arXiv subjects

Mark Van Raamsdonk

Publications and source records attributed to Mark Van Raamsdonk.

At least 19 recordsLinked to original sources

arXiv2026

Algebras for generalized entanglement wedges

In asymptotically AdS spacetimes, the mathematical structure of the set of entanglement wedges reflects the algebraic structure of the underlying holographic description. For more general spacetimes, Bousso and Penington (BP) have recently proposed a generalization of entanglement wedges sharing many of the same properties as usual entanglement wedges. In this paper, we explore the hypothesis that each generalized entanglement wedge can be associated with an algebra in the (generally unknown) fundamental description (in a semiclassical limit). We postulate features of the map from entanglement wedges to algebras that provide a natural algebraic interpretation for some of the basic mathematical properties of the set of entanglement wedges. Quantitatively, we suggest a possible generalization of the Ryu-Takayanagi formula that associates the gravitational entropy of a generalized entanglement wedge with an entropic quantity for the associated algebra. Through this assignment, inclusion monotonicity and strong-subadditivity properties shown by BP for generalized entanglement wedges would follow from various inequalities satisfied by algebraic entropies. We include a detailed appendix reviewing relevant algebraic background, including a discussion of algebraic entropies and their inequalities.

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arXiv2026

Menagerie of Euclidean constructions for 3D holographic cosmologies

We construct a large number of exact solutions of three-dimensional gravity with heavy matter particles that generalize the construction of Antonini, Sasieta, and Swingle (AS${}^2$), argued to define CFT states dual to a spacetime with a closed baby universe cosmology. Our construction starts with an arbitrary heavy-particle closed universe cosmology of the type constructed in Maloney, Meruliya, and Van Raamsdonk [arXiv:2503.12227], and via a gluing procedure adds an arbitrary number of AdS tubes connecting the past and future conformal boundaries of the associated Euclidean wormhole solution. With our construction, it is straightforward to produce examples where the cosmology is approximately homogeneous and isotropic. We describe a necessary condition for the cosmological wormhole saddle to dominate the Euclidean path integral with the specified boundary conditions. We argue that the original AS${}^2$ construction usually does not meet this condition, and describe alternative saddles that are likely to dominate. We discuss various possibilities for how the cosmological saddle might be made to dominate in our generalized construction.

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arXiv2025

Evolution of the eigenvalues and eigenstates of the single-particle reduced density operator during two-particle scattering

A particle initially in a pure state but interacting with some environment evolves into a discrete ensemble of pure states, the eigenstates of its reduced density operator, with ensemble probabilities given by the corresponding eigenvalues. In this work, we use numerics to present explicit results for the time-dependence of these eigenvalues and eigenstates for simple scattering experiments in one and two dimensions. This provides a time-resolved picture of the scattering process, showing in detail how an initial state described entirely in terms of continuous parameters evolves into a discrete set of possible outcomes, each with an associated probability and time-evolving wavefunction. We find that for scattering of Gaussian wavepackets in one dimension, the late time spectrum is dominated by two large eigenvalues nearly equal to the transmission and reflection probabilities associated with the central value of momentum. The corresponding eigenstates appear as single-peaked reflected or transmitted wavepackets. The remaining smaller eigenvalues, which increase to a maximum during scattering and then decrease to small values, correspond to reflected or transmitted wavepackets with multiple spatially separated parts. In this case and also for two-dimensional scattering, we find that successively smaller eigenvalues correspond to probability distributions with successively more peaks. These multi-peaked states correspond to outcomes of the scattering experiment where a particle initially in a single wavepacket ends up in a superposition of separated wavepackets after scattering.

