In a recent paper [J. P. M. Pitelli, Phys. Rev. D {\bf 99}, 108701 (2019)], one of us showed that the vacuum state associated to conformal fields on a Poicaré patch of anti-de Sitter spacetime is not $\text{AdS}$ invariant for fields satisfying non-trivial boundary conditions (by non-trivial we mean neither Dirichlet nor Neumann) at the conformal boundary. In this way, two isometrically related observers in anti-de Sitter space have different notions of no particle content. Therefore, an observer who is suddenly transported to a different (but isometrically related) frame will feel a bath of particles. This process contradicts our intuitive notion based on our experience in Minkowski spacetime, where the vacuum is Lorentz invariant, and no particle is produced between boosted frames. We show that the total number of produced particles is finite, but grows without limit when we approach (via isometric transformation) Dirichlet or Neumann boundary conditions since in these cases the vacuum is invariant.
We discuss the quantization of linearized gravity in the background de Sitter spacetime using a gauge-invariant formalism to write the perturbed gravitational field in the static patch. This field is quantized after fixing the gauge completely. The response rate of this field to monochromatic multipole sources is then computed in the thermal equilibrium state with the well known Gibbons-Hawking temperature. We compare this response rate with the one obtained in the Bunch-Davies-like vacuum state defined in the Poincaré patch. These response rates are found to be the same as expected. This agre…
We consider time-ordered (or Feynman) propagators between two different $α-$states of a linear de Sitter Quantum Field in the global de Sitter manifold and in the Poincaré patch. We separately examine $α-β$, In-In and In-Out propagators and find the imaginary contribution to the effective actions. The In-In propagators are real in both the Poincaré patch and in the global de Sitter manifold. On the other side the In-Out propagators at coincident points contain finite imaginary contributions in both patches in even dimensions, but they are not equivalent. In odd dimensions in both patches the i…
Quantum field theory on anti-de Sitter spacetime requires the introduction of boundary conditions at its conformal boundary, due essentially to the absence of global hyperbolicity. Here we calculate the renormalized stress-energy tensor $T_{μν}$ for a scalar field $ϕ$ on the Poincaré patch of $\text{AdS}_2$ and study how it depends on those boundary conditions. We show that, except for the Dirichlet and Neumann cases, the boundary conditions break the maximal $\textrm{AdS}$ invariance. As a result, $\langleϕ^2\rangle$ acquires a space dependence and $\langle T_{μν}\rangle$ is no longer proport…
We explicitly show that the one loop IR correction to the two--point function in de Sitter space scalar QFT does not reduce just to the mass renormalization. The proper interpretation of the loop corrections is via particle creation revealing itself through the generation of the quantum averages $<a^+_p a_p>$, $<a_p a_{-p}>$ and $<a^+_p a^+_{-p}>$, which slowly change in time. We show that this observation in particular means that loop corrections to correlation functions in de Sitter space can not be obtained via analytical continuation of those calculated on the sphere. We find harmonics for…
We perform canonical quantization of the Stueckelberg Lagrangian for massive vector fields in the conformally flat patch of de Sitter space in the Bunch-Davies vacuum and find their Wightman two-point functions by the mode-sum method. We discuss the zero-mass limit of these two-point functions and their limits where the Stueckelberg parameter $ξ$ tends to zero or infinity. It is shown that our results reproduce the standard flat-space propagator in the appropriate limit. We also point out that the classic work of Allen and Jacobson for the two-point function of the Proca field and a recent wor…
We construct the graviton two-point function for a two-parameter family of linear covariant gauges in n-dimensional de Sitter space. The construction is performed via the mode-sum method in the Bunch-Davies vacuum in the Poincaré patch, and a Fierz-Pauli mass term is introduced to regularize the infrared (IR) divergences. The resulting two-point function is de Sitter-invariant, and free of IR divergences in the massless limit (for a certain range of parameters) though analytic continuation with respect to the mass for the pure-gauge sector of the two-point function is necessary for this result…
The two-point Wightman function of the free photon field defined in a gauge-invariant manner is known to be equivalent to the field-strength two-point function in any spacetime that is topologically trivial. We show that the gauge-invariant graviton two-point function defined in a similar manner is equivalent to the Weyl-tensor two-point function in Minkowski space and in the Poincare patch of de Sitter space. This implies that in the Poincare patch of de Sitter space the gauge-invariant graviton two-point function decays like (distance)^(-4) as a function of coordinate distance for spacelike …
