Perturbative quantum field theory in de Sitter space is known to give rise to a variety of contributions that diverge with time (secular terms). Despite significant progress, a complete understanding of the physical origin of these divergences remains an outstanding problem. In this paper, we will study the origin of secular divergences in de Sitter space for interacting theories that are near attractive conformal fixed points. We show that the secular divergences are determined by the anomalous dimensions of the same theory in flat space and can be re-summed using the dynamical renormalization group. This behavior is mandatory at the conformal fixed point but we show that it holds away from the fixed point as well. We analyze this problem in general using conformal perturbation theory and study conformally coupled scalar fields in four and $4-ε$ dimensions as examples.
We examine the thermodynamic behaviour of charged, asymptotically de Sitter black holes embedded in a finite-radius isothermal cavity, with a Born-Infeld gauge field replacing the ordinary Maxwell field. We find that the non-linearities of Born-Infeld theory lead to the presence of reentrant phase transitions in the canonical ensemble, whose existence and character are determined by the maximal electric field strength of the theory. We also examine the phase structure in the grand canonical ensemble, and demonstrate the presence of a new reentrant phase transition from radiation, to an interme…
We study the dynamical behavior of the dilaton in the background of three-dimensional Kerr-de Sitter space which is inspired from the low-energy string effective action. The perturbation analysis around the cosmological horizon of Kerr-de Sitter space reveals a mixing between the dilaton and other fields. Introducing a gauge (dilaton gauge), we can disentangle this mixing completely and obtain one decoupled dilaton equation. However it turns out that this belongs to the tachyon. The stability of de Sitter solution with J=0 is discussed. Finally we compute the dilaton absorption cross section t…
We consider the perturbative treatment of the minimally coupled, massless, self-interacting scalar field in Euclidean de Sitter space. Generalizing work of Rajaraman, we obtain the dynamical mass m^2 \propto sqrt{lambda} H^2 of the scalar for non-vanishing Lagrangian masses and the first perturbative quantum correction in the massless case. We develop the rules of a systematic perturbative expansion, which treats the zero-mode non-perturbatively, and goes in powers of sqrt{lambda}. The infrared divergences are self-regulated by the zero-mode dynamics. Thus, in Euclidean de Sitter space the int…
In General Relativity coupled to a non-linear electromagnetic field, together with a negative cosmological constant, we obtain the general static spherical symmetric black hole solution with magnetic charges, which is asymptotic to anti-de Sitter (AdS) space-times. In particular, for a degenerate case the solution becomes a Hayward-AdS black hole, which is regular everywhere in the full space-time. The existence of such a regular black hole solution preserves the weak energy condition while the strong energy condition is violated. We then derive the first law and the Smarr formula of the black…
We propose the use of D-brane realizations of Dynamical Supersymmetry Breaking (DSB) gauge sectors as sources of uplift in compactifications with moduli stabilization onto de Sitter vacua. This construction is fairly different from the introduction of anti D-branes, yet allows for tunably small contributions to the vacuum energy via their embedding into warped throats. The idea is explicitly exemplified by the embedding of the 1-family $SU(5)$ DSB model in a local warped throat with fluxes, which we discuss in detail in terms of orientifolds of dimer diagrams.
The Goheer-Kleban-Susskind no-go theorem says that the symmetry of de Sitter space is incompatible with finite entropy. The meaning and consequences of the theorem are discussed in the light of recent developments in holography and gravitational path integrals. The relation between the GKS theorem, Boltzmann fluctuations, wormholes, and exponentially suppressed non-perturbative phenomena suggests: the classical symmetry between different static patches is broken; and that eternal de Sitter space -- if it exists at all -- is an ensemble average.
