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Anthony Aguirre

Anthony Aguirre appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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astro-ph.COgr-qchep-thquant-phcond-mat.stat-mechcond-mat.quant-gascs.CYArtificial Intelligenceastro-phastro-ph.GAnlin.CDphysics.class-phq-fin.TR

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Published work

24 published item(s)

preprint2026arXiv

Are we Doomed to an AI Race? Why Self-Interest Could Drive Countries Towards a Moratorium on Superintelligence

This paper uses game theory to argue that, contrary to the prevailing view, a moratorium on Artificial Superintelligence (ASI) can be in a state's self-interest. By formalizing trategic interactions between geopolitical superpowers, we model the trade-off between the benefits of technological supremacy and the catastrophic risks of uncontrolled ASI. The analysis reveals that as the perceived cost of loss of control increases sufficiently relative to other parameters, it becomes in each state's self-interest to impose a moratorium. We further provide empirical evidence suggesting that the global perception of ASI risk is rising, making a stable, rational moratorium increasingly plausible in the current geopolitical landscape.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

State-to-State Cosmology: a new view on the cosmological arrow of time and the past hypothesis

Cosmological boundary conditions for particles and fields are often discussed as a Cauchy problem, in which configurations and conjugate momenta are specified on an "initial" time slice. But this is not the only way to specify boundary conditions, and indeed in action-principle formulations we often specify configurations at two times and consider trajectories joining them. Here, we consider a classical system of particles interacting with short range two body interactions, with boundary conditions on the particles' positions for an initial and a final time. For a large number of particles that are randomly arranged into a dilute gas, we find that a typical system trajectory will spontaneously collapse into a small region of space, close to the maximum density that is obtainable, before expanding out again. If generalizable, this has important implications for the cosmological arrow of time, potentially allowing a scenario in which both boundary conditions are generic and also a low-entropy state "initial" state of the universe naturally occurs.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

AI loyalty: A New Paradigm for Aligning Stakeholder Interests

When we consult with a doctor, lawyer, or financial advisor, we generally assume that they are acting in our best interests. But what should we assume when it is an artificial intelligence (AI) system that is acting on our behalf? Early examples of AI assistants like Alexa, Siri, Google, and Cortana already serve as a key interface between consumers and information on the web, and users routinely rely upon AI-driven systems like these to take automated actions or provide information. Superficially, such systems may appear to be acting according to user interests. However, many AI systems are designed with embedded conflicts of interests, acting in ways that subtly benefit their creators (or funders) at the expense of users. To address this problem, in this paper we introduce the concept of AI loyalty. AI systems are loyal to the degree that they are designed to minimize, and make transparent, conflicts of interest, and to act in ways that prioritize the interests of users. Properly designed, such systems could have considerable functional and competitive - not to mention ethical - advantages relative to those that do not. Loyal AI products hold an obvious appeal for the end-user and could serve to promote the alignment of the long-term interests of AI developers and customers. To this end, we suggest criteria for assessing whether an AI system is sufficiently transparent about conflicts of interest, and acting in a manner that is loyal to the user, and argue that AI loyalty should be considered during the technological design process alongside other important values in AI ethics such as fairness, accountability privacy, and equity. We discuss a range of mechanisms, from pure market forces to strong regulatory frameworks, that could support incorporation of AI loyalty into a variety of future AI systems.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Classical dynamical coarse-grained entropy and comparison with the quantum version

