A technique to build perturbative series for the spectator field’s correlation functions in de Sitter space through the Fokker-Planck equation is proposed. We derive from the first-order differential equation the iterative integral relation for equal- and multi-time correlation functions. With an appropriate integration, the obtained two-point and four-point correlation functions are in agreement with quantum field theory’s ones.

Italy

Alexander Kamenshchik

Polina Petriakova

From the Fokker-Planck equation to perturbative QFT’s results in de Sitter space

We study the stress-energy tensor of a massless, conformally-coupled, quantum scalar field in a rigidly-rotating thermal state on three- and four-dimensional anti-de Sitter space-time. We first find the stress-energy tensor using relativistic kinetic theory, modelling the field as a thermal gas of massless bosons. We then compute the renormalized stress-energy tensor of the scalar field in quantum field theory and compare it with that resulting from relativistic kinetic theory.

United Kingdom

Jacob C. Thompson

Elizabeth Winstanley

Quantum effects in rotating thermal states on anti-de Sitter space-time

This paper investigates basic properties of the de Sitter static patch using simple two-point functions in the probe approximation. We find that de Sitter equilibrates in a superdiffusive manner, unlike most physical systems which equilibrate diffusively. We also examine the scrambling time. In de Sitter, the two-point functions of free fields do not decay for sometime because quanta can reflect off the pole of the static patch. This suggests a minimum scrambling time of the order log(1$\textit{/G}$ ), even for perturbations introduced on the stretched horizon, indicating fast scrambling inside de Sitter static patch. We also discuss the interplay between thermodynamic temperature and inverse correlation time, sometimes called “tomperature.”

United States

Alexey Milekhin

Jiuci Xu

On scrambling, tomperature and superdiffusion in de Sitter space

We argue for the existence of bounds on the tensions of $\textit{p}$-branes in de Sitter space in terms of the Hubble rate and the strength of a class of Chern-Simons-like couplings. The world-volume couplings involve Abelian 1-form gauge fields in the bulk and possibly field strengths intrinsic to the brane. In many cases these couplings are the D-brane Chern-Simons terms present in string theory, while in other cases they are the interactions of axion domain walls with U(1) fields. Our arguments use the same logic and assumptions as the recent Festina Lente proposal (thus utilizing the properties of Nariai de Sitter black holes) and generalize it to extended objects, thereby providing a bottom-up set of constraints independent of any particular UV completion. We compare these bounds to the properties of (wrapped) D-branes in Type II string theory in the weak coupling limit, under the assumption that these properties are not modified significantly in de Sitter constructions. We find that all constraints are satisfied by D-branes, providing further evidence for the Festina Lente conjecture. For the particular case of 2-branes with Chern-Simons interactions we obtain a bound, which however can be evaded if the theory contains a light axion. Similarly, we find the bounds do not apply to axion domain walls due to the presence of the axion.

Saquib Hassan

Georges Obied

John March-Russell

De Sitter space constraints on brane tensions and couplings

We develop the pole-skipping structure in de Sitter (dS) spacetime and find that their leading frequencies satisfy the relation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>ω</mi><mrow><mi>d</mi><mi>S</mi></mrow></msub><mo>=</mo><mi>i</mi><mn>2</mn><mi>π</mi><msub><mi>T</mi><mrow><mi>d</mi><mi>S</mi></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>s</mi><mo stretchy="false">)</mo></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>d</mi><mi>S</mi></mrow></msub><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn><mi>π</mi><mi>L</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>s</mi></math> denotes spin. In the two-dimensional dS spacetime, the pole-skipping points near the cosmic horizon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi><mo>=</mo><mi>L</mi></math> for the scalar field of spin 0 and the fermionic field of spin <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> correspond one to one with those in the classical limit as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>λ</mi><mo stretchy="false">→</mo><mn>0</mn></math> in double-scaled Sachdev-Ye-Kitaev model when the temperature is infinite (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>DSSYK</mi></mrow><mi>∞</mi></msub></math>). This provides a numerical correspondence between quantum gravity in the static patch of two-dimensional dS spacetime and a one-dimensional quantum system, which we consider as a realization of the DS/dS correspondence.

