We employ holographic duality to compute $\langle T_{μν} \rangle$ in strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory and then study evolution of the semiclassical Einstein field equations sourced by $\langle T_{μν} \rangle$. Linearizing about de Sitter space, we find that the semiclassical equations of motion reduce to a four dimensional scalar wave equation coupled to a five dimensional scalar wave equation. We compute the mode spectrum of these equations and find that there exists a critical value of the Hubble constant $H_c$ for which de Sitter space is unstable when $H < H_c$ and mode stable when $H > H_c$.
It is shown that the recent corpuscular description of gravity generically excludes de Sitter spacetime in any semiclassical version of f(R) gravity. A phantom phenomenology of the cosmic dynamics is also naturally excluded.
We present a method to semiclassically compute the pair creation rate of bosons and fermions in de Sitter spacetime. The results in the bosonic case agree with the ones in the literature. We find that for the constant electric field the fermionic and bosonic pair creation rate are the same. This analogy of bosons and fermions in the semiclassical limit is known from several flat spacetime examples.
We calculate IR divergent graviton one-loop corrections to scalar correlators in de Sitter space, and show that the leading IR contribution may be reproduced via simple semiclassical consistency relations. One can likewise use such semiclassical relations to calculate leading IR corrections to correlators in slow-roll inflation. The regulated corrections shift the tensor/scalar ratio and consistency relation of single field inflation, and non-gaussianity parameters averaged over very large distances. For inflation of sufficient duration, for example arising from a chaotic inflationary scenario…
Massless interacting scalar fields in de Sitter space have long been known to experience large fluctuations over length scales larger than Hubble distances. A similar situation arises in condensed matter physics in the vicinity of a critical point, and in this better-understood situation these large fluctuations indicate the failure in this regime of mean-field methods. We argue that for non-Goldstone scalars in de Sitter space, these fluctuations can also be interpreted as signaling the complete breakdown of the semi-classical methods widely used throughout cosmology. By power-counting the in…
In general, the Gibbons-Hawking temperature based on the Euclidean functional approach shows that de Sitter space in the Bunch-Davies vacuum is globally thermal. In the exactly soluble semiclassical Jackiw-Teitelboim model, we investigate thermal property of de Sitter space by taking into account the quantum back reaction of the geometry. The proper temperature of de Sitter space in the Bunch-Davies vacuum is found to vanish. In case of a certain quantum state breaking the de Sitter symmetry, de Sitter space can be made thermally exited; however, in this case the dilaton singularity cannot be …
We compute the length of spacelike geodesics anchored at opposite sides of certain double-sided flow geometries in two dimensions. These geometries are asymptotically anti-de Sitter but they admit either a de Sitter or a black hole event horizon in the interior. While in the geometries with black hole horizons, the geodesic length always exhibit linear growth at late times, in the flow geometries with de Sitter horizons, geodesics with finite length only exist for short times of the order of the inverse temperature and they do not exhibit linear growth. We comment on the implications of these …
In the semiclassical limit of de Sitter gravity a separation of scales takes place that divides the theory into a "cosmic" sector and a "microscopic" sector. A similar separation takes place in the double-scaled limit of SYK theory. We examine the scaling behaviors that accompany these limits and find parallels that support the previously conjectured duality between Jackiw-Teitelboim gravity (with positive cosmological constant), and double-scaled SYK. This paper is a companion to "dS JT Gravity and Double-Scaled SYK" by Adel Rahman, to appear simultaneously with this paper.
We consider the linearized semiclassical Einstein equations for small deviations around de Sitter spacetime including the vacuum polarization effects of conformal fields. Employing the method of order reduction, we find the exact solutions for general metric perturbations (of scalar, vector and tensor type). Our exact (nonperturbative) solutions show clearly that in this case de Sitter is stable with respect to small metric deviations and a late-time attractor. Furthermore, they also reveal a breakdown of perturbative solutions for a sufficiently long evolution inside the horizon. Our results …
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…
We consider the semiclassical Einstein equations (SEE) in the presence of a quantum scalar field with self-interaction $λϕ^4$. Working in the Hartree truncation of the two-particle irreducible (2PI) effective action, we compute the vacuum expectation value of the energy-momentum tensor of the scalar field, which act as a source of the SEE. We obtain the renormalized SEE by implementing a consistent renormalization procedure. We apply our results to find self-consistent de Sitter solutions to the SEE in situations with or without spontaneous breaking of the $Z_2$-symmetry.