We present fully dynamical solutions to Einstein-scalar theory in asymptotically Anti-de-Sitter spacetime with a scalar potential containing particularly rich physics. Depending on one parameter in the potential we find an especially interesting regime, which exhibits a thermodynamically stable, but dynamically unstable black brane, even at zero momentum. We show this using the non-linear dynamics, and give a clear interpretation in terms of the spectrum of linearized perturbations. Our results translate directly to their dual strongly coupled non-conformal field theories.
Perturbative corrections to correlation functions for interacting theories in de Sitter spacetime often grow secularly with time, due to the properties of fluctuations on super-Hubble scales. This growth can lead to a breakdown of perturbation theory at late times. We argue that Dynamical Renormalization Group (DRG) techniques provide a convenient framework for interpreting and resumming these secularly growing terms. In the case of a massless scalar field in de Sitter with quartic self-interaction, the resummed result is also less singular in the infrared, in precisely the manner expected if …
We work on the relation between the local thermodynamic instability and the dynamical instability of large black holes in four-dimensional anti-de Sitter space proposed by Gubser and Mitra. We find that all perturbations suppressing the metric fluctuations at linear order become dynamically unstable when black holes lose the local thermodynamic stability. We discuss how dynamical instabilities can be explained by the Second Law of Thermodynamics.
We employ a recent, general gauge computation of the one loop graviton contribution to the vacuum polarization on de Sitter to solve for one loop corrections to the photon mode function. The vacuum polarization takes the form of a gauge independent, spin 2 contribution and a gauge dependent, spin 0 contribution. We show that the leading secular corrections derive entirely from the spin 2 contribution.
Dynamical Chern-Simons (DCS) theory is an extension of General Relativity in which the gravitational field is coupled to a scalar field through a parity violating term. We study perturbations of anti-de Sitter black holes and branes in such a theory, and show that the relevant equations reduce to a set of coupled ODEs which can be solved efficiently through a series expansion. We prove numerically that black holes and branes in DCS gravity are stable against gravitational and scalar perturbations in the entire parameter space. Furthermore, by applying the AdS/CFT duality, we relate black hole …
We present a detailed analysis of a recently introduced version of Causal Dynamical Triangulations (CDT) that does not rely on a distinguished time slicing. Focussing on the case of 2+1 spacetime dimensions, we analyze its geometric and causal properties, present details of the numerical set-up and explain how to extract "volume profiles". Extensive Monte Carlo measurements of the system show the emergence of a de Sitter universe on large scales from the underlying quantum ensemble, similar to what was observed previously in standard CDT quantum gravity. This provides evidence that the disting…
In this work we show that universal gauge vector fields can be localized on the recently proposed 5D thick tachyonic braneworld which involves a de Sitter cosmological background induced on the 3-brane. Namely, by performing a suitable decomposition of the vector field, the resulting 4D effective action corresponds to a massive gauge field, while the profile along the extra dimension obeys a Schroedinger-like equation with a Poeschl-Teller potential. It turns out that the massless zero mode of the gauge field is bound to the expanding 3-brane and allows us to recover the standard 4D electromag…
We propose a special solution of Einstein equations in the general Vaidya form representing a dynamical black hole having horizon cross-sections with toroidal topology. The concrete model enables us to study for the first time dynamical horizons with toroidal topology, its area law, and the question of matter flux inside the horizon, without using a cut-and-paste technology to construct the solution.