We develop the framework of classical Observational entropy, which is a mathematically rigorous and precise framework for non-equilibrium thermodynamics, explicitly defined in terms of a set of observables. Observational entropy can be seen as a generalization of Boltzmann entropy to systems with indeterminate initial conditions, and describes the knowledge achievable about the system by a macroscopic observer with limited measurement capabilities; it becomes Gibbs entropy in the limit of perfectly fine-grained measurements. This quantity, while previously mentioned in the literature, has been investigated in detail only in the quantum case. We describe this framework reasonably pedagogically, then show that in this framework, certain choices of coarse-graining lead to an entropy that is well-defined out of equilibrium, additive on independent systems, and that grows towards thermodynamic entropy as the system reaches equilibrium, even for systems that are genuinely isolated. Choosing certain macroscopic regions, this dynamical thermodynamic entropy measures how close these regions are to thermal equilibrium. We also show that in the given formalism, the correspondence between classical entropy (defined on classical phase space) and quantum entropy (defined on Hilbert space) becomes surprisingly direct and transparent, while manifesting differences stemming from non-commutativity of coarse-grainings and from non-existence of a direct classical analogue of quantum energy eigenstates.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Probabilistic bound on extreme fluctuations in isolated quantum systems

We ask to what extent an isolated quantum system can eventually "contract" to be contained within a given Hilbert subspace. We do this by starting with an initial random state, considering the probability that all the particles will be measured in a fixed subspace, and maximizing this probability over all time. This is relevant, for example, in a cosmological context, which may have access to indefinite timescales. We find that when the subspace is much smaller than the entire space, this maximal probability goes to $1/2$ for real initial wave functions, and to $π^2/16$ when the initial wave function has been drawn from a complex ensemble. For example when starting in a real generic state, the chances of collapsing all particles into a small box will be less than but come arbitrarily close to $50\%$. This contraction corresponds to an entropy reduction by a factor of approximately two, thus bounding large downward fluctuations in entropy from generic initial states.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Typical and extreme entropies of long-lived isolated quantum systems

In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting particles in a one-dimensional lattice, we numerically solve for the full quantum behavior of the system. We characterize the fluctuations, and find the maximal, minimal, and typical entropy of each type that the system can eventually attain through its evolution. While both entropies are low for some "special" configurations and high for more "generic" ones, there are several fundamental differences in their behavior. Observational entropy behaves in accord with classical Boltzmann entropy (e.g. equilibrium is a condition of near-maximal entropy and uniformly distributed particles, and minimal entropy is a very compact configuration). Entanglement entropy is rather different: minimal entropy "empties out" one partition while maximal entropy apportions the particles between the partitions, and neither is typical. Beyond these qualitative results, we characterize both entropies and their fluctuations in some detail as they depend on temperature, particle number, and box size.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Understanding black hole evaporation using explicitly computed Penrose diagrams

Explicitly computed Penrose diagrams are plotted for a classical model of black hole formation and evaporation, in which black holes form by the accretion of infalling spherical shells of matter and subsequently evaporate by emitting spherical shells of Hawking radiation. This model is based on known semiclassical effects, but is not a full solution of semiclassical gravity. The method allows arbitrary interior metrics of the form $ds^2=-f(r)\,dt^2+f(r)^{-1}\,dr^2+r^2\,dΩ^2$, including singular and nonsingular models. Matter dynamics are visualized by explicitly plotting proper density in the diagrams, as well as by tracking the location of trapped surfaces and energy condition violations. The most illustrative model accurately approximates the standard time evolution for black hole thermal evaporation; its time dependence and causal structure are analyzed by inspection of the diagram. The resulting insights contradict some common intuitions and assumptions, and we point out some examples in the literature with assumptions that do not hold up in this more detailed model. Based on the new diagrams, we argue for an improved understanding of the Hawking radiation process, propose an alternate definition of "black hole" in the presence of evaporation, and suggest some implications regarding information preservation and unitarity.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Asymmetric condensed dark matter

We explore the viability of a boson dark matter candidate with an asymmetry between the number densities of particles and antiparticles. A simple thermal field theory analysis confirms that, under certain general conditions, this component would develop a Bose-Einstein condensate in the early universe that, for appropriate model parameters, could survive the ensuing cosmological evolution until now. The condensation of a dark matter component in equilibrium with the thermal plasma is a relativistic process, hence the amount of matter dictated by the charge asymmetry is complemented by a hot relic density frozen out at the time of decoupling. Contrary to the case of ordinary WIMPs, dark matter particles in a condensate must be lighter than a few tens of eV so that the density from thermal relics is not too large. Big-Bang nucleosynthesis constrains the temperature of decoupling to the scale of the QCD phase transition or above. This requires large dark matter-to-photon ratios and very weak interactions with standard model particles.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Simulating the universe(s) II: phenomenology of cosmic bubble collisions in full General Relativity