We compute the Casimir energy of the photon field in a de Sitter space and find it to be proportional to the size of the horizon, the same form of the holographic dark energy. We suggest to make metamaterials to mimic de Sitter space in laboratory and measure the predicted Casimir energy.
We introduce higher-derivative Gauss-Bonnet correction terms in the gravity sector and we relate the modified gravity theory in the bulk to the strongly coupled quantum field theory on a de Sitter boundary. We study the process of holographic thermalization by examining three nonlocal observables, the two-point function, the Wilson loop and the holographic entanglement entropy. We study the time evolution of these three observables and we find that as the strength of the Gauss-Bonnet coupling is increased, the saturation time of the thermalization process to reach thermal equilibrium becomes s…
We study strongly coupled mass-deformed-CFT on a fixed de Sitter spacetime in three dimensions via holography. We elucidate the global causal structure of the four-dimensional spacetime dual to the de Sitter invariant vacuum state. The conformal boundaries of de Sitter appear as spacelike defects sourced by the mass deformation, which extend into the bulk as curvature singularities in AdS. We compute all one- and two-point functions of the deformed-CFT stress tensor and a scalar operator order-by-order in the mass deformation for a simple holographic model. These correlation functions admit a …
We calculate the holographic three-point functions in N = 4 super-Yang-Mills theory in the case when two of the operators are semiclassical and one is dual to a supergravity mode. We further discuss the transition to the regime when all three operators are semiclassical.
We describe the dynamics of strongly coupled field theories in de Sitter spacetime using the holographic gauge/gravity duality. The main motivation for this is to explore the possibility of dynamical phase transitions during cosmological evolution. Specifically, we study two classes of theories: (i) conformal field theories on de Sitter in the static patch which are maintained in equilibrium at temperatures that may differ from the de Sitter temperature and (ii) confining gauge theories on de Sitter spacetime. In the former case we show the such states make sense from the holographic viewpoint…
Motivated by the understanding of holography as realized in tensor networks, we develop a bulk procedure that can be interpreted as generating a sequence of coarse-grained holographic states. The coarse-graining procedure involves identifying degrees of freedom entangled at short distances and disentangling them. This is manifested in the bulk by a flow equation that generates a codimension-1 object, which we refer to as the holographic slice. We generalize the earlier classical construction to include bulk quantum corrections, which naturally involves the generalized entropy as a measure of t…
The effect of the spontaneous nucleation of black holes in de Sitter space is reviewed, and the main steps of the calculation in Nucl.Phys. B 582, 313, 2000 of the one-loop amplitude of this process are summarized. The existence of such an effect suggests that de Sitter space is not a ground state of quantum gravity with a positive cosmological constant.
We study the holographic representation of the entanglement entropy, recently proposed by Ryu and Takayanagi, in a braneworld context. The holographic entanglement entropy of a de Sitter brane embedded in an anti-de Sitter (AdS) spacetime is evaluated using geometric quantities, and it is compared with two kinds of de Sitter entropy: a quarter of the area of the cosmological horizon on the brane and entropy calculated from the Euclidean path integral. We show that the three entropies coincide with each other in a certain limit. Remarkably, the entropy obtained from the Euclidean path integral …
We propose to embed de Sitter space into five dimensional anti-de Sitter space to compute some physical quantities of interest, using the AdS/CFT correspondence. The static de Sitter can be considered as the conformal structure of the boundary of the hyperbolic AdS5 with a horizon, thus energy as well as entropy can be computed. The global dS can be embedded into a half-global AdS5, and the dS entropy can be regarded as entanglement entropy in this case. Finally, the inflationary dS can also be regarded as the boundary of AdS5, and this can be extended to include general cosmology with a posit…
We study a massive scalar field theory in de Sitter space. Using worldline instanton approach, we calculate probability of pair production in weak-field limit. In addition to exponential factor we derive pre-exponential factor. Within this approach the vanishing probability for odd-dimensional de Sitter space gets a clear geometrical interpretation. We find leading contribution to imaginary part of two point correlator in $ϕ^3$-theory.
Holographic tensor networks associated to tilings of (1+1)-dimensional de Sitter spacetime are introduced. Basic features of these networks are discussed, compared, and contrasted with conjectured properties of quantum gravity in de Sitter spacetime. Notably, we highlight a correspondence between the quantum information capacity of the network and the cosmological constant.