We discuss a new scenario for early cosmology when the inflationary de Sitter phase emerges dynamically. This genuine quantum effect occurs as a result of dynamics of the topologically nontrivial sectors in a strongly coupled QCD- like gauge theory in an expanding universe. We test these ideas by explicit computations in hyperbolic space $ \mathbb{H}^3_κ\times \mathbb{S}^1_{κ^{-1}}$. We argue that the key element for this idea to work is the presence of nontrivial holonomy computed along $\mathbb{S}^1_{κ^{-1}}$. The effect is non-local in nature, non-analytical in coupling constant and can not…
We show that D-dimensional de Sitter space is unstable to the nucleation of non-singular geometries containing spacetime regions with different numbers of macroscopic dimensions, leading to a dynamical mechanism of compactification. These and other solutions to Einstein gravity with flux and a cosmological constant are constructed by performing a dimensional reduction under the assumption of q-dimensional spherical symmetry in the full D-dimensional geometry. In addition to the familiar black holes, black branes, and compactification solutions we identify a number of new geometries, some of wh…
We investigate thermodynamic and dynamical stability of a family of six-dimensional braneworld solutions with de Sitter branes. First, we investigate thermodynamic stability in terms of de Sitter entropy. We see that the family of solutions is divided into two distinct branches: the high-entropy branch and the low-entropy branch. By analogy with ordinary thermodynamics, the high-entropy branch is expected to be stable and the low-entropy branch to be unstable. Next, we investigate dynamical stability by analyzing linear perturbations around the solutions. Perturbations are decomposed into scal…
We study the emergence of de Sitter space in Euclidean dynamical triangulations (EDT). Working within the semi-classical approximation, it is possible to relate the lattice parameters entering the simulations to the partition function of Euclidean quantum gravity. We verify that the EDT geometries behave semi-classically, and by making contact with the Hawking-Moss instanton solution for the Euclidean partition function, we show how to extract a value of the renormalized Newton's constant from the simulations. This value is consistent with that of our previous determination coming from the int…
We briefly review the remarkable connections between light-front QCD, gravity in AdS space, and conformal quantum mechanics. We discuss, in particular, the group theoretical and geometrical aspects of the underlying one-dimensional quantum field theory. The resulting effective theory leads to a phenomenologically successful confining interaction potential in the relativistic light-front wave equation which incorporates relevant non-perturbative dynamical aspects of hadron physics.
We consider the theory of four-fermion interactions with N-component fermions in de Sitter space. It is found that the effective potential for a composite operator in the theory is calculable in the leading order of the 1/N expansion. The resulting effective potential is analyzed by varying both the four-fermion coupling constant and the curvature of the space-time. The critical curvature at which the dynamically generated fermion mass disappears is found to exist and is calculated analytically. The dynamical fermion mass is expressed as a function of the space-time curvature.
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 examine the behavior of correlation functions for a massless scalar field in de Sitter space with a quartic interaction. We find that two-loop corrections are relevant, and that the resummation of these corrections generates a complicated structure whereby high momentum modes stay massless while low momentum modes develop a dynamical mass.
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…
We analyze, in the paradigm of open quantum systems, the reduced dynamics of a freely-falling two-level detector in de Sitter space-time in weak interaction with a reservoir of fluctuating quantized conformal scalar fields in the de Sitter invariant vacuum. We find that the detector is asymptotically driven to a thermal state at the Gibbons-Hawking temperature, regardless of its initial state. Our discussion therefore shows that the Gibbons-Hawking effect of de Sitter space-time can be understood as a manifestation of thermalization phenomena that involves decoherence and dissipation in open q…
The model of d5 higher derivative (HD) gravity admitting Schwarzschild--anti de Sitter Black Hole (S-AdS BH) as exact solution is considered. The surface counterterms are added to the complete action, they are fixed by the condition of finiteness of bulk AdS spacetime when brane goes to infinity. As a result the brane (observable Universe) is defined dynamically in terms of d5 theory parameters (brane tension is fixed). Brane radius is always bigger than horizon radius and the 4d Universe itself could be static or inflationary. Natural ganeralization of this model gives warped compactification…
We investigate solutions that are dynamically evolving between asymptotically de Sitter and asymptotically anti-de Sitter regions in the context of Einstein gravity coupled to general matter fields in d dimensions. We demonstrate the existence of a no go theorem whenever the matter content of the theory is 'reasonable', i.e. such that the weak energy condition is satisfied. We show that there exist solutions for which the energy conditions are violated in a finite region of the spacetime. We speculate on the holographic interpretation of these gravitational backgrounds by combining ideas from …
The correspondence between supergravity (and string theory) on $AdS$ space and boundary conformal field theory relates the thermodynamics of ${\cal N}=4$ super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large $AdS$ Schwarzschild black hole must scale ``holographically'' with the volume o…
In the paper, the temperature associated with a dynamical spherically symmetric black hole or with a cosmological horizon is investigated from the point of view of a point-like detector. First, we briefly review the Hamilton-Jacobi tunneling method for a generic dynamical spherically symmetric space-time, and present two applications of the tunneling method. Then, we apply a well-known relativistic quantum theoretical technique, namely the Unruh-DeWitt detector formalism for a conformally coupled scalar field in a generic FRW space-time. As an application, for the generic static black hole cas…
We study the one-loop corrections to the four-point function in the Anti de Sitter space-time for a $ϕ^4$ field theory. Our calculation shows the existence of non-local counterterms which however respect the AdS isometry. Our arguments are quite general and applicable to other (non-conformal) AdS field theories. We also explain why calculations in Euclidean and Lorentzian signatures should differ even at the leading order in non globaly hyperbolic manifolds.