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arXiv2025

Suggestions of decreasing dark energy from supernova and BAO data: an update

In a previous work 2305.04946, we found that supernova and baryon acoustic oscillation data support the hypothesis that late time cosmic acceleration is caused by the potential energy of a scalar field descending its potential, as suggested by holographically defined models of quantum gravity. In this note, we update our analysis using the Dark Energy Survey 5 year supernova data set (DES-SN5YR) and the baryon acoustic oscillation data from the Dark Energy Spectroscopic Instrument Data Release 2 (DESI DR2). Approximating the scalar potential via a first order Taylor series $V \approx V_0 + V_1 ϕ$ about the present value, and making use of only recent-time data from DES-SN5YR and DESI DR2, we find that the slope parameter is constrained as $V_1 = 1.49 \pm 0.25$ in a standard likelihood analysis. This is naively a $>5 σ$ discrepancy with $Λ$CDM (which has $V_1 =0$), though a more detailed analysis not assuming a Gaussian likelihood distribution suggests $4 σ$ significance. Based only on the $Δχ^2 = -13.7$ improvement of fit while ignoring parameter space volumes disfavours $Λ$CDM at a $3 σ$ significance level. These significance measures are substantially improved from our previous analysis using older data sets. We also reproduce the DESI DR2 parameter constraints based on the same combination of data and find that the $Λ$CDM is more strongly disfavoured in the context of the linear potential extension (dubbed $V_0V_1$) as compared with the $w_0 w_a$ extension of $Λ$CDM. A caveat is that for both $w_0 w_a$ and $V_0 V_1$, much of the significance relies on the historical $z < 0.1$ supernova samples included in the DES-SN5YR data set.

astro-ph.CO↗

arXiv2025

Finite entropy sums in quantum field theory

Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems, these divergences may cancel, giving finite quantities that provide information-theoretic data about the underlying state. In this note, we show that all such quantities can be written as linear combinations of three basic types of quantities: i) the entropy of a spatial subsystem minus the entropy of its complementary subsystem, ii) the mutual information between non-adjacent subsystems, and iii) the tripartite information for triples of disjoint sub-systems. For a fixed decomposition of a spatial slice into regions, we describe a basis of sums of entropies for collections of for these regions for which all divergences related to both region boundaries and higher-codimension intersections of regions cancel. Key mathematical technology used in this work (Fourier transforms on the Boolean cube and Möbius transformations of functions on partially ordered sets) and several of the main proof ideas were suggested by AI (ChatGPT5). We offer a few comments on the use of AI in physics and mathematics, based on our experience.

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arXiv2025

Cosmology with non-conformal holographic matter

We investigate the effect on cosmological evolution of a strongly coupled quantum field that undergoes renormalization group flow from a UV CFT to an IR CFT. The field theory is defined by perturbation of a holographic CFT by a relevant operator associated with a bulk scalar field that evolves from a local maximum of its potential near the boundary to a local minimum of its potential deep in the bulk. By studying the gravity solutions dual to this theory on $\mathbb{R}^3 \times S^1$, we find that the equation of state parameter $w$ for the field theory has the conformal behavior $w=1/3$ for high and low temperatures, but dips to lower values for intermediate temperatures. Thus, at scales where the field theory has significant scale-dependence, its effect on cosmological evolution is intermediate between matter and radiation. Compared to the unperturbed UV CFT (which acts as radiation), the energy density experiences less dilution during the expansion as a result of the RG flow, and the rate of expansion is greater.

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arXiv2025

Building up spacetime with quantum entanglement

In this essay based on 0907.2939, we argue that the emergence of classically connected spacetimes is intimately related to the quantum entanglement of degrees of freedom in a non-perturbative description of quantum gravity. Disentangling the degrees of freedom associated with two regions of spacetime results in these regions pulling apart and pinching off from each other in a way that can be quantified by standard measures of entanglement.