We describe two different, but equivalent semiclassical views of black hole physics in which the equivalence principle and unitarity are both accommodated. In one, unitarity is built-in, while the black hole interior emerges only effectively as a collective phenomenon involving horizon (and possibly other) degrees of freedom. In the other, more widely studied approach, the existence of the interior is manifest, while the unitarity of the underlying dynamics can be captured only indirectly by incorporating certain nonperturbative effects of gravity. These two pictures correspond to a distant de…
Summary of three talks on the Holographic Space Time models of early universe cosmology, particle physics, and the asymptotically de Sitter final state of our universe.
A metric is proposed to explore the noncommutative form of the Anti-de Sitter space due to quantum effects. It has been proved that the non commutativity in AdS space induces a single component gravitoelectric field. The holographic Ryu-Takayanagi (RT) algorithm is then applied to compute the entanglement entropy in dual $CFT_2$. This calculation can be exploited to compute UV-IR cutoff dependent central charge of the certain noncommutative $CFT_2$. This non commutative computation of the entanglement entropy can be interpreted in the form of the surface/state correspondence. We have shown tha…
We argue that the flat spacetime with inexact quantum mechanics in it is dual to the de Sitter spacetime with exact quantum mechanics in it, and the positive cosmological constant of this de Sitter spacetime is in the second order of the degree of the violation of the bulk quantum mechanics in the flat spacetime. The flat spacetime is holographic and has a dual time-contracted boundary conformal field theory with two redefined central charges at null infinity. The vanishing smallness of the observed positive cosmological constant suggests the extraordinary exactness of the bulk quantum mechani…
We compute the quantum string entropy S_s(m, H) from the microscopic string density of states of mass m in Anti de Sitter space-time. For high m, (high Hm -->c/α'), no phase transition occurs at the Anti de Sitter string temperature T_{s} which is higher than the flat space (Hagedorn) temperature t_{s}. (the Hubble constant H acts as producing a smaller string constant and thus, a higher tension). T_s is the precise quantum dual of the semiclassical (QFT) Anti de Sitter temperature scale . We compute the quantum string emission by a black hole in Anti de Sitter space-time (bhAdS). In the early…
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…
We explore asymptotically AdS$_2$ solutions of a particular two-dimensional dilaton-gravity theory. In the deep interior, these solutions flow to the cosmological horizon of dS$_2$. We calculate various matter perturbations at the linearised and non-linear level. We consider both Euclidean and Lorentzian perturbations. The results can be used to characterise the features of a putative dual quantum mechanics. The chaotic nature of the de Sitter horizon is assessed through the soft mode action at the AdS$_2$ boundary, as well as the behaviour of shockwave type solutions.
It has been proposed recently to consider in the framework of cosmology an extension of the semiclassical Einstein's equations in which the Einstein tensor is considered as a random function. This paradigm yields a hierarchy of equations between the $n$-point functions of the quantum, normal ordered, stress energy-tensor and those associated to the stochastic Einstein tensor. Assuming that the matter content is a conformally coupled massive scalar field on de Sitter spacetime, this framework has been applied to compute the power spectrum of the quantum fluctuations and to show that it is almos…
In a wide class of cosmological models, a positive cosmological constant drives cosmological evolution toward an asymptotically de Sitter phase. Here we connect this behavior to the increase of entropy over time, based on the idea that de Sitter spacetime is a maximum-entropy state. We prove a cosmic no-hair theorem for Robertson-Walker and Bianchi I spacetimes that admit a Q-screen ("quantum" holographic screen) with certain entropic properties: If generalized entropy, in the sense of the cosmological version of the Generalized Second Law conjectured by Bousso and Engelhardt, increases up to …
Using entanglement in dS/CFT correspondence, we show that a 4-dimensional de Sitter spacetime in the bulk fluctuates. We calculated the fluctuations of the entanglement entropy, which backreacts with the geometry of the bulk spacetime indicated by the fluctuations of the horizon radius. The variance of the fluctuations is suppressed by $G_N$ and multiplied by $H_{dS}^2$. Therefore, it will be more significant during the primordial era where it is also well described by de Sitter geometry. We also show that the distribution of the fluctuations is also skewed with the local non-linearity paramet…
We argue that classical spacetimes represent amplified information in the holographic theory of quantum gravity. In general, classicalization of a quantum system involves amplification of information at the cost of exponentially reducing the number of observables. In quantum gravity, the geometry of spacetime must be the analogously amplified information. Bulk local semiclassical operators probe this information without disturbing it; these correspond to logical operators acting on code subspaces of the holographic theory. From this viewpoint, we study how bulk local operators may be realized …
Recently, investigations have begun into a holographic duality for two-dimensional de Sitter space. In this paper, we evaluate the associated central charge, using a modified version of the canonical Hamiltonian method that was first advocated by Catelani {\it et al}. Our computation agrees with that of a prior work (Cadoni {\it et al}), but we argue that the method used here is, perhaps, aesthetically preferable on holographic grounds. We also confirm an agreement between the Cardy and thermodynamic entropy, thus providing further support for the conjectured two-dimensional de Sitter/conforma…
We propose the holographic interpretation of the 1-point conformal block on a torus in the semiclassical regime. To this end we consider the linearized version of the block and find its coefficients by means of the perturbation procedure around natural seed configuration corresponding to the zero-point block. From the AdS/CFT perspective the linearized block is given by the geodesic length of the tadpole graph embedded into the thermal AdS plus the holomorphic part of the thermal AdS action.
