arXiv subjects

Yasaman K. Yazdi

Publications and source records attributed to Yasaman K. Yazdi.

At least 19 recordsLinked to original sources

arXiv2026

Spectral Spacetime Entropy for Quasifree Theories

Motivated by the necessity to UV-regularise entanglement entropy, we present a spectral method for calculating the entropy of quasifree states, for both bosonic and fermionic field theories. This construction is defined in spacetime rather than on a hypersurface, enabling the covariant regularisation of entropies, and its calculation in generic spacetime regions. We derive these formulae, which have previously appeared in the literature, in a new manner and highlight certain aspects of them, such as their connection to the density matrix and its eigenvalues. The spacetime nature of the formulation makes it particularly apt in the context of semiclassical and quantum gravity and in connection to black hole entropy. Another useful property of the formulation is its application to settings where no notion of a Cauchy surface exists, such as in the causal set theory approach to quantum gravity. We show example applications of the formulae which demonstrate their ability to reproduce known results. We also show a calculation in a causal set in $1+1$ dimensions which makes use of several of the unique and useful features of the formalism. In this last example, we obtain a novel result of a slightly modified entanglement entropy scaling coefficient, giving a possible signature of spacetime discreteness.

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arXiv2026

Spectral Density of the Causal Propagator

The causal propagator (or Pauli-Jordan function), which multiplied by $i$ is the spacetime commutator of the field $[ϕ(x),ϕ(x')]$, plays an essential role in scalar quantum field theory. We discuss the role of the causal propagator and its spectrum in recent developments in defining quantum field theory in a more explicitly covariant manner, as well as in causal set theory. We then present a conjecture for its asymptotic spectral density in a free theory, and give examples that lend evidence to the conjectured scaling. Our work has implications for Lorentzian spectral geometry in much the same way as Weyl's asymptotic law has for Riemannian spectral geometry.

gr-qc↗

arXiv2025

Fluctuations and Correlations in Causal Set Theory

We study the statistical fluctuations (such as the variance) of causal set quantities, with particular focus on the causal set action. To facilitate calculating such fluctuations, we develop tools to account for correlations between causal intervals with different cardinalities. We present a convenient decomposition of the fluctuations of the causal set action into contributions that depend on different kinds of correlations. This decomposition can be used in causal sets approximated by any spacetime manifold $\mathcal M$. Our work paves the way for investigating a number of interesting discreteness effects, such as certain aspects of the Everpresent $Λ$ cosmological model.

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arXiv2024

Aspects of Everpresent $Λ$ (II): Cosmological Tests of Current Models

This paper investigates Everpresent $Λ$, a stochastic dark energy model motivated by causal set theory and unimodular gravity, and confronts it with two key observational data sets, Supernova Ia (SN Ia) and Cosmic Microwave Background (CMB) data. A key feature of this model is that $Λ$ fluctuates over time and on average the magnitude of its fluctuations is of the order of the dominant energy density (be it radiation or matter) for the given epoch. In particular, we focus on a phenomenological implementation of Everpresent $Λ$ known as Model 1. The random fluctuations in Everpresent $Λ$ realizations are generated using seed numbers, and we find that for a small fraction of seeds Model 1 is capable of producing realizations that fit SN Ia data better than $Λ$CDM. We further investigate what features distinguish these realizations from the more general behaviour, and find that the "good'' realizations have relatively small fluctuations at low redshifts ($z<1.5$), which do not closely track the matter density. We find that Model 1 struggles to improve on $Λ$CDM at describing the CMB data. However, by suppressing the values of $Λ$ near the last scattering surface, as suggested in arXiv:1703.06265, we find a large improvement in the best fit of the model, though still with a $χ^2$ value much larger than that of $Λ$CDM. We also study the allowed variation of the dark energy density by the CMB constraints in a more model-independent manner, and find that some variation (especially prior to recombination) is possible and in fact can lead to improvement over $Λ$CDM and reduce the Hubble tension, in line with some early dark energy proposals. However, for the kinds of variations considered, the favoured fluctuations are smaller in magnitude than is typical in current Everpresent $Λ$ models.

astro-ph.CO↗

arXiv2024

Aspects of Everpresent $Λ$ (I): A Fluctuating Cosmological Constant from Spacetime Discreteness

