De Sitter Space Research Articles

Conformal Yang-Mills field in (A)dS space

Ordinary-derivative (second-derivative) Lagrangian formulation of classical conformal Yang-Mills field in the (A)dS space of six, eight, and ten dimensions is developed. For such conformal field, we develop two gauge invariant Lagrangian formulations which we refer to as generic formulation and decoupled formulation. In both formulations, the usual Yang-Mills field is accompanied by additional vector and scalar fields where the scalar fields are realized as Stueckelberg fields. In the generic formulation, the usual Yang-Mills field is realized as a primary field, while the additional vector fields are realized as auxiliary fields. In the decoupled formulation, the usual Yang-Mills field is realized as massless field, while the additional vector fields together with the Stueckelberg are realized as massive fields. Some massless/massive fields appear with the wrong sign of kinetic terms, hence demonstrating explicitly that the considered models are not unitary. The use of embedding space method allows us to treat the isometry symmetries of (A)dS space manifestly and obtain conformal transformations of fields in a relatively straightforward way. By accompanying each vector field by the respective gauge parameter, we introduce an extended gauge algebra. Levy-Maltsev decomposition of such algebra is noted. Use of the extended gauge algebra setup allows us to present concise form for the Lagrangian and gauge transformations of the conformal Yang-Mills field. Higher-derivative representation of the Lagrangian is also obtained.

Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model

How can we define complexity in dS space from microscopic principles? Based on recent developments pointing towards a correspondence between a pair of double-scaled Sachdev-Ye-Kitaev (DSSYK) models/ 2D Liouville-de Sitter (LdS2) field theory/ 3D Schwarzschild de Sitter (SdS3) space in [1–3], we study concrete complexity proposals in the microscopic models and their dual descriptions. First, we examine the spread complexity of the maximal entropy state of the doubled DSSYK model. We show that it counts the number of entangled chord states in its doubled Hilbert space. We interpret spread complexity in terms of a time difference between antipodal observers in SdS3 space, and a boundary time difference of the dual LdS2 CFTs. This provides a new connection between entanglement and geometry in dS space. Second, Krylov complexity, which describes operator growth, is computed for physical operators on all sides of the correspondence. Their late time evolution behaves as expected for chaotic systems. Later, we define the query complexity in the LdS2 model as the number of steps in an algorithm computing n-point correlation functions of boundary operators of the corresponding antipodal points in SdS3 space. We interpret query complexity as the number of matter operator chord insertions in a cylinder amplitude in the DSSYK, and the number of junctions of Wilson lines between antipodal static patch observers in SdS3 space. Finally, we evaluate a specific proposal of Nielsen complexity for the DSSYK model and comment on its possible dual manifestations.

What if string theory has a de Sitter excited state?

We propose precise effective field theory criteria to obtain a four-dimensional de Sitter space within M-theory. To this effect, starting with the state space described by the action of metric perturbations, fluxes etc over the supersymmetric Minkowski vacuum in eleven-dimensions, we discuss the most general low energy effective action in terms of the eleven-dimensional fields including non-perturbative and non-local terms. Given this, our criteria to obtain a valid four-dimensional de Sitter solution at far IR involve satisfying the Schwinger-Dyson equations of the associated path integral, as well as obeying positivity constraints on the dual IIA string coupling and its time derivative. For excited states, the Schwinger-Dyson equations imply an effective emergent potential different from the original potential. We show that while vacuum solutions and arbitrary coherent states fail to satisfy these criteria, a specific class of excited states called the Glauber-Sudarshan states obey them. Using the resurgent structure of observables computed using the path integral over the Glauber-Sudarshan states, four-dimensional de Sitter in the flat slicing can be constructed using a Glauber-Sudarshan state in M-theory.Among other novel results, we discuss the smallness of the positive cosmological constant, including the curious case where the cosmological constant is very slowly varying with time. We also discuss the resolution of identity with the Glauber-Sudarshan states, generation and the convergence properties of the non-perturbative and the non-local effects, the problems with the static patch and other related topics. We analyze briefly the issues related to the compatibility of the Wilsonian effective action with Borel resummations and discuss how they influence the effective field theory description in a four-dimensional de Sitter space.