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arXiv2025

Ordinary wormholes

Euclidean wormholes have played a key role in the recent ``disorder averaged" approaches to quantum gravity and holography, but are typically only considered in somewhat special theories of gravity, such as theories in low dimensions or theories with exotic matter content (such as axions). These exotic theories have advantage that both the matter and gravitational sectors can be treated completely classically. However, once this constraint is relaxed we find that Euclidean wormholes arise generically, with no special constraints on the matter content. The key point is that there is a self-consistent approximation where the metric is treated classically but matter is treated quantum mechanically. The resulting wormholes are {\it ordinary} in the sense that they rely on the usual approximations used in, for example, the construction of star or FRW solutions in general relativity. Indeed, these are the Euclidean continuations of ordinary FRW solutions with big bang/crunch singularities. We describe several examples of these ordinary wormholes and discuss the relation to existing constructions and the holographic interpretation in terms of a dual CFT.

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arXiv2024

Holographic black hole cosmologies

We describe and study a holographic construction of big-bang / big-crunch cosmological spacetimes where the matter consists of a lattice of black holes. The cosmological spacetime is dual to an entangled state of a collection of holographic CFTs associated with the second asymptotic regions of the black holes. For a cosmology with spatial slice geometry $Σ$, this state is constructed via a Euclidean path integral for the CFT on a geometry obtained by connecting two copies of $Σ$ by a lattice of tubes. In three-dimensional gravity, we describe the cosmological solutions and the associated Euclidean saddles explicitly. For the case of (globally) flat cosmology, we determine when the Euclidean solution associated with the cosmology provides the dominant saddle compared to other natural candidates that preserve the symmetries of the boundary space. We find that the cosmological saddle dominates when the black holes are sufficiently large and close together. Our cosmology has a mixed state version where the physics behind the black hole horizons is unspecified and the Euclidean construction involves a pair of CFTs with an ensemble of operator insertions correlated between the two CFTs. Various purifications (adding second asymptotic regions for the black holes) correspond to various ways to promote this ensemble to an interaction by adding auxiliary degrees of freedom that couple the two CFTs in the Euclidean picture. These auxiliary degrees of freedom provide a Hilbert space for the cosmology in the Lorentzian picture.

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arXiv2024

Holographic motivations and observational evidence for decreasing dark energy

Negative lambda gravitational effective field theories dual to holographic CFTs have potentially realistic cosmological solutions. Generic cosmological solutions of these effective field theories have scalar field evolution that can lead to a period of accelerated expansion when the scalar field is at positive values of its potential (Fig. 1). If such a model describes our universe, significant evolution of dark energy is expected over a Hubble time as the scalar descends from positive to negative values of its potential towards the AdS extremum. Our recent observational study 2305.04946 based on supernova and baryon acoustic oscillation (BAO) observations suggests that significant evolution of dark energy associated with a descending scalar field may be preferred by data (Fig. 2). Taking a linear approximation to the scalar potential around the present value, a standard likelihood analysis gives an $e^{- χ^2/2}$ distribution in which $dV/dt$ is presently negative in $99.99 \%$ of the distribution, with a mean fractional variation of the potential of $36 \%$ over the period $z \lessapprox 2$ over which supernova data is available. In this note, we review these theoretical and observational results and provide an update on the question of how the physics of these cosmological solutions can be related to the physics of the underlying CFT.

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arXiv2024

Suggestions of decreasing dark energy from supernova and BAO data

The potential energy from a time-dependent scalar field provides a possible explanation for the observed cosmic acceleration. In this paper, we investigate how data from supernova and bary acoustic oscillation surveys constrain the possible evolution of a single scalar field over the period of time (roughly half the age of the universe) for which these data are available. Taking a linear approximation to the scalar potential $V(ϕ) = V_0 + V_1 ϕ$ around the present value, a likelihood analysis appears to significantly prefer models with a decreasing potential energy at present, with approximately $99.99 \%$ of the $\exp(-χ^2/2)$ distribution having $V_1 > 0$ in a convention where $\dotϕ \le 0$ at present. The models favoured by the distribution typically have an order one decrease $\langle |{\rm Range}[V(ϕ(t))] / V(t_0)| \rangle \approx 0.36$ in the scalar potential energy over the time frame corresponding to $z < 2$. According to the likelihood analysis, the $Λ$CDM model with no variation in dark energy appears to be significantly disfavoured in the context of the linear potential model, but this should be interpreted cautiously since model selection criteria that make use of $Δχ^2$ while ignoring parameter space volumes still favour $Λ$CDM. Working with a second order approximation to the potential, the supernova data can be fit well for a wide range of possible potentials, including models where the universe has already stopped accelerating.