We provide a comprehensive discussion of the Everpresent $Λ$ cosmological model arising from fundamental principles in causal set theory and unimodular gravity. In this framework the value of the cosmological constant ($Λ$) fluctuates, in magnitude and in sign, over cosmic history. At each epoch, $Λ$ stays statistically close to the inverse square root of the spacetime volume. Since the latter is of the order of $H^2$ today, this provides a way out of the cosmological constant puzzle without fine tuning. Our discussion includes a review of what is known about the topic as well as new motivations and insights supplementing the original arguments. We also study features of a phenomenological implementation of this model, and investigate the statistics of simulations based on it. Our results show that while the observed values of $H_0$ and $Ω_Λ^0$ are not typical outcomes of the model, they can be achieved through a modest number of simulations. We also confirm some expected features of $Λ$ based on this model, such as the fact that it stays statistically close to the value of the total ambient energy density (be it matter or radiation dominated), and that it is likely to change sign roughly every Hubble timescale.

gr-qc↗

arXiv2023

On the (Non)Hadamard Property of the SJ State in a $1+1$D Causal Diamond

The Sorkin-Johnston (SJ) state is a candidate physical vacuum state for a scalar field in a generic curved spacetime. It has the attractive feature that it is covariantly and uniquely defined in any globally hyperbolic spacetime, often reflecting the underlying symmetries if there are any. A potential drawback of the SJ state is that it does not always satisfy the Hadamard condition. In this work, we study the extent to which the SJ state in a $1+1$D causal diamond is Hadamard, finding that it is not Hadamard at the boundary. We then study the softened SJ state, which is a slight modification of the original state to make it Hadamard. We use the softened SJ state to investigate whether some peculiar features of entanglement entropy in causal set theory may be linked to its non-Hadamard nature.

hep-th↗

arXiv2023

Everything You Always Wanted to Know About How Causal Set Theory Can Help with Open Questions in Cosmology, but Were Afraid to Ask

We briefly survey open questions in cosmology that either have been or could potentially be addressed with the help of the causal set theory approach to quantum gravity. Our discussion includes topics ranging from dark matter and dark energy to primordial quantum fluctuations and horizon entropy. By putting together all in one place these cosmologically relevant directions of work within causal set theory, we hope to impart a bird's-eye view of this important research theme.

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arXiv2022

Entanglement Entropy and Causal Set Theory

We review a formulation of the entanglement entropy of a quantum scalar field in terms of its spacetime two-point correlation functions. We discuss applications of this formulation to studying entanglement entropy in various settings in causal set theory. These settings include sprinklings of causal diamonds in various dimensions in flat spacetime, de Sitter spacetime, massless and massive theories, multiple disjoint regions, and nonlocal quantum field theories.

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arXiv2022

Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory

A more complete understanding of entanglement entropy in a covariant manner could inform the search for quantum gravity. We build on work in this direction by extending previous results to disjoint regions in $1+1$D. We investigate the entanglement entropy of a scalar field in disjoint intervals within the causal set framework, using the spacetime commutator and correlator, $i\mathbfΔ$ and $\mathbf{W}$ (or the Pauli-Jordan and Wightman functions), respectively. A new truncation scheme for disjoint causal diamonds is presented, which follows from the single diamond truncation scheme. We investigate setups including two and three disjoint causal diamonds, as well as a single causal diamond that shares a boundary with a larger global causal diamond. In all the cases that we study, our results agree with the expected area laws. In addition, we study the mutual information in the two disjoint diamonds setup. The ease of our calculations indicate our methods to be a useful tool for numerically studying such systems. We end with a discussion of some of the strengths and future applications of the spacetime formulation we use in our entanglement entropy computations, both in causal set theory and in the continuum.

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arXiv2021

Insights on Entanglement Entropy in $1+1$ Dimensional Causal Sets

Entanglement entropy in causal sets offers a fundamentally covariant characterisation of quantum field degrees of freedom. A known result in this context is that the degrees of freedom consist of a number of contributions that have continuum-like analogues, in addition to a number of contributions that do not. The latter exhibit features below the discreteness scale and are excluded from the entanglement entropy using a "truncation scheme". This truncation is necessary to recover the standard spatial area law of entanglement entropy. In this paper we build on previous work on the entanglement entropy of a massless scalar field on a causal set approximated by a 1+1D causal diamond in Minkowski spacetime. We present new insights into the truncated contributions, including evidence that they behave as fluctuations and encode features specific to a particular causal set sprinkling. We extend previous results in the massless theory to include Rényi entropies and include new results for the massive theory. We also discuss the implications of our work for the treatment of entanglement entropy in causal sets in more general settings.