Observing the relics of collisions between bubble universes would provide direct evidence for the existence of an eternally inflating Multiverse; the non-observation of such events can also provide important constraints on inflationary physics. Realizing these prospects requires quantitative predictions for observables from the properties of the possible scalar field Lagrangians underlying eternal inflation. Building on previous work, we establish this connection in detail. We perform a fully relativistic numerical study of the phenomenology of bubble collisions in models with a single scalar field, computing the comoving curvature perturbation produced in a wide variety of models. We also construct a set of analytic predictions, allowing us to identify the phenomenologically relevant properties of the scalar field Lagrangian. The agreement between the analytic predictions and numerics in the relevant regions is excellent, and allows us to generalize our results beyond the models we adopt for the numerical studies. Specifically, the signature is completely determined by the spatial profile of the colliding bubble just before the collision, and the de Sitter invariant distance between the bubble centers. The analytic and numerical results support a power-law fit with an index $1< κ\lesssim 2$. For collisions between identical bubbles, we establish a lower-bound on the observed amplitude of collisions that is set by the present energy density in curvature.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Simulating the universe(s): from cosmic bubble collisions to cosmological observables with numerical relativity

The theory of eternal inflation in an inflaton potential with multiple vacua predicts that our universe is one of many bubble universes nucleating and growing inside an ever-expanding false vacuum. The collision of our bubble with another could provide an important observational signature to test this scenario. We develop and implement an algorithm for accurately computing the cosmological observables arising from bubble collisions directly from the Lagrangian of a single scalar field. We first simulate the collision spacetime by solving Einstein's equations, starting from nucleation and ending at reheating. Taking advantage of the collision's hyperbolic symmetry, simulations are performed with a 1+1-dimensional fully relativistic code that uses adaptive mesh refinement. We then calculate the comoving curvature perturbation in an open Friedmann-Robertson-Walker universe, which is used to determine the temperature anisotropies of the cosmic microwave background radiation. For a fiducial Lagrangian, the anisotropies are well described by a power law in the cosine of the angular distance from the center of the collision signature. For a given form of the Lagrangian, the resulting observational predictions are inherently statistical due to stochastic elements of the bubble nucleation process. Further uncertainties arise due to our imperfect knowledge about inflationary and pre-recombination physics. We characterize observational predictions by computing the probability distributions over four phenomenological parameters which capture these intrinsic and model uncertainties. This represents the first fully-relativistic set of predictions from an ensemble of scalar field models giving rise to eternal inflation, yielding significant differences from previous non-relativistic approximations. Thus, our results provide a basis for a rigorous confrontation of these theories with cosmological data.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

How the diffuse Universe cools

In this work we investigate the cooling channels of diffuse gas (i.e. n_H<0.1 cm^-3) in cosmology. We aim to identify the wavelengths where most of the energy is radiated in the form of emission lines or continuum radiation, and the main elements and ions responsible for the emission. We use a subset of cosmological, hydrodynamical runs from the OWLS project to calculate the emission of diffuse gas and its evolution with time. We find that at z=0 (z=2) about 70 (80) per cent of the energy emitted by diffuse gas is carried by emission lines, with the continuum radiation contributing the remainder. Hydrogen lines in the Lyman series are the primary contributors to the line emission, with a share of 16 (20) per cent. Oxygen lines are the main metal contributors at high redshift, while silicon, carbon and iron lines are strongest at low redshift, when the contributions of AGB stars and supernova Ia explosions to the metal budget become important and when there is more hot gas. The ionic species carrying the most energy are OIII, CII, CIII, SiII, SiIII, FeII and SIII. The great majority of energy is emitted in the UV band (lambda=100-4000 A), both as continuum radiation and line emission. With almost no exception, all the strongest lines fall in this band. At high energies, continuum radiation is dominant (e.g., 80 per cent in the X-ray band), while lines contribute progressively more at lower energies. While the results do depend on the details of the numerical implementation of the physical processes modelled in the simulations, the comparison of results from different simulations demonstrates that the variations are overall small, and that the conclusions are fairly robust. Given the overwhelming importance of UV emission for the cooling of diffuse gas, it is desirable to build instruments dedicated to the detection and characterisation of diffuse UV emission.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Information Transmission Between Financial Markets in Chicago and New York