astro-ph.CO↗

arXiv2023

Mapping the space of quantum expectation values

For a quantum system with Hilbert space ${\cal H}$ of dimension $N$ and a set $S$ of $n$ Hermitian operators ${\cal O}_i$, a basic question is to understand the set $E_S \subset \mathbb{R}^n$ of points $\vec{e}$ where $e_i = {\rm tr}(ρ{\cal O}_i)$ for an allowed state $ρ$. A related question is to determine whether a given set of expectation values $\vec{e}$ lies in $E_S$ and in this case to describe the most general state with these expectation values. In this paper, we describe various ways to characterize $E_S$, reviewing basic results that are perhaps not widely known and adding new ones. One important result (originally due to E. Wichmann) is that for a set $S$ of linearly independent traceless operators, every set of expectation values $\vec{e}$ in the interior of $E_S$ is achieved uniquely by a state of the form $ρ({\vecβ}) = e^{-\sum_i β_i {\cal O}_i}/{\rm tr}(e^{-\sum_i β_i {\cal O}_i})$ for ${\cal O}_i \in S$. In fact, the map $\vecβ \to \vec{E}(\vecβ) = {\rm tr}(\vec{\cal O} ρ({\vecβ}))$ is a diffeomorphism from $\mathbb{R}^n$ to the interior of $E_S$ with symmetric, positive Jacobian; using this fact, we provide an algorithm to invert $\vec{E}(\vecβ)$ and thus determine a state $ρ({\vecβ(\vec{e})})$ with specified expectation values $\vec{e}$ provided that these lie in $E_S$. The algorithm is based on defining a first order differential equation in the space of parameters $\vecβ$ that is guaranteed to converge to $\vecβ(\vec{e})$ in a precise way, with $|\vec{E}(\vecβ(t)) - \vec{e}| = C e^{-t}$.

quant-ph↗

arXiv2023

Enhanced Negative Energy with a Massless Dirac Field

Motivated by traversable wormhole constructions that require large amounts of negative energy, we explore constraints on the amount of negative energy that can be carried by a free Dirac field in a slab-shaped region between two parallel spatial planes. Specifically, we ask what is the minimum possible uniform energy density that can exist at some time, considering all possible states and all possibilities for the physics outside the slab. The vacuum state where we identify the two sides of the slab with antiperiodic boundary conditions gives one possible state with uniform negative energy, but we argue that states with more negative energy exist above 1+1 dimensions. Technically, we reduce the problem to studying a massive Dirac field on an interval in 1+1 dimensions and numerically search for states with uniform energy density in a lattice regulated model. We succeed in finding states with enhanced negative energy (relative to the antiperiodic vacuum) which also appear to have a sensible continuum limit. Our results for the mass-dependence of the minimum uniform energy density in 1+1 dimensions suggest that for a 3+1 dimensional massless Dirac fermion, it is possible to have states with arbitrarily large uniform negative energy density in an arbitrarily wide slab.

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arXiv2023

Accelerating cosmology from a holographic wormhole

We consider cosmological models in which the cosmology is related via analytic continuation to a Euclidean asymptotically AdS planar wormhole geometry defined holographically via a pair of three-dimensional Euclidean CFTs. We argue that these models can generically give rise to an accelerating phase for the cosmology due to the potential energy of scalar fields associated with relevant scalar operators in the CFT. We explain how cosmological observables are related to observables in the wormhole spacetime and argue that this leads to a novel perspective on naturalness puzzles in cosmology.