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arXiv2021

Towards Spacetime Entanglement Entropy for Interacting Theories

Entanglement entropy of quantum fields in gravitational settings is a topic of growing importance. This entropy of entanglement is conventionally computed relative to Cauchy hypersurfaces where it is possible via a partial tracing to associate a reduced density matrix to the spacelike region of interest. In recent years Sorkin has proposed an alternative, manifestly covariant, formulation of entropy in terms of the spacetime two-point correlation function. This formulation, developed for a Gaussian scalar field theory, is explicitly spacetime in nature and evades some of the possible non-covariance issues faced by the conventional formulation. In this paper we take the first steps towards extending Sorkin's entropy to non-Gaussian theories where Wick's theorem no longer holds and one would expect higher correlators to contribute. We consider quartic perturbations away from the Gaussian case and find that to first order in perturbation theory, the entropy formula derived by Sorkin continues to hold but with the two-point correlators replaced by their perturbation-corrected counterparts. We then show that our results continue to hold for arbitrary perturbations (of both bosonic and fermionic theories). This is a non-trivial and, to our knowledge, novel result. Furthermore we also derive closed-form formulas of the entanglement entropy for arbitrary perturbations at first and second order. Our work also suggests avenues for further extensions to generic interacting theories.

hep-th↗

arXiv2021

Entanglement Entropy of Causal Set de Sitter Horizons

de Sitter cosmological horizons are known to exhibit thermodynamic properties similar to black hole horizons. In this work we study causal set de Sitter horizons, using Sorkin's spacetime entanglement entropy (SSEE) formula, for a conformally coupled quantum scalar field. We calculate the causal set SSEE for the Rindler-like wedge of a symmetric slab of de Sitter spacetime in $d=2,4$ spacetime dimensions using the Sorkin-Johnston vacuum state. We find that the SSEE obeys an area law when the spectrum of the Pauli-Jordan operator is appropriately truncated in both the de Sitter slab as well as its restriction to the Rindler-like wedge. Without this truncation, the SSEE satisfies a volume law. This is in agreement with Sorkin and Yazdi's calculations for the causal set SSEE for nested causal diamonds in $\mathbb{M}^2$, where they showed that an area law is obtained only after truncating the Pauli-Jordan spectrum. In this work we explore different truncation schemes with the criterion that the SSEE so obtained obeys an area law.

gr-qc↗

arXiv2020

Lorentzian Spectral Geometry with Causal Sets

We study discrete Lorentzian spectral geometry by investigating to what extent causal sets can be identified through a set of geometric invariants such as spectra. We build on previous work where it was shown that the spectra of certain operators derived from the causal matrix possess considerable but not complete power to distinguish causal sets. We find two especially successful methods for classifying causal sets and we computationally test them for all causal sets of up to $9$ elements. One of the spectral geometric methods that we study involves holding a given causal set fixed and collecting a growing set of its geometric invariants such as spectra (including the spectra of the commutator of certain operators). The second method involves obtaining a limited set of geometric invariants for a given causal set while also collecting these geometric invariants for small `perturbations' of the causal set, a novel method that may also be useful in other areas of spectral geometry. We show that with a suitably chosen set of geometric invariants, this new method fully resolves the causal sets we considered. Concretely, we consider for this purpose perturbations of the original causal set that are formed by adding one element and a link. We discuss potential applications to the path integral in quantum gravity.

