Einstein Gravity can be formulated as a gauge theory with the tangent space respecting the Lorentz symmetry. In this paper we show that the dimension of the tangent space can be larger than the dimension of the manifold and by requiring the invariance of the theory with respect to 5d Lorentz group (de Sitter group) Einstein theory is reproduced unambiguously. The other possibility is to have unitary symmetry on a complex tangent space of the same dimension as the manifold. In this case the resultant theory is Einstein-Strauss Hermitian gravity. The tangent group is important for matter couplings. We show that in the de Sitter case the 4 dimensional space time vector and scalar are naturally unified by a hidden symmetry being components of a 5d vector in the tangent space. With a de Sitter tangent group spinors can exist only when they are made complex or taken in doublets in a way similar to N=2 supersymmetry.
General relativity can be unambiguously formulated with Lorentz, de Sitter and anti-de Sitter tangent groups, which determine the fermionic representations. We show that besides of the Lorentz group only anti-de Sitter tangent group is consistent with all physical requirements.
We discuss properties of fuzzy de Sitter space defined by means of algebra of the de Sitter group $\mathrm{SO}(1,4)$ in unitary irreducible representations. It was shown before that this fuzzy space has local frames with metrics that reduce, in the commutative limit, to the de Sitter metric. Here we determine spectra of the embedding coordinates for $(ρ,s=\frac 12)$ unitary irreducible representations of the principal continuous series of the $\mathrm{SO}(1,4)$. The result is obtained in the Hilbert space representation, but using representation theory it can be generalized to all representati…
We prove that, under the standard conformal scaling, a massless field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. This result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch-Davies vacuum.
The symmetry group of the de Sitter spacetime, accommodates fields of various masses and spin among its unitary irreducible representations. These unitary representations are labeled by the spin and the weight contribution to the scaling dimension and depending on the mass and spin of the field the weight may take either purely real or purely imaginary values. In this work, we construct the late time boundary operators for a massive scalar field propagating in de Sitter spacetime, in arbitrary dimensions. We show that contrary to the case of Anti de Sitter, purely imaginary weights also corres…
Recently proposed "multicritical" higher-derivative gravities in Anti de Sitter space carry logarithmic representations of the Anti de Sitter isometry group. While generically non-unitary already at the quadratic, free-theory level, in special cases these theories admit a unitary subspace. The simplest example of such behavior is "tricritical" gravity. In this paper, we extend the study of parity-even tricritical gravity in d = 3, 4 to the first nonlinear order. We show that the would-be unitary subspace suffers from a linearization instability and is absent in the full non-linear theory.
We rederive the characters of all unitary irreducible representations of the $(d+1)$-dimensional de Sitter spacetime isometry algebra $\mathfrak{so}(1,d+1)$, and propose a dictionary between those representations and massive or (partially) massless fields on de Sitter spacetime. We propose a way of taking the flat limit of representations in (anti-) de Sitter spaces in terms of these characters, and conjecture the spectrum resulting from taking the flat limit of mixed-symmetry fields in de Sitter spacetime. We comment on a possible equivalent of the scalar singleton for the de Sitter (dS) spac…
We analyze asymptotic symmetry algebras in (2+1)-dimensional non-AdS higher-spin gravity with a focus on AdS$_2\times\mathbb{R}$ and $\mathbb{H}_2\times\mathbb{R}$. We find a consistent set of boundary conditions for spin-3 gravity in the non-principal embedding and calculate the corresponding asymptotic symmetry algebra in the classical and quantum mechanical case. In addition, we check for unitary representations of the resulting quantum $\mathcal{W}_3^{(2)}$ algebra and give an interpretation of the corresponding CFT.
Our main goal here is to provide an introduction on some of the well established properties of the representation theory of SO(d+1,1), for those considering to think on physical problems set in de Sitter space in terms of these representations. With this purpose we review two intertwining maps, the map G that is used in constructing a well defined inner product for the complementary series representations and the map Q that is involved in constructing composite representations. We give explicit examples from the late-time boundary of de Sitter on the practical use of the complementary series i…
We continue the study of inflationary fluctuations in Holographic Space Time models of inflation. We argue that the holographic theory of inflation provides a physical context for what is often called dS/CFT. The holographic theory is a quantum theory which, in the limit of a large number of e-foldings, gives rise to a field theory on $S^3$, which is the representation space for a unitary representation of SO(1,4). This is not a conventional CFT, and we do not know the detailed non-perturbative axioms for correlation functions. However, the two- and three-point functions are completely determi…
Recent works have revealed that quantum extremal islands can contribute to the fine-grained entropy of black hole radiation reproducing the unitary Page curve. In this paper, we use these results to assess if an observer in de Sitter space can decode information hidden behind their cosmological horizon. By computing the fine-grained entropy of the Gibbons-Hawking radiation in a region where gravity is weak we find that this is possible, but the observer's curiosity comes at a price. At the same time the island appears, which happens much earlier than the Page time, a singularity forms which th…
We consider the operation of contraction of unitary irreducible representations of the de Sitter group $ SO(4,1) $. It is shown that a direct sum of unitary irreducible representations of the Poincaré group with different signs of the rest mass is obtained as a result of contraction. The results obtained are used to interpret the phenomena of "dark matter" and "dark energy" in terms of the elementary quantum systems of de Sitter's world.
