We present remarkably simple covariant expressions for the graviton and ghost propagators in anti–de Sitter (AdS) spacetime valid in any spacetime dimension. In gravity there is a two-parameter family of covariant gauge-fixing conditions and the simplification occurs for a special choice of these parameters. In this gauge the graviton propagator satisfies <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mo>∇</mo></mrow><mrow><mi>μ</mi></mrow></msup><mi>μ</mi><msup><mrow><mo>∇</mo></mrow><mrow><mi>ν</mi></mrow></msup><mi>μ</mi><msub><mrow><mi>G</mi></mrow><mrow><mi>μ</mi><mi>ν</mi><mo>,</mo><msup><mrow><mi>α</mi></mrow><mrow><mo>′</mo></mrow></msup><msup><mrow><mi>β</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo stretchy="false">(</mo><mi>μ</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></mrow></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> is the geodesic distance between two points, and this condition implies an improved infrared behavior. This gauge choice is not possible in flat spacetime.

United Kingdom

Radu N. Moga

Kostas Skenderis

Remarkably simple covariant graviton propagator in anti–de Sitter spacetime

Italy

Alexander Kamenshchik

Polina Petriakova

Erratum: IR finite correlation functions in de Sitter space, a smooth massless limit, and an autonomous equation

We investigate two different definitions of a scalar field effective potential in quantum field theory in de Sitter spacetime: the standard textbook definition, and the constraint effective potential proposed by O’Raifeartaigh et al. in 1986. While these definitions are equivalent in Minkowski spacetime, they differ significantly in de Sitter spacetime. We demonstrate this by computing them both explicitly at one-loop order in perturbation theory. It is well known that the perturbative expansion of the standard effective potential fails to converge for light fields. In contrast, the constraint effective potential does not suffer from this infrared problem, and it can therefore be computed using perturbation theory. We discuss the physical interpretation of the two effective potentials. In particular, we provide evidence supporting an earlier conjecture that the constraint effective potential is the correct one to use in the stochastic Starobinsky-Yokoyama theory.

Lucas Vicente García-Consuegra

CERN

Arttu Rajantie

Scalar effective potentials in de Sitter spacetime

We study the quantum Ising model on (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional anti-de Sitter space using matrix product states (MPS) and matrix product operators (MPOs). We explore the bulk phase diagram of the theory on regular tessellations of hyperbolic space with coordination number seven and find disordered and ordered phases separated by a phase transition. We find that the boundary-boundary spin correlation function exhibits power law scaling deep in the disordered phase of the Ising model consistent with holography. At the critical point, we find the boundary entanglement entropy scales logarithmically with subsystem size but away from this, we see a linear scaling. In comparison, the full system exhibits a volume law scaling, which is expected in chaotic and/or highly connected systems. We also measure out of time ordered correlators (OTOCs) to explore the scrambling behavior of the theory.

United States

Abhishek Samlodia

Simon Catterall

Alexander F. Kemper

Yannick Meurice

Goksu Can Toga

Quantum Ising model on (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional anti–de Sitter space using tensor networks

We study the double cone geometry proposed by Saad-Shenker-Stanford in de Sitter space. We show that with the inclusion of static patch observers, the double cone leads to a linear ramp consistent with random matrix behavior, where the ramp comes from the relative timeshift between two clocks sitting at opposite static patches.

China

Zhenbin Yang

Yuzhen Zhang

Wenwen Zheng

Remarks on the de Sitter double cone

Recently, Ref. [1] proved the energy conservation formula for particle decay in Kerr spacetime: <math altimg='si10.svg'><mrow><msub><mi>m</mi><mn>0</mn></msub><mo linebreak='goodbreak'>=</mo><msub><mi>m</mi><mn>1</mn></msub><mspace width='0.16em' /><msub><mi>&#947;</mi><mn>01</mn></msub><mo linebreak='goodbreak'>+</mo><msub><mi>m</mi><mn>2</mn></msub><mspace width='0.16em' /><msub><mi>&#947;</mi><mn>02</mn></msub></mrow></math>, where <italic>m</italic> <inf>0</inf> is the initial particle, <italic>m</italic> <inf>1</inf> and <italic>m</italic> <inf>2</inf> are the decay products, and <italic>&#947;</italic> <inf>01</inf>, <italic>&#947;</italic> <inf>02</inf> are the relative Lorentz factors between particle 0 and particle 1, and between particle 0 and particle 2, respectively. This conclusion shows that the particle splitting process exhibits a mass defect, which is converted into kinetic energy in the center-of-mass frame. In this paper, we extend it to Kerr&#8211;de Sitter spacetime. Through derivation, we obtain the same energy conservation result as in Kerr spacetime. In addition, we find that, for a fixed cosmological constant, a larger decay radius leads to a larger specific angular momentum of particle 0, larger masses of particles 1 and 2, a smaller absolute value of their specific energy, smaller relative Lorentz factors among the three particles, and smaller four-velocities of the three particles. For a fixed decay radius, a larger cosmological constant leads to larger specific angular momenta of particle 0 and particle 2, smaller masses of particles 1 and 2, a larger absolute value of their specific energy, larger relative Lorentz factors among the three particles, and larger four-velocities of the three particles.