A dynamical aspect of quantum gravity on de Sitter spacetime is investigated by holography or the dS/CFT correspondence. We show that de Sitter spacetime emerges from a free Sp(N) vector model by complexifying the ghost fields and flowing them in parallel to the imaginary axis. We confirm that the emergence of de Sitter spacetime is ensured by conformal symmetry. We also compute the quantum corrections to the cosmological constant up to the next-to-leading order of the 1/N expansion in a proposed holographic approach. As a result the sub-leading corrections have the opposite sign to the classi…
Using the AdS/CFT correspondence, we construct the holographic dual of a tunneling instanton describing Schwinger pair creation in de Sitter space. Our approach allows us to extract the critical value of the electric field for which the potential barrier disappears, rendering the vacuum unstable. In addition, we compute the large-$λ$, large-$N_c$ corrections to the nucleation rate and we find that it agrees with previous expectations based on perturbative computations. As a by-product of this investigation, we study the causal structure of the string dual to the nucleated pair as seen by diffe…
Using a noncommutative inspired anti-de Sitter-Einstein-Born-Infeld black hole with both non-commutative mass and charge distributions, we analyse a holographic superconductor in the context of the AdS/CFT correspondence. We show that the coupling of the Born-Infeld parameter and the noncommutative perturbations provides an enhancing mechanism for higher values of the expectation value of the condensate and that noncommutativity counter-balances nonlinearity of the electrodynamics to keep the ratio $ω_g/T_c \approx 8$.
We demonstrate that for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent time-like direction in dS is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS.
The correspondence between string theory in Anti-de Sitter space and super Yang Mills theory is an example of the Holographic principle according to which a quantum theory with gravity must be describable by a boundary theory. However, arguments given so far are incomplete because, while the bulk theory has been related to a boundary theory, the holographic bound saying that the boundary theory has only one bit of information per Planck area has not been justified. We show here that this bound is the physical interpretation of one of the unusual aspects of the correspondence between Anti-de Si…
We study holographic thermalization in spacetimes with a chemical potential and a non-trivial dilaton field. Three non-local observables are used to probe the whole process and investigate the effect of the ratio of the chemical potential over temperature $χ$ and the dilaton-Maxwell coupling constant $α$. It is found that the saturation time is not always a monotonically increasing function of $χ$, the situation depends on $α$. When $0 \leqα\leq 1$, larger $χ$ yields longer saturation time, while for $α>1$, the situation becomes more complex. More interesting, we found that although $α$ indeed…
In this paper we study various aspects of entanglement entropy in strongly-coupled de Sitter quantum field theories in various dimensions. We find gravity solutions that are dual to field theories in a fixed de Sitter background, both in equilibrium and out-of-equilibrium configurations. The latter corresponds to the Vaidya generalization of the AdS black hole solutions with hyperbolic topology. We compute analytically the entanglement entropy of spherical regions and show that there is a transition when the sphere is as big as the horizon. We also explore thermalization in time-dependent situ…
In four lectures, delivered at the TASI 2010 summer school, I cover selected topics in the application of the gauge-string duality to nuclear and condensed matter physics. On the nuclear side, I focus on multiplicity estimates from trapped surfaces in AdS_5, and on the consequences of conformal symmetry for relativistic hydrodynamics. On the condensed matter side, I explain the fermion response to the zero-temperature limit of p-wave holographic superconductors.
The number of asymptotically de Sitter (non-singular) solutions of 5d dilatonic gravity with positive cosmological constant is found. These solutions are similar to the previously known asymptotically AdS spaces where dilaton may generate the singularity. Using these solutions the consistent $c$-function is proposed in the same way as in AdS/CFT. The consistency of RG flow gives further support for dS/CFT correspondence. From holographic RG flow equations we calculate the holographic 4d conformal anomaly with dilatonic contributions. This conformal anomaly turns out to be the same as in AdS/CF…
