arXiv subjects

Chethan Krishnan

Publications and source records attributed to Chethan Krishnan.

At least 37 records · Page 2Linked to original sources

arXiv2023

Towards A Realistic Dipole Cosmology: The Dipole $Λ$CDM Model

Dipole cosmology is the maximally Copernican generalization of the FLRW paradigm that can incorporate bulk flows in the cosmic fluid. In this paper, we first discuss how multiple fluid components with independent flows can be realized in this set up. This is the necessary step to promote ``tilted" Bianchi cosmologies to a viable framework for cosmological model building involving fluid mixtures (as in FLRW). We present a dipole $Λ$CDM model which has radiation and matter with independent flows, with (or without) a positive cosmological constant. A remarkable feature of models containing radiation (including dipole $Λ$CDM) is that the $relative$ flow between radiation and matter can increase at late times, which can contribute to eg., the CMB dipole. This can happen generically in the space of initial conditions. We discuss the significance of this observation for late time cosmic tensions.

astro-ph.CO↗

arXiv2023

Dipole Cosmology: The Copernican Paradigm Beyond FLRW

We introduce the $dipole$ $cosmological$ $principle$, the idea that the Universe is a maximally Copernican cosmology, compatible with a cosmic flow. It serves as the most symmetric paradigm that generalizes the FLRW ansatz, in light of the increasingly numerous (but still tentative) hints that have emerged in the last two decades for a non-kinematic component in the CMB dipole. Einstein equations in our "dipole cosmology" are still ordinary differential equations -- but instead of the two Friedmann equations, now we have four. The two new functions can be viewed as an anisotropic scale factor that breaks the isotropy group from $SO(3)$ to $U(1)$, and a "tilt" that captures the cosmic flow velocity. The result is an axially isotropic, tilted Bianchi V/VII$_h$ cosmology. We assess the possibility of model building within the dipole cosmology paradigm, and discuss the dynamics of expansion rate, anisotropic shear and tilt, in various examples. A key observation is that the cosmic flow (tilt) can grow even while the anisotropy (shear) dies down. Remarkably, this can happen even in an era of late time acceleration.

astro-ph.CO↗

arXiv2023

Fuzzballs and Random Matrices

Black holes are believed to have the fast scrambling properties of random matrices. If the fuzzball proposal is to be a viable model for quantum black holes, it should reproduce this expectation. This is considered challenging, because it is natural for the modes on a fuzzball microstate to follow Poisson statistics. In a previous paper, we noted a potential loophole here, thanks to the modes depending not just on the $n$-quantum number, but also on the $J$-quantum numbers of the compact dimensions. For a free scalar field $ϕ$, by imposing a Dirichlet boundary condition $ϕ=0$ at the stretched horizon, we showed that this $J$-dependence leads to a linear ramp in the Spectral Form Factor (SFF). Despite this, the status of level repulsion remained mysterious. In this letter, motivated by the profile functions of BPS fuzzballs, we consider a generic profile $ϕ= ϕ_0(θ)$ instead of $ϕ=0$ at the stretched horizon. For various notions of genericity (eg. when the Fourier coefficients of $ϕ_0(θ)$ are suitably Gaussian distributed), we find that the $J$-dependence of the spectrum exhibits striking evidence of level repulsion, along with the linear ramp. We also find that varying the profile leads to natural interpolations between Poisson and Wigner-Dyson(WD)-like spectra. The linear ramp in our previous work can be understood as arising via an extreme version of level repulsion in such a limiting spectrum. We also explain how the stretched horizon/fuzzball is different in these aspects from simply putting a cut-off in flat space or AdS (ie., without a horizon).

hep-th↗

arXiv2023

A Tilt Instability in the Cosmological Principle

We show that the Friedmann-Lemaître-Robertson-Walker (FLRW) framework has an instability towards the growth of fluid flow anisotropies, even if the Universe is accelerating. This flow (tilt) instability in the matter sector is invisible to Cosmic No-Hair Theorem-like arguments, which typically only flag shear anisotropies in the metric. We illustrate our claims in the setting of ``dipole cosmology'', the maximally Copernican generalization of FLRW that can accommodate a flow. Simple models are sufficient to show that the cosmic flow need not track the shear, even in the presence of a positive cosmological constant. We also emphasize that the growth of the tilt hair is fairly generic if the total equation of state $w(t) \rightarrow -1$ at late times (as it does in standard cosmology), irrespective of the precise model of dark energy. The generality of our theoretical result puts various recent observational claims about late time anisotropies and cosmic dipoles in a new light.