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arXiv2023

Bubbles of cosmology in AdS/CFT

Gravitational effective theories associated with holographic CFTs have cosmological solutions, which are typically big-bang / big-crunch cosmologies. These solutions are not asymptotically AdS, so they are not dual to finite-energy states of the CFT. However, we can find solutions with arbitrarily large spherical bubbles of such cosmologies embedded in asymptotically AdS spacetimes where the exterior of the bubble is Schwarzschild-AdS. In this paper, we explore such solutions and their possible CFT dual descriptions. Starting with a cosmological solution with $Λ< 0$ plus arbitrary matter density, radiation density, and spatial curvature, we show that a comoving bubble of arbitrary size can be embedded in a geometry with AdS-Schwarzschild exterior across a thin-shell domain wall comprised of pressureless matter. We show that in most cases (in particular, for arbitrarily large bubbles with an arbitrarily small negative spatial curvature) the entropy of the black hole exceeds the (radiation) entropy in the cosmological bubble, suggesting that a faithful CFT description is possible. We show that unlike the case of a de Sitter bubble, the Euclidean continuation of these cosmological solutions is sensible and suggests a specific construction of CFT states dual to the cosmological solutions via Euclidean path integral.

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arXiv2023

Accelerating cosmology from $Λ<0$ gravitational effective field theory

A large class of $Λ< 0$ cosmologies have big-bang / big crunch spacetimes with time-symmetric backgrounds and asymptotically AdS Euclidean continuations suggesting a possible holographic realization. We argue that these models generically have time-dependent scalar fields, and these can lead to realistic cosmologies at the level of the homogeneous background geometry, with an accelerating phase prior to the turnaround and crunch. We first demonstrate via explicit effective field theory examples that models with an asymptotically AdS Euclidean continuation can also exhibit a period of accelerated expansion without fine tuning. We then show that certain significantly more tuned examples can give predictions arbitrarily close to a $Λ$CDM model. Finally, we demonstrate via an explicit construction that the potentials of interest can arise from a superpotential, thus suggesting that these solutions may be compatible with an underlying supersymmetric theory.

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arXiv2022

Cosmology without time-dependent scalars is like quantum field theory without RG flow

Time-dependent scalar fields provide a candidate explanation for the dark energy. For these to vary on cosmological time scales, the derivative of the scalar potential in Planck units should have roughly the same magnitude as the potential itself. We emphasize that scalars with this property are present in any four-dimensional gravitational effective theory with a known UV completion via holography, provided that the dual CFT has scalar operators with dimensions of order one. Cosmological solutions without time-dependent scalars are analogous to solutions dual to the vacuum states of such CFTs while solutions with time-dependent scalars are analogous to solutions dual to the vacuum state of quantum field theories with RG flow where these CFTs provide the UV or IR fixed point. If time-dependent scalars do explain the dark energy, the gravitational effective theory describing our universe could be a $Λ< 0$ model associated to a holographic CFT.

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arXiv2022

Can one hear the shape of a wormhole?

A large class of flat big bang - big crunch cosmologies with negative cosmological constant are related by analytic continuation to asymptotically AdS traversable wormholes with planar cross section. In recent works (arXiv: 2102.05057, 2203.11220) it was suggested that such wormhole geometries may be dual to a pair of 3D holographic CFTs coupled via auxiliary degrees of freedom to give a theory that confines in the infrared. In this paper, we explore signatures of the presence of such a wormhole in the state of the coupled pair of 3D theories. We explain how the wormhole geometry is reflected in the spectrum of the confining theory and the behavior of two-point functions and entanglement entropies. We provide explicit algorithms to reconstruct the wormhole scale factor (which uniquely determines its geometry) from entanglement entropies, heavy operator two-point functions, or light operator two-point functions (which contain the spectrum information). In the last case, the physics of the bulk scalar field dual to the light operator is closely related to the quantum mechanics of a one-dimensional particle in a potential derived from the scale factor, and the problem of reconstructing the scale factor from the two-point function is directly related to the problem of reconstructing this Schrödinger potential from its spectrum.

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