Quantum scalar field on fuzzy de Sitter space. Part I. Field modes and vacua

We study a scalar field on a noncommutative model of spacetime, the fuzzy de Sitter space, which is based on the algebra of the de Sitter group SO(1, d) and its unitary irreducible representations. We solve the Klein-Gordon equation in d = 2, 4 and show, using a specific choice of coordinates and operator ordering, that all commutative field modes can be promoted to solutions of the fuzzy Klein-Gordon equation. To explore completeness of this set of modes, we specify a Hilbert space representation and study the matrix elements (integral kernels) of a scalar field: in this way the complete set of solutions of the fuzzy Klein-Gordon equation is found. The space of noncommutative solutions has more degrees of freedom than the commutative one, whenever spacetime dimension is d > 2. In four dimensions, the new non-geometric, internal modes are parametrised by S2 × W, where W is a discrete matrix space. Our results pave the way to analysis of quantum field theory on the fuzzy de Sitter space.

Doubly special relativity as a nonlocal quantum field theory

In this work, we explore the quantum theories of the free massive scalar, the massive fermionic, and the electromagnetic fields in a doubly special relativity scenario. This construction is based on a geometrical interpretation of the kinematics of this kind of theory. In order to describe the modified actions, we find that a higher (indeed infinite) derivative field theory is needed, from which the deformed kinematics can be read. From our construction, we are able to restrict the possible models of doubly special relativity to those that preserve linear Lorentz invariance. We quantize the theories and also obtain a deformed version of the Maxwell equations. We analyze the electromagnetic vector potential for both an electric pointlike source and magnetic dipole. We observe that the electric and magnetic fields do not diverge at the origin for some models described with an anti–de Sitter momentum space, but they do for a de Sitter space in both problems. Published by the American Physical Society 2024

Cosmological correlators for Bogoliubov initial states

We consider late-time correlators in de Sitter (dS) space for initial states related to the Bunch-Davies vacuum by a Bogoliubov transformation. We propose to study such late-time correlators by reformulating them in the familiar language of Witten diagrams in Euclidean anti-de Sitter space (EAdS), showing that they can be perturbatively re-cast in terms of corresponding dS boundary correlators in the Bunch-Davies vacuum and in turn, Witten diagrams in EAdS. Unlike the standard relationship between late-time correlators in the Bunch-Davies vacuum and EAdS Witten diagrams, this involves points on the upper and lower sheet of the EAdS hyperboloid which account for antipodal singularities of the two-point functions. Such Bogoliubov states include an infinite one parameter family of de Sitter invariant vacua as a special case, where the late-time correlators are constrained by conformal Ward identities. In momentum space, it is well known that their late-time correlators exhibit singularities in collinear (“folded”) momentum configurations. We give a position space interpretation of such solutions to the conformal Ward identities, where in embedding space they can be generated from the solution without collinear singularities by application of the antipodal map. We also discuss the operator product expansion (OPE) limit of late-time correlators in a generic dS invariant vacuum. Many results are derived using the Mellin space representation of late-time correlators, which in this work we extend to accommodate generic dS invariant vacua.

Complexity equals anything can grow forever in de Sitter space

Complexity equals anything can grow forever in de Sitter space

Violation of weak cosmic censorship in de Sitter space

Inspired by the recent discovery of a violation of strong cosmic censorship (SCC) for the near-extremal Reissner-Nordström black holes in de Sitter space (RN-dS), we investigate if the weak cosmic censorship conjecture (WCCC) can also be violated in RN-dS with a fixed cosmological constant. Our method is based on the recent formulation of examining WCCC by the constraint of the second law, which in this case requires the sum of areas of the event and cosmic horizons cannot decrease during the infall process of Wald’s gedanken experiment. We find that the WCCC can be violated for the near-extremal RN-dS in some regimes of second-order perturbation of field configurations. Given the charge parameter of RN-dS, we can find the lowest value of the subextremality parameter, beyond which the WCCC holds. Our results imply that there might be possible correlations between the violation of SCC and WCC. Because of a lack of an unambiguous relation between the gravitational mass and matter’s kinematic mass in asymptotically de Sitter space, we cannot compare the corresponding regimes of parameter space for the violations of SCC and WCCC. We also discuss the subtlety in formulating the first- and second-law approaches to examine WCCC. Published by the American Physical Society 2024