High frequency trading has led to widespread efforts to reduce information propagation delays between physically distant exchanges. Using relativistically correct millisecond-resolution tick data, we document a 3-millisecond decrease in one-way communication time between the Chicago and New York areas that has occurred from April 27th, 2010 to August 17th, 2012. We attribute the first segment of this decline to the introduction of a latency-optimized fiber optic connection in late 2010. A second phase of latency decrease can be attributed to line-of-sight microwave networks, operating primarily in the 6-11 GHz region of the spectrum, licensed during 2011 and 2012. Using publicly available information, we estimate these networks' latencies and bandwidths. We estimate the total infrastructure and 5-year operations costs associated with these latency improvements to exceed $500 million.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Quantum Instability of the Emergent Universe

We perform a semi-classical analysis of the Emergent Universe scenario for inflation. Fixing the background, and taking the inflaton to be homogenous, we cast the inflaton's evolution as a one-dimensional quantum mechanics problem. We find that the tuning required over a long time scale for this inflationary scenario is unstable quantum mechanically. Considering the inflaton field value as a wavepacket, the spreading of the wavepacket destroys any chance of both starting and ending with a well-formed state. Thus, one cannot have an Einstein static universe to begin with that evolves into a well-defined beginning to inflation a long time later.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Born in an Infinite Universe: a Cosmological Interpretation of Quantum Mechanics

We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantum measurement in different regions, with relative frequencies given by the square of the wave function amplitudes. Our formal argument hinges on properties of what we term the quantum confusion operator, which projects onto the Hilbert subspace where the Born rule fails, and we comment on its relation to the oft-discussed quantum frequency operator. This analysis unifies the classical and quantum levels of parallel universes that have been discussed in the literature, and has implications for several issues in quantum measurement theory. It also shows how, even for a single measurement, probabilities may be interpreted as relative frequencies in unitary (Everettian) quantum mechanics. We also argue that after discarding a zero-norm part of the wavefunction, the remainder consists of a superposition of indistinguishable terms, so that arguably "collapse" of the wavefunction is irrelevant, and the "many worlds" of Everett's interpretation are unified into one. Finally, the analysis suggests a "cosmological interpretation" of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the observer's inability to self-locate in this collection.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Multiple Cosmic Collisions and the Microwave Background Power Spectrum

Collisions between cosmic bubbles of different vacua are a generic feature of false vacuum eternal inflation scenarios. While previous studies have focused on the consequences of a single collision event in an observer's past, we begin here an investigation of the more general scenario allowing for many "mild" collisions intersecting our past light cone (and one another). We discuss the general features of multiple collision scenarios and consider their impact on the cosmic microwave background (CMB) temperature power spectrum, treating the collisions perturbatively. In a large class of models, one can approximate a multiple collision scenario as a superposition of individual collision events governed by nearly isotropic and scale-invariant distributions, most appearing to take up less than half of the sky. In this case, the shape of the expected CMB temperature spectrum maintains statistical isotropy and typically features a dramatic increase in power in the low multipoles relative to that of the best-fit $Λ$CDM model, which is in tension particularly with the observed quadrupole. We argue that this predicted spectrum is largely model-independent and can be used to outline features of the underlying statistical distributions of colliding bubbles consistent with CMB temperature measurements.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