We study a real, massive Klein-Gordon field in the Poincaré fundamental domain of the $(d+1)$-dimensional anti-de Sitter (AdS) spacetime, subject to a particular choice of dynamical boundary conditions of generalized Wentzell type, whereby the boundary data solves a non-homogeneous, boundary Klein-Gordon equation, with the source term fixed by the normal derivative of the scalar field at the boundary. This naturally defines a field in the conformal boundary of the Poincaré fundamental domain of AdS. We completely solve the equations for the bulk and boundary fields and investigate the existenc…
We argue that a natural boundary condition for gravity in asymptotically AdS spaces is to hold the {\em renormalized} boundary stress tensor density fixed, instead of the boundary metric. This leads to a well-defined variational problem, as well as new counter-terms and a finite on-shell action. We elaborate this in various (even and odd) dimensions in the language of holographic renormalization. Even though the {\em form} of the new renormalized action is distinct from the standard one, once the cut-off is taken to infinity, their {\em values} on classical solutions coincide when the trace an…
We study the O(N) scalar field theory with quartic self-coupling in de Sitter space. When the field is light in units of the expansion rate, perturbative methods break down at very low momenta due to large infrared logarithmic terms. Using the nonperturbative large-N limit, we compute the four-point vertex function in the deep infrared regime. The resummation of an infinite series of perturbative (bubble) diagrams leads to a modified power law which is analogous to the generation of an anomalous dimension in critical phenomena. We discuss in detail the role of high momentum (subhorizon) modes,…
Maximally symmetric curved-brane solutions are studied in dilatonic braneworld models which realise the self-tuning of the effective four-dimensional cosmological constant. It is found that no vacua in which the brane has de Sitter or anti-de Sitter geometry exist, unless one modifies the near-boundary asymptotics of the bulk fields. In the holographic dual picture, this corresponds to coupling the UV CFT to a curved metric (possibly with a defect). Alternatively, the same may be achieved in a flat-space QFT with suitable variable scalar sources. With these ingredients, it is found that maxima…
We consider degrees of freedom for a quantum de Sitter spacetime. The problem is studied from both a Lorentzian and a Euclidean perspective. From a Lorentzian perspective, we compute dynamical properties of the static patch de Sitter horizon. These are compared to dynamical features of black holes. We point out differences suggestive of non-standard thermal behaviour for the de Sitter horizon. We establish that geometries interpolating between an asymptotically AdS$_2 \times S^2$ space and a dS$_4$ interior are compatible with the null energy condition, albeit with a non-standard decreasing ra…
Self-energies of a minimally coupled scalar field with quartic and trilinear interactions are calculated in a de Sitter background, using a position space propagator. For quartic interactions, we recover earlier results for the seagull diagram, namely that it contributes an effective mass for the scalar field at leading order in the infrared enhancement in a steady-state de Sitter background. We further show that the sunset diagram also contributes to this effective mass and argue that these two contributions are sufficient in order to determine a self-consistent dynamical mass. In addition, t…
We investigate stability of two branches of Freund-Rubin compactification from thermodynamic and dynamical perspectives. Freund-Rubin compactification allows not only trivial solutions but also warped solutions describing warped product of external de Sitter space and internal deformed sphere. We study dynamical stability by analyzing linear perturbations around solutions in each branch. Also we study thermodynamic stability based on de Sitter entropy. We show complete agreement of thermodynamic and dynamical stabilities of this system. Finally, we interpret the results in terms of effective e…