Action, entropy and pair creation rate of charged black holes in de Sitter space

We compute and clarify the interpretation of the on-shell Euclidean action for Reissner-Nordström black holes in de Sitter space. We show the on-shell action is minus the sum of the black hole and cosmological horizon entropy for arbitrary mass and charge in any number of dimensions. This unifying expression helps to clear up a confusion about the Euclidean actions of extremal and ultracold black holes in de Sitter, as they can be understood as special cases of the general expression. We then use this result to estimate the probability for the pair creation of black holes with arbitrary mass and charge in an empty de Sitter background, by employing the formalism of constrained instantons. Finally, we suggest that the decay of charged de Sitter black holes is governed by the gradient flow of the entropy function and that, as a consequence, the regime of light, superradiant, rapid charge emission should describe the potential decay of extreme charged Nariai black holes to singular geometries.

Generalized entanglement capacity of de Sitter space

Near horizons, quantum fields of low spin exhibit densities of states that behave asymptotically like 1+1 dimensional conformal field theories. In effective field theory, imposing some short-distance cutoff, one can compute thermodynamic quantities associated with the horizon, and the leading cutoff sensitivity of the heat capacity is found to equal to the leading cutoff sensitivity of the entropy. One can also compute contributions to the thermodynamic quantities from the gravitational path integral. For the cosmological horizon of the static patch of de Sitter space, a natural conjecture for the relevant heat capacity is shown to equal the Bekenstein-Hawking entropy. These observations allow us to extend the well-known notion of the generalized entropy to a generalized heat capacity for the static patch of de Sitter (dS). The finiteness of the entropy and the nonvanishing of the generalized heat capacity suggest it is useful to think about dS as a state in a finite dimensional quantum gravity model that is not maximally uncertain. Published by the American Physical Society 2024

Exploring the physical properties of anisotropic compact objects and constraining their mass–radius relations beyond standard limit in [formula omitted]-gravity

The progress in theoretical modeling of compact high-mass stars in the context of alternative gravity has become important in minimizing challenges associated with neutron star (NS) radius measurements. On this basis, we have presented a rigorous study of compact objects beyond the standard limit in gravity F(Q) in particular F(Q)=b1Q+b2 where b1 and b2 are constants. After formulating the basic equations and finding their relevant solutions by assuming a well-behaved ansatz for the metric potential as well as for anisotropy monitored by the parameters μ1,μ2,b1, along with imposing the boundary conditions on the system under treatment, we have developed a stellar model for anisotropic stars. Specifically, we explored the physical properties of these anisotropic stars and provided novel mass–radius (M−R) relations with models falling in the mass gap of the events GW190814 and GW200210, as well as the effects of slow rotation and moment of inertia on these findings. Interestingly, the behavior of the M−R curves represents a polytropic-type equation of state (EOS) for a negative Λ, while a positive Λ corresponds to a quark matter EOS. However, the analysis reveals that the predicted radii of the compact object observed in the GW190814 event, with a mass of 2.5–2.67 M⊙, is approximately 11.4 km for the de Sitter (dS) case and 11.8 km for the anti-de Sitter (AdS) case, assuming a specific value of the parameter b1=1.1. Furthermore, for b1>1.1, the model predicts the existence of more compact stars with a maximum mass of approximately 3M⊙, which is in good agreement with the R2 model of NSs maintaining the Sly EOS. From the I−M curves, it can be observed that higher values of b1 and μ1 in F(Q) gravity can sustain high moments of inertia (I) of stars with high masses. Interestingly, we obtained the range of I for the dS space as [1.92,3.92]×1045gcm2 and for the AdS space as [2.01,4.03]×1045gcm2 for 1.0≤b1≤1.2.