The origin of metals in the circum-galactic medium of massive galaxies at z=3

We present a detailed study of the metal-enriched circum-galactic medium of a massive galaxy at z=3 using "ErisMC", a new cosmological hydrodynamic "zoom-in" simulations of a disk galaxy with mass comparable to the Milky Way. The run adopts a blastwave scheme for supernova feedback that generates galactic outflows without explicit wind particles, a star formation recipe based on a high gas density threshold, and high temperature metal cooling. ErisMC's main progenitor at z=3 resembles a "Lyman break" galaxy of mass M_vir=2.4e11 M_sun, virial radius R_vir=48 kpc, and star formation rate 18 M_sun/yr, and its metal-enriched CGM extends to 200 (physical) kpc from its center. Approximately 41, 9, and 50 percent of all gas-phase metals at z=3 are locked in a hot (T> 3e5 K), warm (3e5 >T> 3e4 K), and cold (T< 3e4 K) medium, respectively. We identify three sources of heavy elements: 1) the main host, responsible for 60% of all the metals found within 3R_vir; 2) its satellite progenitors, responsible for 28% of all the metals within 3R_vir, and for only 5% of those beyond 3R_vir; and nearby dwarfs, which give origin to 12% of all the metals within 3R_vir and 95% of those beyond 3R_vir. Late (z<5) galactic "superwinds" account for only 9% of all the metals observed beyond 2R_vir, the bulk having been released at redshifts 5< z < 8 by early star formation and outflows. In the CGM, lower overdensities are typically enriched by `older', colder metals. Heavy elements are accreted onto Eris along filaments via low-metallicity cold inflows, and are ejected hot via galactic outflows at a few hundred km/s. The outflow mass-loading factor is of order unity for the main halo, but can exceed 10 for nearby dwarfs. We stress that our "zoom-in" simulation focuses on the CGM of a single massive system and cannot describe the enrichment history of the IGM as a whole. (abridged)

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preprint2011arXiv

Out of equilibrium: understanding cosmological evolution to lower-entropy states

Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing the thermodynamic arrow of time. We study the time development of such fluctuations, especially the very large fluctuations relevant to cosmology. Under fairly general assumptions, the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium. We use this idea to elucidate the spacetime structure of various fluctuations in (stable and metastable) de Sitter space and thermal anti-de Sitter space.

0 citations0 reviewsNo code linkedOpen access
preprint2010arXiv

Runaway dilatonic domain walls

We explore the stability of domain wall and bubble solutions in theories with compact extra dimensions. The energy density stored inside of the wall can destabilize the volume modulus of a compactification, leading to solutions containing either a timelike singularity or a region where space decompactifies, depending on the metric ansatz. We determine the structure of such solutions both analytically and using numerical simulations, and analyze how they arise in compactifications of Einstein--Maxwell theory and Type IIB string theory. The existence of instabilities has important implications for the formation of networks of topological defects and the population of vacua during eternal inflation.

0 citations0 reviewsNo code linkedOpen access
preprint2010arXiv

The enrichment history of cosmic metals

We use a suite of cosmological, hydrodynamical simulations to investigate the chemical enrichment history of the Universe. Specifically, we trace the origin of the metals back in time to investigate when various gas phases were enriched and by what halo masses. We find that the age of the metals decreases strongly with the density of the gas in which they end up. At least half of the metals that reside in the diffuse intergalactic medium (IGM) at redshift zero (two) were ejected from galaxies above redshift two (three). The mass of the haloes that last contained the metals increases rapidly with the gas density. More than half of the mass in intergalactic metals was ejected by haloes with total masses less than 1e11 solar masses and stellar masses less than 1e9 solar masses. The range of halo masses that contributes to the enrichment is wider for the hotter part of the IGM. By combining the `when' and `by what' aspects of the enrichment history, we show that metals residing in lower density gas were typically ejected earlier and by lower mass haloes.