We study time evolution in two simple models of de Sitter quantum gravity, Jackiw-Teitelboim gravity and a minisuperspace approximation to Einstein gravity with a positive cosmological constant. In the former we find that time evolution is isometric rather than unitary, and find suggestions that this is true in Einstein gravity as well. The states that are projected out under time evolution are initial conditions that crunch. Along the way we establish a matrix model dual for Jackiw-Teitelboim gravity where the dilaton varies on the boundary.
Entanglement and factorization in axion-de Sitter universes
Institute for Theoretical Physics, KU Leuven（荷语鲁汶大学理论物理研究所）；Qubits and Spacetime Unit, Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学量子比特与时空单元）
We find the propagator and calculate the tree level scattering amplitude between two covariantly conserved sources in an Anti-de Sitter background for the most general D-dimensional quadratic, four-derivative, gravity with a Pauli-Fierz mass. We also calculate the Newtonian potential for various limits of the theory in flat space. We show how the recently introduced three dimensional New Massive Gravity is uniquely singled out among higher derivative models as a (tree level) unitary model and that its Newtonian limit is equivalent to that of the usual massive gravity in flat space.
Fermionic fields of higher spin in de Sitter space
King’s College London（伦敦国王学院）；KU Leuven（荷语鲁汶大学）；UMONS（蒙斯大学）；Instituto de Física de La Plata - CONICET（拉普拉塔物理研究所-阿根廷国家科学研究委员会）；Universidad Nacional de La Plata（拉普拉塔国立大学）
The covariant free fields of any spin on anti-de Sitter spacetimes are studied, pointing out that these transform under isometries according to covariant representations of the anti-de Sitter isometry group, induced by those of the Lorentz group. Applying the method of ladder operators it is shown that the covariant representations with unique spin are equivalent with discrete unitary irreducible representations of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations may depend on th…
An alternative refined de Sitter conjecture giving rise to a natural combination of the first and second derivatives of the scalar potential was proposed recently by David Andriot and Christoph Roupec (Fortsch. Phys. 67 (2019) no.1-2, 1800105). In this work, we study the inflation models in a general scalar-tensor theory with exponential and hyperbolic tangent forms of potential as well as model with quantum corrected potential and examine whether these three models of inflation can satisfy this further refining de Sitter swampland conjecture or not. Regarding our analysis with proper choices …
Higgs mechanism to massive higher-spin gauge fields is an outstanding open problem. We investigate this issue in the context of Kaluza-Klein compactification. Starting from a free massless higher-spin field in $(d+2)$-dimensional anti-de Sitter space and compactifying over a finite angular wedge, we obtain an infinite tower of heavy, light and massless higher-spin fields in $(d+1)$-dimensional anti-de Sitter space. All massive higher-spin fields are described gauge invariantly in terms of Stüeckelberg fields. The spectrum depends on the boundary conditions imposed at both ends of the wedges. W…
We study the fuzzy hyperboloids AdS^2 and dS^2 as brane solutions in matrix models. The unitary representations of SO(2,1) required for quantum field theory are identified, and explicit formulae for their realization in terms of fuzzy wavefunctions are given. In a second part, we study the (A)dS^2 brane geometry and its dynamics, as governed by a suitable matrix model. In particular, we show that trace of the energy-momentum tensor of matter induces transversal perturbations of the brane and of the Ricci scalar. This leads to a linearized form of Henneaux-Teitelboim-type gravity, illustrating …
We construct local probes in the static patch of Euclidean dS$_3$ gravity. These probes are Wilson line operators, designed by exploiting the Chern-Simons formulation of 3D gravity. Our prescription uses non-unitary representations of $so(4)\simeq su(2)_L\times su(2)_R$, and we evaluate the Wilson line for states satisfying a singlet condition. We discuss how to reproduce the Green's functions of massive scalar fields in dS$_3$, the construction of bulk fields, and the quasinormal mode spectrum. We also discuss the interpretation of our construction in Lorentzian signature in the inflationary …
We construct all the bulk and boundary unitary cubic curvature parity invariant gravity theories in three dimensions in (anti)-de Sitter spaces. For bulk unitarity, our construction is based on the principle that the free theory of the cubic curvature theory reduces to one of the three known unitary theories which are the cosmological Einstein-Hilbert theory, the quadratic theory of the scalar curvature or the new massive gravity (NMG). Bulk and boundary unitarity in NMG is in conflict; therefore, cubic theories that are unitary both in the bulk and on the boundary have free theories that redu…
Black hole-de Sitter space as the fastest transmitter and receiver
Ningbo University（宁波大学）；Hangzhou Institute for Advanced Study (HIAS), University of Chinese Academy of Sciences (UCAS)（中国科学院大学杭州高等研究院）；Institute of Theoretical Physics, Chinese Academy of Sciences (CAS)（中国科学院理论物理研究所）；University of Chinese Academy of Sciences (UCAS)（中国科学院大学）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）
We present the geometry of spacetimes that are tangentially approximated by de Sitter spaces whose cosmological constants vary over spacetime. Cartan geometry provides one with the tools to describe manifolds that reduce to a homogeneous Klein space at the infinitesimal level. We consider a Cartan geometry in which the underlying Klein space is at each point a de Sitter space, for which the combined set of pseudo-radii forms a nonconstant function on spacetime. We show that the torsion of such a geometry receives a contribution that is not present for a cosmological constant. The structure gro…