Loops in AdS: from the spectral representation to position space. Part III

We study loop amplitudes in anti de-Sitter space via the spectral representation. We consider loops of spinning fields and in particular gauge fields, and derive various identities connecting different families of loop diagrams, at different number of loops, different spins, different masses. Such identities are useful for the computation of Witten diagrams. Considering the theory of large-Nf conformal scalar QED defined on AdS space, we derive an analytic expression for the exact 4-point correlation function at sub-leading order in 1Nf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{N_f} $$\\end{document}. Additionally, we derive analytic expressions for bulk 2-point functions and boundary 4-point functions for various families of diagrams, which we denote as “blob diagrams”. Finally we study 4-point ladder diagrams with spinning fields, and we derive integral expressions for the spectral representation of a k-loop ladder diagram.

Entanglement harvesting and quantum discord of alpha vacua in de Sitter space

The CPT invariant vacuum states of a scalar field in de Sitter space, called α-vacua, are not unique. We explore the α-vacua from the quantum information perspective by a pair of static Unruh-DeWitt (UDW) detectors coupled to a scalar field with either monopole or dipole coupling, which are in time-like zero separation or space-like antipodal separation. The analytical form of the reduced final state of the UDW detector is derived. We study the entanglement harvesting and quantum discord of the reduced state, which characterize the quantum entanglement and quantum correlation of the underlying α-vacua, respectively. Our results imply that the quantum entanglement gravitated by de Sitter gravity behaves quite differently for time-like and space-like separations. It experiences “sudden death” for the former and grows for the latter as the measuring time or the value of α increases. This demonstrates the nonlocal nature of quantum entanglement. For the quantum discord, we find no “sudden death” behavior, and it experiences superhorizon suppression, which explains the superhorizon decoherence in the inflationary universe scenario. Overall, the time-like or space-like quantum entanglement and correlation behave differently on their dependence of α, measuring time and spectral gaps, with details discussed in this work.

De Sitter at all loops: the story of the Schwinger model

We consider the two-dimensional Schwinger model of a massless charged fermion coupled to an Abelian gauge field on a fixed de Sitter background. The theory admits an exact solution, first examined by Jayewardena, and can be analyzed efficiently using Euclidean methods. We calculate fully non-perturbative, gauge-invariant correlation functions of the electric field as well as the fermion and analyze these correlators in the late-time limit. We compare these results with the perturbative picture, for example by verifying that the one-loop contribution to the fermion two-point function, as predicted from the exact solution, matches the direct computation of the one-loop Feynman diagram. We demonstrate many features endemic of quantum field theory in de Sitter space, including the appearance of late-time logarithms, their resummation to de Sitter invariant expressions, and Boltzmann suppressed non-perturbative phenomena, with surprising late-time features.

The cosmological switchback effect. Part II

Recent developments in static patch holography proposed that quantum gravity in de Sitter space admits a dual description in terms of a quantum mechanical theory living on a timelike surface near the cosmological horizon. In parallel, geometric observables associated with the Einstein-Rosen bridge of a black hole background were suggested to compute the computational complexity of the state dual to a gravitational theory. In this work, we pursue the study of the complexity=volume and complexity=action conjectures in a Schwarzschild-de Sitter geometry perturbed by the insertion of a shockwave at finite boundary times. This analysis extends previous studies that focused either on the complexity=volume 2.0 conjecture, or on the case of a shockwave inserted along the cosmological horizon. We show that the switchback effect, describing the delay in the evolution of complexity in reaction to a perturbation, is a universal feature of the complexity proposals in asymptotically de Sitter space. The geometric origin of this phenomenon is related to the causal connection between the static patches of de Sitter space when a positive pulse of null energy is inserted in the geometry.

Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, nS and nT, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) Mp(n) representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the Mp(n) group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of Mp(2) are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition −∞<t<∞). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for n→∞), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic Mp(n) group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it.