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preprint2009arXiv

A status report on the observability of cosmic bubble collisions

In the picture of eternal inflation as driven by a scalar potential with multiple minima, our observable universe resides inside one of many bubbles formed from transitions out of a false vacuum. These bubbles necessarily collide, upsetting the homogeneity and isotropy of our bubble interior, and possibly leading to detectable signatures in the observable portion of our bubble, potentially in the Cosmic Microwave Background or other precision cosmological probes. This constitutes a direct experimental test of eternal inflation and the landscape of string theory vacua. Assessing this possibility roughly splits into answering three questions: What happens in a generic bubble collision? What observational effects might be expected? How likely are we to observe a collision? In this review we report the current progress on each of these questions, improve upon a few of the existing results, and attempt to lay out directions for future work.

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preprint2009arXiv

Dark Stars: Begynnelsen

The first phase of stellar evolution in the history of the universe may be Dark Stars, powered by dark matter heating rather than by fusion. Weakly interacting massive particles, which are their own antiparticles, can annihilate and provide an important heat source for the first stars in the universe. This and the following contribution present the story of Dark Stars. In this first part, we describe the conditions under which dark stars form in the early universe: 1) high dark matter densities, 2) the annihilation products get stuck inside the star, and 3) dark matter heating wins over all other cooling or heating mechanisms.

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preprint2009arXiv

Dark Stars: Död och Återuppståndelse

The first phase of stellar evolution in the history of the universe may be Dark Stars, powered by dark matter heating rather than by fusion. Weakly interacting massive particles, which are their own antiparticles, can annihilate and provide an important heat source for the first stars in the universe. This and the previous contribution present the story of Dark Stars. In this second part, we describe the structure of Dark Stars and predict that they are very massive ($\sim 800 M_\odot$), cool (6000 K), bright ($\sim 10^6 L_\odot$), long-lived ($\sim 10^6$ years), and probable precursors to (otherwise unexplained) supermassive black holes. Later, once the initial dark matter fuel runs out and fusion sets in, dark matter annihilation can predominate again if the scattering cross section is strong enough, so that a Dark Star is born again.

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preprint2005arXiv

Dynamics and instability of false vacuum bubbles

This paper examines the classical dynamics of false vacuum regions embedded in surrounding regions of true vacuum, in the thin-wall limit. The dynamics of all generally relativistically allowed solutions -- most but not all of which have been previously studied -- are derived, enumerated, and interpreted. We comment on the relation of these solutions to possible mechanisms whereby inflating regions may be spawned from non-inflating ones. We then calculate the dynamics of first order deviations from spherical symmetry, finding that many solutions are unstable to such aspherical perturbations. The parameter space in which the perturbations on bound solutions inevitably become nonlinear is mapped. This instability has consequences for the Farhi-Guth-Guven mechanism for baby universe production via quantum tunneling.

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preprint2002arXiv

Metallicity of the Intergalactic Medium Using Pixel Statistics: I. Method

Studies of absorption spectra of high-z QSOs have revealed that the intergalactic medium at z ~ 2-3 is enriched to ~ 0.1%-1% solar for gas densities more than a few times the mean cosmic density, but have not yet produced an accurate metallicity estimate, nor constrained variations in the metallicity with density, redshift, or spatial location. This paper discusses the ``pixel optical depth'' (POD) method of QSO spectrum analysis, using realistic simulated spectra from cosmological simulations. In this method, absorption in Ly-alpha is compared to corresponding metal absorption on a pixel-by-pixel basis, yielding for each analyzed spectrum a single statistical correlation encoding metal enrichment information. Our simulations allow testing and optimization of each step of the technique's implementation. Tests show that previous studies have probably been limited by C IV self-contamination and O VI contamination by HI lines; we have developed and tested an effective method of correcting for both contaminants. We summarize these and other findings, and provide a useful recipe for the POD technique's application to observed spectra. Our tests reveal that the POD technique applied to spectra of presently available quality is effective in recovering useful metallicity information even in underdense gas. We present an extension of the POD technique to directly recover the intergalactic metallicity as a function of gas density. For a given ionizing background, both the oxygen and carbon abundance can be measured with errors of at most a factor of a few over at least an order of magnitude in density, using a single high-quality spectrum.

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