hep-th↗

arXiv2019

Studies on the SJ Vacuum in de Sitter Spacetime

In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime for free scalar field theory. For the massless theory we find that the SJ vacuum can neither be obtained from the $O(4)$ Fock vacuum of Allen and Folacci nor from the non-Fock de Sitter invariant vacuum of Kirsten and Garriga. Using a causal set discretisation of a slab of 2d and 4d de Sitter spacetime, we find the causal set SJ vacuum for a range of masses $m \geq 0$ of the free scalar field. While our simulations are limited to a finite volume slab of global de Sitter spacetime, they show good convergence as the volume is increased. We find that the 4d causal set SJ vacuum shows a significant departure from the continuum Motolla-Allen $α$-vacua. Moreover, the causal set SJ vacuum is well-defined for both the minimally coupled massless $m=0$ and the conformally coupled massless $m=m_c$ cases. This is at odds with earlier work on the continuum de Sitter SJ vacuum where it was argued that the continuum SJ vacuum is ill-defined for these masses. Our results hint at an important tension between the discrete and continuum behaviour of the SJ vacuum in de Sitter and suggest that the former cannot in general be identified with the Mottola-Allen $α$-vacua even for $m>0$.

gr-qc↗

arXiv2019

Manifold-Topology from K-Causal Order

To a significant extent, the metrical and topological properties of spacetime can be described purely order-theoretically. The $K^+$ relation has proven to be useful for this purpose, and one could wonder whether it could serve as the primary causal order from which everything else would follow. In that direction, we prove, by defining a suitable order-theoretic boundary of $K^+(p)$, that in a $K$-causal spacetime, the manifold-topology can be recovered from $K^+$. We also state a conjecture on how the chronological relation $I^+$ could be defined directly in terms of $K^+$.

gr-qc↗

arXiv2018

Entanglement Entropy in Causal Set Theory

Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide in a natural manner the UV cutoff needed to render entanglement entropy finite. Formulating a notion of entanglement entropy in a causal set is not straightforward because the type of canonical hypersurface-data on which its definition typically relies is not available. Instead, we appeal to the more global expression given in arXiv:1205.2953 which, for a gaussian scalar field, expresses the entropy of a spacetime region in terms of the field's correlation function within that region (its "Wightman function" $W(x,x')$). Carrying this formula over to the causal set, one obtains an entropy which is both finite and of a Lorentz invariant nature. We evaluate this global entropy-expression numerically for certain regions (primarily order-intervals or "causal diamonds") within causal sets of 1+1 dimensions. For the causal-set counterpart of the entanglement entropy, we obtain, in the first instance, a result that follows a (spacetime) volume law instead of the expected (spatial) area law. We find, however, that one obtains an area law if one truncates the commutator function ("Pauli-Jordan operator") and the Wightman function by projecting out the eigenmodes of the Pauli-Jordan operator whose eigenvalues are too close to zero according to a geometrical criterion which we describe more fully below. In connection with these results and the questions they raise, we also study the "entropy of coarse-graining" generated by thinning out the causal set, and we compare it with what one obtains by similarly thinning out a chain of harmonic oscillators, finding the same, "universal" behaviour in both cases.

hep-th↗

arXiv2017

Accretion in Radiative Equipartition (AiRE) Disks

Standard accretion disk theory (Shakura & Sunyaev 1973) predicts that the total pressure in disks at typical (sub-)Eddington accretion rates becomes radiation pressure dominated. However, radiation pressure dominated disks are thermally unstable. Since these disks are observed in approximate steady state over the instability time-scale, our accretion models in the radiation pressure dominated regime (i.e. inner disk) need to be modified. Here, we present a modification to the SS model, where radiation pressure is in equipartition with gas pressure in the inner region. We call these flows Accretion in Radiative Equipartition (AiRE) Disks. We introduce the basic features of AiRE disks and show how they modify disk properties such as the Toomre parameter and central temperature. We then show that the accretion rate of AiRE disks is limited from above and below, by Toomre and nodal sonic point instabilities, respectively. The former leads to a strict upper limit on the mass of supermassive black holes as a function of cosmic time (and spin), while the latter could explain the transition between hard and soft states of X-ray binaries.

astro-ph.HE↗

arXiv2017

Zero Modes and Entanglement Entropy

Ultraviolet divergences are widely discussed in studies of entanglement entropy. Also present, but much less understood, are infrared divergences due to zero modes in the field theory. In this note, we discuss the importance of carefully handling zero modes in entanglement entropy. We give an explicit example for a chain of harmonic oscillators in 1D, where a mass regulator is necessary to avoid an infrared divergence due to a zero mode. We also comment on a surprising contribution of the zero mode to the UV-scaling of the entanglement entropy.

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