Constraint on the Cosmic Curvature in a Model with the Schwarzschild–de Sitter Metric from Supernovae and Gamma-Ray Burst Observational Data

In developing his cosmological model of 1917, de Sitter theoretically predicted the phenomenon of cosmological redshift (the de Sitter effect), which he did long before the discovery of this phenomenon in observations. The de Sitter effect is gravitational by its nature, as it is due to differences between the coordinate systems of the observer and the distant source. However, the relationship between the redshift and distance derived from the de Sitter metric is at odds with observations, since this relationship is nonlinear (quadratic) for small redshifts, while the observed relationship between the same quantities is strictly linear. This paper discusses the possibility that cosmological redshift is gravitational by its nature, as in de Sitter’s 1917 model. At the same time, here, as in de Sitter’s model, an elliptical space is used, the main characteristic of which is the identification of its antipodal points. But, unlike de Sitter’s model, here, in order to ensure strict linear dependence of the redshift on distance, the origin of the reference system is transferred to the observer’s antipodal point. The Schwarzschild–de Sitter metric used in this model allows you to estimate the curvature of space from observational data. To achieve this, a theoretical Hubble diagram is built within the framework of the model with the Schwarzschild–de Sitter metric, which is compared with observations from the Pantheon+ catalogue of type Ia supernovae and the Amati catalogue of gamma-ray bursts in the redshift range of 0<z<8. As a result of this comparison, we found that the lower estimate of the radius of curvature of space was quite large: 2.4×1015 Mpc. This means that the observational data indicate a negligible curvature of space.

Quantum backreactions in (A)dS3 massive gravity and logarithmic asymptotic behavior

We study the interplay between higher-curvature terms and the backreaction of quantum fluctuations in three-dimensional massive gravity in asymptotically (anti–)de Sitter space. We focus on the theory at the special point of the parameter space where the two maximally symmetric vacua coincide. In the case of positive cosmological constant, this corresponds to the partially massless point, at which the classical theory admits de Sitter black holes and exhibits an extra conformal symmetry at linear level. We explicitly find the quantum corrected black hole geometry in the semiclassical approximation and show that it induces a relaxation of the standard asymptotic conditions. Nonetheless, the new asymptotic behavior is still preserved by an infinite-dimensional algebra, which, in addition to Virasoro, contains logarithmic supertranslations. Finally, we show that all the results we obtain for the quadratic massive gravity theory can be extended to theories including cubic and quartic terms in the curvature. Published by the American Physical Society 2024

Celestial holography revisited. Part II. Correlators and Källén-Lehmann

In this work we continue the investigation of the extrapolate dictionary for celestial holography recently proposed in [1], at both the perturbative and non-perturbative level. Focusing on scalar field theories, we give a complete set of Feynman rules for extrapolate celestial correlation functions and their radial reduction in the hyperbolic slicing of Minkowski space. We prove to all orders in perturbation theory that celestial correlators can be rewritten in terms of corresponding Witten diagrams in EAdS which, in the hyperbolic slicing of Minkowski space, follows from the fact that the same is true in dS space. We then initiate the study of non-perturbative properties of celestial correlators, deriving the radial reduction of the Källén-Lehmann spectral representation of the exact Minkowski two-point function. We discuss the analytic properties of the radially reduced spectral function, which is a meromorphic function of the spectral parameter, and highlight a connection with the Watson-Sommerfeld transform.

Cosmic purity lost: perturbative and resummed late-time inflationary decoherence

We compute the rate with which unobserved fields decohere other fields to which they couple, both in flat space and in de Sitter space, for spectator scalar fields prepared in their standard adiabatic vacuum. The process is very efficient in de Sitter space once the modes in question pass outside the Hubble scale, displaying the tell-tale phenomenon of secular growth that indicates the breakdown of perturbative methods on a time scale parameterically long compared with the Hubble time. We show how to match the perturbative evolution valid at early times onto a late-time Lindblad evolution whose domain of validity extends to much later times, thereby allowing a reliable resummation of the perturbative result beyond the perturbative regime. Super-Hubble modes turn out to be dominantly decohered by unobserved modes that are themselves also super-Hubble. If applied to curvature perturbations during inflation our observations here could close a potential loophole in recent calculations of the late-time purity of the observable primordial fluctuations.