the worldsheet theory of confining strings in 3D gluodynamics. We also derive the dressed S -matrix as a flat space limit of the near AdS 2 holography. We show that in order to preserve the flat space unitarity the conventional Schwarzian dressing of boundary correlators needs to be slightly extended. Finally, we propose a new simple expression for flat space amplitudes of massive particles in terms of correlators of holographic CFT’s.

Canada

Sergei Dubovsky

Victor Gorbenko

Asymptotic fragility, near AdS 2 holography and T T ¯ $$ T\overline{T} $$

A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast Î´ and momentum density Ï(k) scale as k2 and k, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of Â Î´ is indeed valid to all orders.

Iran

Ali Akbar Abolhasani

Netherlands

Enrico Pajer

Systematic renormalization of the effective theory of Large Scale Structure

Various inflationary scenarios can often be distinguished from one another by looking at the squeezed limit behavior of correlation functions. Therefore, it is useful to have a framework designed to study this limit in a more systematic and efficient way. We propose using an expansion in terms of weakly coupled super-horizon degrees of freedom, which is argued to generically exist in a near de Sitter space-time. The modes have a simple factorized form which leads to factorization of the squeezed-limit correlation functions with power-law behavior in klong/kshort. This approach reproduces the known results in single-, quasi-single-, and multi-field inflationary models. However, it is applicable even if, unlike the above examples, the additional degrees of freedom are not weakly coupled at sub-horizon scales. Stronger results are derived in two-field (or sufficiently symmetric multi-field) inflationary models. We discuss the observability of the non-Gaussian 3-point function in the large-scale structure surveys, and argue that the squeezed limit behavior has a higher detectability chance than equilateral behavior when it scales as (klong/kshort)Î with ÎÂ &lt;Â 1âwhere local non-Gaussianity corresponds to ÎÂ =Â 0.

Marko Simonović

Effective theory of squeezed correlation functions

A recent paper argued that it is not possible to infer the energy scale of inflation from the amplitude of tensor fluctuations in the Cosmic Microwave Background, because the usual connection is substantially altered if there are a large number of universally coupled fields present during inflation, with mass less than the inflationary Hubble scale. We give a simple argument demonstrating that this is incorrect.