astro-ph.CO↗

arXiv2023

Soft Hair on Schwarzschild: A Wrinkle in Birkhoff's Theorem

The double null form of the Schwarzschild metric is usually arrived at by demanding Eddington-Finkelstein (EF) conditions at the horizon. This leads to certain logarithmic fall-offs that are too slow along null directions at $\mathscr{I}$, resulting in divergences in the covariant surface charges. These coordinates are therefore $not$ asymptotically flat. In this paper, we find a natural alternative double null form for Schwarzschild that is adapted to $\mathscr{I}^{+}$ or $\mathscr{I}^{-}$ instead of the horizon. In its final form, the metric has only power law fall-offs and fits into the recently introduced Special Double Null (SDN) gauge, with finite surface charges. One remarkable feature of SDN gauge is that spherical symmetry and vacuum Einstein equations allow an infinite number of asymptotic integration constants in the metric, on top of the mass. This is an apparent violation of Birkhoff's theorem. We note however that all except two of these new parameters are absent in the charges, and therefore correspond to trivial hair. The remaining two parameters do show up in the charges, depending on the choice of allowed fall-offs. We provide an understanding of this observation -- Birkhoff's theorem fixes Schwarzschild only $up$ $to$ $diffeomorphisms$, but diffeomorphisms need not vanish at infinity and can in principle become global symmetries. If such asymptotic diffeomorphisms are spherically symmetric, their associated soft modes can become Birkhoff hair. The relevant global symmetries here are certain hypertranslation shifts in the $v$-coordinate at $\mathscr{I}^{+}$ (and $u$ at $\mathscr{I}^{-}$), which are inaccessible in other gauges.

gr-qc↗

arXiv2023

Synthetic Fuzzballs: A Linear Ramp from Black Hole Normal Modes

We consider a black hole with a stretched horizon as a toy model for a fuzzball microstate. The stretched horizon provides a cut-off, and therefore one can determine the normal (as opposed to quasi-normal) modes of a probe scalar in this geometry. For the BTZ black hole, we compute these as a function of the level $n$ and the angular quantum number $J$. Conventional level repulsion is absent in this system, and yet we find that the Spectral Form Factor (SFF) shows clear evidence for a dip-ramp-plateau structure with a linear ramp of slope $\sim 1$ on a log-log plot, with or without ensemble averaging. We show that this is a robust feature of stretched horizons by repeating our calculations on the Rindler wedge (times a compact space). We also observe that this is {\em not} a generic feature of integrable systems, as illustrated by standard examples like integrable billiards and random 2-site coupled SYK model, among others. The origins of the ramp can be traced to the hierarchically weaker dependence of the normal mode spectrum on the quantum numbers of the compact directions, and the resulting quasi-degeneracy. We conclude by noting an analogy between the 4-site coupled SYK model and the quartic coupling responsible for the non-linear instability of capped geometries. Based on this, we speculate that incorporating probe self-interactions will lead to stronger connections to random matrix behavior.

hep-th↗

arXiv2023

Charges for Hypertranslations and Hyperrotations

Hypertranslations and hyperrotations are asymptotic symmetries of flat space, on top of the familiar supertranslations and superrotations. They were discovered in arXiv:2205.01422 by working in the Special Double Null (SDN) gauge, where $\mathscr{I}^{+}$ and $\mathscr{I}^{-}$ are approached along $null$ directions. It was observed there that while the hair degrees of freedom associated to these diffeomorphisms show up in the covariant surfaces charges, the diffeomorphisms themselves do not. This made their status intermediate in some ways between global symmetries and trivial gauge transformations, making interpretation ambiguous. In this paper, we revisit the fall-offs considered in arXiv:2205.01422 which were strictly subleading to Minkowski in conventional double null coordinates. We identify a new class of fall-offs where this assumption is relaxed, but whose charges nonetheless remain finite. Remarkably, the leading behavior is still Riemann flat, indicating that these are soft modes. With this more refined definition of asymptotic flatness, we show that leading hypertranslations and leading hyperrotations explicitly show up in the charges. This makes them genuine global symmetries of asymptotically flat Einstein gravity in the SDN gauge. We write down the new algebra of asymptotic Killing vectors that subsumes the BMS algebra.