China

Haiming Yuan

Xian-Hui Ge

South Korea

Keun-Young Kim

Pole skipping in two-dimensional de Sitter spacetime and double-scaled SYK model

Using the formalism of geometrothermodynamics, we investigate the phase-transition structure and microstructure of the Kerr-Anti-de Sitter black hole and show the relationship with its shadow structure. By treating the curvature radius as a thermodynamic variable, we ensure scaling consistency and model the system as quasi-homogeneous. In the canonical ensemble, we identify critical points and characterize both first- and second-order phase transitions independently of pressure. In the grand-canonical ensemble, we reveal a distinct phase structure, including the Hawking-Page transition. We derive analytical expressions for the Kerr-Anti-de Sitter black hole shadow and its critical parameters, using shadow thermodynamics to construct asymmetric shadow profiles that capture the phase-transition structure. Finally, we show that the singularities of the geometrothermodynamic curvature in the shadow align with divergences in thermodynamic response functions, confirming the correspondence between shadows, phase transitions, and microstructure.

Mexico

Jose Miguel Ladino

Carlos E. Romero-Figueroa

Kazakhstan

Hernando Quevedo

Phase transitions, shadows, and microstructure of Kerr-Anti-de Sitter Black Holes from geometrothermodynamics

We explore a centaur geometry in Jackiw-Teitelboim gravity, which is an asymptotically anti–de Sitter (AdS) spacetime but in the IR admits a de Sitter (dS) bubble, with another AdS geometry in the deep IR. Thus, this geometry admits a holographic dual in the sense that it is asymptotically AdS. In an attempt to understand this geometry, we calculate the density of states of the putative boundary dual for such mixed geometries by evaluating the on-shell action. We compute the density of states analytically in the classical limit. The resultant density of states suggests that the degrees of freedom in the IR are reduced in such a putative boundary theory due to the IR modification corresponding to the dS bubble.

Japan

Taiwan

Norihiro Iizuka

Sunil Kumar Sake

Note on a centaur geometry: Probing IR de Sitter spacetime holography

It is well known that the area of the de Sitter cosmological horizon is related to the entropy of the bulk spacetime. Recent work has however shown that the horizon encodes more information about the bulk spacetime than just the entropy. In this work, we show that the horizon contains all of the gauge invariant (diffeomorphism and U(1)) information about (static albeit unstable) configurations of charged and rotating objects placed deep inside the de Sitter spacetime. We study highly symmetric objects, such as dipoles and cubes, built of objects with electric charge and angular momentum at their vertices. We show how these configurations affect the geometry of the cosmological horizon and imprint detailed information about the objects in the bulk onto the cosmological horizon.

Willy Fischler

Hare Krishna

Sarah Racz

There is more to the de Sitter horizon than just the area

Assuming that (1) the Universe underwent a postinflationary accelerated expansion phase driven by a fluid with equation of state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>P</mi><mo>=</mo><mi>w</mi><mi>ρ</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>1</mn><mo>&lt;</mo><mi>w</mi><mo>&lt;</mo><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn></math>, that (2) the cosmic horizon in an accelerating, quasi–de Sitter Universe has a temperature inversely proportional to the proper size of the horizon, and that (3) we are static observers, we calculate the frozen-in density of a stable particle of mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi></math> produced by the cosmic horizon that does not undergo any number-changing processes in the late Universe. We find that, as a function of the equation of state and the temperature when radiation domination starts and the quasi–de Sitter phase ends, the mass of the dark matter producing the observed cosmological abundance via this mechanism ranges from 10 keV up to close to the Planck scale.

Stefano Profumo

Dark matter from quasi–de Sitter horizons

We propose a new formula for the entropy of a dynamical cosmological event horizon, which is valid to leading order for perturbations of a stationary asymptotically de Sitter spacetime. By introducing a nontrivial correction term, we generalize Gibbons and Hawking’s first law of event horizons to non-stationary eras. We also develop the non-stationary physical process first law between two arbitrary horizon cross-sections for the cosmological event horizon.

Jinan Zhao

The entropy of dynamical de Sitter horizons