We obtain numerical solutions for rotating topological solitons of the nonlinear $σ$-model in three-dimensional Anti-de Sitter space. Two types of solutions, $i)$ and $ii)$, are found. The $σ$-model fields are everywhere well defined for both types of solutions, but they differ in their space-time domains. Any time slice of the space-time for the type $i)$ solution has a causal singularity, despite the fact that all scalars constructed the curvature tensor are bounded functions. No evidence of a horizon is seen for any of the solutions, and therefore the type $i)$ solutions have naked singular…
Black holes possess trapping regions which lead to intriguing dynamical effects. By properly scattering test fields off a black hole, one can extract energy from it, leading to the growth of the amplitude of the test field in expense of the black hole's energy. Such a dynamical phenomenon is called superradiance. Here, we study charged-scalar-field instabilities of Reissner-Nordström black holes immersed in a $d-$dimensional de Sitter Universe. By performing a thorough frequency-domain analysis we compute the unstable quasinormal resonances and link their presence with a novel family of quasin…
We study the quantum theory of an O(N) scalar field on de Sitter geometry at leading order in a nonperturbative 1/N-expansion. This resums the infinite series of so-called superdaisy loop diagrams. We obtain the de Sitter symmetric solutions of the corresponding, properly renormalized, dynamical field equations and compute the complete effective potential. Because of its self-interactions, the field acquires a strictly positive square mass which screens potential infrared divergences. Moreover, strongly enhanced ultralong-wavelength fluctuations prevent the existence of a spontaneously broken …
We examine in $(2+1)$-dimensional anti-de Sitter (AdS) space the phenomena of entanglement harvesting - the process in which a pair of detectors (two-level atoms) extract entanglement from a quantum field through local interactions with the field. We begin by reviewing the Unruh-DeWitt detector and its interaction with a real scalar field in the vacuum state, as well as the entanglement harvesting protocol in general. We then examine how the entanglement harvested by a pair of such detectors depends on their spacetime trajectory, separation, spacetime curvature, and boundary conditions satisfi…
Newton-Hooke group is the nonrelativistic limit of de Sitter (anti-de Sitter) group, which can be enlarged with transformations that describe constant acceleration, as well as central charges. We consider a higher order Lagrangian that is quasi-invariant under the acceleration-extended Newton-Hooke symmetry, and obtain the Schrödinger equation quantizing the Hamiltonian corresponding to its first order form. We show that the Schrödinger equation is invariant under the acceleration-extended Newton-Hooke transformations. We also discuss briefly the exotic conformal Newton-Hooke symmetry in 2+1 d…
It is known that odd-dimensional de Sitter space acts as a transparent potential for free fields. Previous studies have explained this phenomena by relating de Sitter free field equations of motion to the time-independent Schrodinger equation with known transparent potentials. In this work we show that de Sitter's transparency is a consequence of an infinite set of "hidden" symmetries. These symmetries arise from an accidental symmetry for the zero-mode of matter fields, as well as the boost isometry of de Sitter space. For simplicity, we consider the case of massive Klein-Gordon theory. We sh…
In this work we shall investigate the cosmological dynamical system of $f(R)$ gravity, by constructing it in such a way so that it is rendered autonomous. We shall study the vacuum $f(R)$ gravity case, but also the case that matter and radiation perfect fluids are present along with the $f(R)$ gravity. The dynamical system is constructed in such a way so that the time-dependence of the system is contained in a single parameter which depends on the Hubble rate and it's second derivative. The autonomous structure of the dynamical system is achieved when this parameter is constant, therefore we f…