Ke Wang

Xiao-Xiong Zeng

Particle decay and energy conservation in Kerr-de Sitter spacetime

The observable Universe has undergone periods of expansion that are well approximated by de Sitter (dS) space. Still lacking is a quantum-mechanical description of dS spacetime, both globally and when restricted to the static patch. We develop a novel prescription, to the best of our knowledge, for computing holographic complexity in the dS static patch to determine its microscopic features. Specifically, we propose that the natural candidate for dS complexity is the volume of extremal “timelike” surfaces restricted to the static patch, anchored to the cosmological horizon or an observer worldline. Our anchoring prescription provides a clear definition of a reference state, overcoming a common ambiguity in prior definitions of de Sitter holographic complexity. The late-time growth of our complexity functional is linear and proportional to the number of degrees of freedom associated with the cosmological horizon and, therefore, does not exhibit hyperfast growth. Our results imply the dS static patch is characterized by a quantum-mechanical system, with a finite-dimensional Hilbert space whose evolution is governed by a chaotic Hamiltonian.

Iceland

Vyshnav Mohan

Sweden

Watse Sybesma

de Sitter complexity grows linearly in the static patch

We investigate a static, asymptotically flat black hole whose central region approaches a de Sitter vacuum. The geometry is controlled by the ADM mass <italic>M</italic> <inf>0</inf> and a core scale <italic>R</italic>, and is generated by an exponentially decaying anisotropic source. After clarifying the stress tensor and the horizon structure, we study scalar-field perturbations, greybody transmission, Hawking emission and the optical image produced by an optically thin infalling flow. The horizon analysis shows that two horizons exist below the critical value <italic>R</italic>/ <italic>M</italic> <inf>0</inf>&#8239;&#8771;&#8239;0.7768, where they merge into an extremal configuration. Increasing the core scale lowers the peak of the scalar effective potential and shifts the quasinormal spectrum away from the Schwarzschild value, with the largest fractional deviations occurring for low multipoles and higher overtones within the WKB domain of validity. The greybody bound indicates stronger filtering as the core becomes more extended, while the QNM&#8211;greybody correspondence gives a complementary estimate of the transmission probability in the eikonal regime. The Hawking temperature decreases as the extremal configuration is approached, suppressing the emission rate and shifting its maximum to lower frequencies. For a simple optically thin infalling flow, ray tracing shows a small decrease in the apparent shadow scale and in the peak intensity as the core scale is increased.

Azerbaijan

Iran

Brazil

N. Heidari

A.A. Araújo Filho

Russia

V. Vertogradov

Türkiye

A. Övgün

Signatures of a de Sitter-core black hole in ringing, transmission and optical appearance

We study the stability of $\textit{d}$-dimensional ($\textit{d}$ = 3, 4, 5) de Sitter and Minkowski spacetimes within the framework of semiclassical gravity sourced by a strongly coupled quantum field with a gravity dual. Our stability results are derived from a careful analysis of the $\textit{d}$-dimensional Lichnerowicz equation with mass-squared $\textit{m}$ and of semiclassical equations involving the dimensionless parameter $\textit{γ}$ . For $\textit{d}$ = 3, we find that Minkowski spacetime is always unstable against perturbations, whereas de Sitter spacetime becomes stable when a dimensionless parameter $\textit{γ}$ exceeds a critical value. In $\textit{d}$ = 4, both de Sitter and Minkowski spacetimes become unstable when the parameter $\textit{γ}$ exceeds its critical value. In contrast, in $\textit{d}$ = 5, de Sitter and Minkowski spacetimes remain stable for almost all values of the parameter $\textit{γ}$ , except for a regime in which higher-curvature corrections become comparable to the Einstein tensor.

Japan

Akihiro Ishibashi

Kengo Maeda

Takashi Okamura

Instability thresholds for de Sitter and Minkowski spacetimes in holographic semiclassical gravity

In this paper, we would like to investigate whether a generalized Einsteinian cubic gravity, in which three possible cubic interactions $$\mathcal{P}$$ , $$\mathcal{C}$$ , and $$\mathcal{C}'$$ are treated on an equal footing, admits a de Sitter solution as its stable cosmological solution. As a result, we are able to confirm the existence of the corresponding de Sitter solution for this gravity by solving analytically its field equations. Remarkably, only the cubic interaction $$\mathcal{P}$$ gives rise to the existence of the de Sitter solution. Then, we convert the field equations into the corresponding dynamical system for a stability analysis purpose. A fixed point of this dynamical system is found and shown to be equivalent to the obtained de Sitter solution. However, the perturbed dynamical system turns out to be incomplete, leaving undetermined information of the stability of the fixed point (or equivalently the de Sitter solution). Fortunately, we show that this loophole can be cured once the well-known Starobinsky term $$R^2$$ is introduced into the action of the generalized Einsteinian cubic gravity, despite the fact that it contributes nothing to the value of the de Sitter solution.

Vietnam

Tuan Do

Effect of $$R^2$$ on the stability of de Sitter solution of the generalized Einsteinian cubic gravity