The generic feature of non-conformal fields in Poincare patch of de Sitter space is the presence of large IR loop corrections even for massive fields. Moreover, in global de Sitter there are loop IR divergences for the massive fields. Naive analytic continuation from de Sitter to Anti-de-Sitter might lead one to conclude that something similar should happen in the latter space as well. However, we show that there are no large IR effects in the one-loop two-point functions in the Poincare patch of Anti-de-Sitter space even for the zero mass minimally coupled scalar fields. As well there are nei…
There are at least three different types of secular effects in the two-point correlation functions in scalar quantum field theories in de Sitter space-time. The first one is specific to de Sitter massless and tachyonic minimally coupled scalar fields. The remaining two are generic and are encountered practically in any non-stationary situation in quantum field theory. Furthermore there are secular effects in the n-point correlation functions for low enough mass. They are also specific to de Sitter quantum field theory. In this paper we focus on the differences between the secular effects in tw…
We investigate a recent proposal for a distinguished vacuum state of a free scalar quantum field in an arbitrarily curved spacetime, known as the Sorkin-Johnston (SJ) vacuum, by applying it to de Sitter space. We derive the associated two-point functions on both the global and Poincaré (cosmological) patches in general d+1 dimensions. In all cases where it is defined, the SJ vacuum belongs to the family of de Sitter invariant alpha-vacua. We obtain different states depending on the spacetime dimension, mass of the scalar field, and whether the state is evaluated on the global or Poincaré patch…
We study massive real scalar $ϕ^4$ theory in the expanding Poincare patch of de Sitter space. We calculate the leading two-loop infrared contribution to the two-point function in this theory. We do that for the massive fields both from the principal and complementary series. As can be expected at this order light fields from the complementary series show stronger infrared effects than the heavy fields from the principal one. For the principal series, unlike the complementary one, we can derive the kinetic equation from the system of Dyson--Schwinger equation, which allows us to sum up the lead…
We study the null-boundaries of Wheeler-de Witt (WdW) patches in three dimensional Poincare-AdS, when the selected boundary timeslice is an arbitrary (non-constant) function, presenting some useful analytic statements about them. Special attention will be given to the piecewise smooth nature of the null-boundaries, due to the emergence of caustics and null-null joint curves. This is then applied, in the spirit of our previous paper arXiv:1806.08376, to the problem of how complexity of the CFT$_2$ groundstate changes under a small local conformal transformation according to the action (CA) prop…
We study the relation between two sets of correlators in interacting quantum field theory on de Sitter space. The first are correlators computed using in-in perturbation theory in the expanding cosmological patch of de Sitter space (also known as the conformal patch, or the Poincaré patch), and for which the free propagators are taken to be those of the free Euclidean vacuum. The second are correlators obtained by analytic continuation from Euclidean de Sitter; i.e., they are correlators in the fully interacting Hartle-Hawking state. We give an analytic argument that these correlators coincide…
In this paper we study the thermalization of a spatially homogeneous system in a strongly coupled CFT. The non-equilibrium initial state is created by switching on a relevant perturbation in the CFT vacuum during Delta t >= t >= -Delta t. Via AdS/CFT, the thermalization process corresponds to the gravitational collapse of a tachyonic scalar field (m^2 = -3) in the Poincare patch of AdS_5. In the limit Delta t < 0.02/T, the thermalization time t_T is found to be quantitatively the same as that of a non-equilibrium state created by a marginal perturbation discussed in Ref. [5]. In the case Delta…
It is well known that the memory effect in flat spacetime is parametrized by the BMS supertranslation. We investigate the relation between the memory effect and diffeomorphism in de Sitter spacetime. We find that gravitational memory is parametrized by a BMS-like supertranslation in the static patch of de Sitter spacetime. We also show a diffeomorphism that corresponds to gravitational memory in the Poincare/cosmological patch. Our method does not need to assume the separation between the source and the detector to be small compared with the Hubble radius, and can potentially be applicable to …
We propose an ansatz which solves the Dyson-Schwinger equation for the real scalar fields in Poincare patch of de Sitter space in the IR limit. The Dyson-Schwinger equation for this ansatz reduces to the kinetic equation, if one considers scalar fields from the principal series. Solving the latter equation we show that under the adiabatic switching on and then off the coupling constant the Bunch-Davies vacuum relaxes in the future infinity to the state with the flat Gibbons-Hawking density of out-Jost harmonics on top of the corresponding de Sitter invariant out-vacuum.