We investigate infrared logarithms in de Sitter space from holographic perspective. We employ a gravitational Fokker-Planck equation to investigate the time evolution of the de Sitter entropy $S=π/(G_N H^2)$, where $H$ is the Hubble parameter and $G_N$ is the Newton's constant. Under the Gaussian approximation, we obtain the dynamical $β$ function of $g=1/S$. It is asymptotically free toward the future. It also possesses the ultraviolet fixed point indicating that the Universe started the de Sitter expansion at the Planck scale. The pre-inflation era exists to prepare a special initial conditi…
The dynamical generation of a four-dimensional classical universe from nothing but fundamental quantum excitations at the Planck scale is a long-standing challenge to theoretical physicists. A candidate theory of quantum gravity which achieves this goal without invoking exotic ingredients or excessive fine-tuning is based on the nonperturbative and background-independent technique of Causal Dynamical Triangulations. We demonstrate in detail how in this approach a macroscopic de Sitter universe, accompanied by small quantum fluctuations, emerges from the full gravitational path integral, and ho…
We continue the recent study of the possibility of constructing a consistent infrared modification of gravity by treating the vierbein and connection as independent dynamical fields. We present the generalized Fierz--Pauli equation that governs the propagation of a massive spin-2 mode in a model of this sort in the backgrounds of arbitrary torsionless Einstein manifolds. We show explicitly that the number of propagating degrees of freedom in these backgrounds remains the same as in flat space-time. This generalizes the recent result that the Boulware--Deser phenomenon does not occur in de Sitt…
In the present paper, Unruh--DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh--DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW …
We investigate scalar field theories in de Sitter space by means of nonperturbative renormalization group techniques. We compute the functional flow equation for the effective potential of O(N) theories in the local potential approximation and we study the onset of curvature-induced effects as quantum fluctuations are progressively integrated out from subhorizon to superhorizon scales. This results in a dimensional reduction of the original action to an effective zero-dimensional Euclidean theory. We show that the latter is equivalent both to the late-time equilibrium state of the stochastic a…
We study the dynamical behavior of the dilaton in the background of three-dimensional Kerr-de Sitter space which is inspired from the low-energy string effective action. The Kerr-de Sitter space describes the gravitational background of a point particle whose mass and spin are given by $1-M$ and $J$ and its curvature radius is given by $\ell$. In order to study the propagation of metric, dilaton, and Kalb-Ramond two-form, we perform the perturbation analysis in the southern diamond of Kerr-de Sitter space including a conical singularity. It reveals a mixing between the dilaton and other unphys…
We comment on approaches to the Cosmological Constant Problem in 4+1 dimensions, with the Standard Model fields confined to a 3-brane. We show that requiring maximal 4D symmetry only on this 3-brane (and not on all other 3-branes that foliate the 4+1-dimensional space) leads to a wide class of de Sitter solutions on the brane, with the Hubble constant sourced by the brane tension and a bulk scalar potential. For Poincaré symmetry on the brane, fine-tuning is always necessary. The de Sitter solutions are generated at a special dynamical point. Small deviations from this point are shown to grow …
We study the dynamical system approach of non minimally coupled scalar field to induced gravity on the brane in the framework of the AdS/CFT correspondence. In this context, we derive the modified Friedmann equation and the equation of motion. The dynamics of this model are studied by rewriting the cosmological field equations in the form of a system of autonomous differential equations. In particular, the analysis is considered by investigating an exponential potential and a monomial form of the non minimal coupling function. We show that, for sufficient conditions, a past de Sitter attractor…