In a spacetime with no global timelike Killing vector, we do not have a natural choice for the vacuum state of matter fields, leading to an ambiguity in defining the Feynman propagators. In this paper, taking the vacuum state to be the instantaneous ground state of the Hamiltonian at each moment, we develop a method for calculating wave functions associated with the vacuum and the corresponding in-in and in-out propagators. We apply this method to free scalar field theory in de Sitter space and obtain de Sitter invariant propagators in various coordinate patches. We show that the in-out propag…
We investigate the effects of an analytic boundary metric for smooth asymptotically anti-de Sitter gravitational solutions. The boundary dynamics is then completely determined by the initial data due to corner conditions that all smooth solutions must obey. We perturb a number of familiar static solutions and explore the boundary dynamics that results. We find evidence for a nonlinear asymptotic instability of the planar black hole in four and six dimensions. In four dimensions we find indications of at least exponential growth, while in six dimensions, it appears that a singularity may form i…
We have studied the induced one-loop energy-momentum tensor of a massive complex scalar field within the framework of nonperturbative quantum electrodynamics (QED) with a uniform electric field background on the Poincaré patch of the two-dimensional de Sitter spacetime ($\mathrm{dS_{2}}$). We also consider a direct coupling the scalar field to the Ricci scalar curvature which is parameterized by an arbitrary dimensionless nonminimal coupling constant. We evaluate the trace anomaly of the induced energy-momentum tensor. We show that our results for the induced energy-momentum tensor in the zero…
The Riemann correlator with appropriately raised indices characterizes in a gauge-invariant way the quantum metric fluctuations around de Sitter spacetime including loop corrections from matter fields. Specializing to conformal fields and employing a method that selects the de Sitter-invariant vacuum in the Poincaré patch, we obtain the exact result for the Riemann correlator through order $H^4/m_\mathrm{p}^4$. The result is expressed in a manifestly de Sitter-invariant form in terms of maximally symmetric bitensors. Its behavior for both short and long distances (sub- and superhorizon scales)…
We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no dynamical quantum fluctuations. Such fluctuations require either an evolving microstate, or time-dependent histories of out-of-equilibrium recording devices, which we argue are absent in stationary states. For a massive scalar field in a fixed de Sitter background, the cosmic no-hair theorem implies that the state of the patch approaches the vacuum, where there are no fluctuations. We argue that an analogous conclusion holds whenever a patch of de Sitter is embedded in a la…
We discuss the algebraic quantization of a real, massive scalar field in the Poincaré patch of the (d+1)-dimensional anti-de Sitter spacetime, with arbitrary boundary conditions. By using the functional formalism, we show that it is always possible to associate to such system an algebra of observables enjoying the standard properties of causality, time-slice axiom and F-locality. In addition, we characterize the wavefront set of the ground state associated to the system under investigation. As a consequence, we are able to generalize the definition of Hadamard states and construct a global alg…
We study extremal surfaces in de Sitter space in the Poincare slicing in the upper patch, anchored on spatial subregions at the future boundary ${\cal I}^+$, restricted to constant boundary Euclidean time slices (focussing on strip subregions). We find real extremal surfaces of minimal area as the boundaries of past lightcone wedges of the subregions in question: these are null surfaces with vanishing area. We also find complex extremal surfaces as complex extrema of the area functional, and the area is not always real-valued. In $dS_4$ the area is real. The area has structural resemblance wit…
We consider a real Klein-Gordon field in the Poincaré patch of $(d+1)$-dimensional anti-de Sitter spacetime, PAdS$_{d+1}$, and impose dynamical boundary condition on the asymptotic boundary of PAdS$_{d+1}$ that depend explicitly on the second time derivative of the field at the boundary. These boundary conditions are of generalized Wentzell type. We construct the Wightman two-point function for the ground state of the Klein-Gordon theory whenever the parameters of the theory (the field mass, curvature coupling and boundary condition parameters) render such ground state admissible. In the cases…