hep-th↗

arXiv2022

HKLL for the Non-Normalizable Mode

We discuss various aspects of HKLL bulk reconstruction for the free scalar field in AdS$_{d+1}$. First, we consider the spacelike reconstruction kernel for the non-normalizable mode in global coordinates. We construct it as a mode sum. In even bulk dimensions, this can be reproduced using a chordal Green's function approach that we propose. This puts the global AdS results for the non-normalizable mode on an equal footing with results in the literature for the normalizable mode. In Poincaré AdS, we present explicit mode sum results in general even and odd dimensions for both normalizable and non-normalizable kernels. For generic scaling dimension $Δ$, these can be re-written in a form that matches with the global AdS results via an antipodal mapping, plus a remainder. We are not aware of a general argument in the literature for dropping these remainder terms, but we note that a slight complexification of a boundary spatial coordinate (which we call an $i ε$ prescription) allows us to do so in cases where $Δ$ is (half-) integer. Since the non-normalizable mode turns on a source in the CFT, our primary motivation for considering it is as a step towards understanding linear wave equations in general spacetimes from a holographic perspective. But when the scaling dimension $Δ$ is in the Breitenlohner-Freedman window, we note that the construction has some interesting features within AdS/CFT.

hep-th↗

arXiv2022

Bulk Locality and Asymptotic Causal Diamonds

In AdS/CFT, the non-uniqueness of the reconstructed bulk from boundary subregions has motivated the notion of code subspaces. We present some closely related structures that arise in flat space. A useful organizing idea is that of an {\em asymptotic} causal diamond (ACD): a causal diamond attached to the conformal boundary of Minkowski space. The space of ACDs is defined by pairs of points, one each on the future and past null boundaries, ${\cal I}^{\pm}$. We observe that for flat space with an IR cut-off, this space (a) encodes a preferred class of boundary ``subregions'', (b) is a plausible way to capture holographic data for local bulk reconstruction, (c) has a natural interpretation as the kinematic space for holography, (d) leads to a holographic entanglement entropy in flat space that matches previous definitions and satisfies strong sub-additivity, and, (e) has a bulk union/intersection structure isomorphic to the one that motivated the introduction of quantum error correction in AdS/CFT. By sliding the cut-off, we also note one substantive way in which flat space holography differs from that in AdS. Even though our discussion is centered around flat space (and AdS), we note that there are notions of ACDs in other spacetimes as well. They could provide a covariant way to abstractly characterize tensor sub-factors of Hilbert spaces of holographic theories.

hep-th↗

arXiv2022

Hypertranslations and Hyperrotations

We study the asymptotic symmetries of Einstein gravity in flat space. Instead of Bondi gauge, we work with the recently introduced special double null gauge, in which $\mathscr{I}^{+}$ and $\mathscr{I}^{-}$ are approached along null directions. We find four new functions worth of asymptotic diffeomorphisms beyond the familiar supertranslations and superrotations, which are of relevance in discussions of finite surface charges. Two of these arise from angle-dependent shifts in the $v$-coordinate near $\mathscr{I}^{+}$. We call these hypertranslations and sub-leading hypertranslations, with analogous statements in the $u$-coordinate near $\mathscr{I}^{-}$. There are also two Diff$(S^2)$ transformations, which we call hyperrotations, that are sub-leading to the Virasoro superrotations. With power law fall-offs in the null coordinate and the standard metric on the sphere at leading order, we prove that this is the exhaustive list of diffeomorphisms whose associated metric parameters can show up in the (finite) surface charges. We compute the algebra of the asymptotic Killing vectors under the Barnich-Troessaert bracket, and find a four-fold infinite generalization of the BMS algebra.

hep-th↗

arXiv2022

A New Gauge for Asymptotically Flat Spacetime

We present a new gauge for asymptotically flat spacetime that can treat future and past null infinities ($\mathscr{I}^{+}$ or $\mathscr{I}^{-}$) democratically. Our gauge is complementary to Bondi and Ashtekar-Hansen gauges, and is adapted to the $S$-matrix being the natural observable. One new feature is that the holographic directions are null. We present a set of consistent fall-offs in terms of null coordinates at $\mathscr{I}^{+}$ and $\mathscr{I}^{-}$, with finite BMS$^{\pm}$ charges. The diagonal BMS$^0$ symmetry of the gravitational $S$-matrix emerges upon demanding {\em asymptotic} CPT invariance. Trivial diffeomorphisms, (absence of) log fall-offs, possible enhancements of BMS algebra, and the possibility of holographic renormalization of data at $\mathscr{I}^{+}_-$ and $\mathscr{I}^{-}_+$, play interesting roles. Gory details of the various new technical features that emerge, are elaborated in a companion paper to this letter.

hep-th↗

arXiv2022

Hints of FLRW Breakdown from Supernovae

A 10\% difference in the scale for the Hubble parameter constitutes a clear problem for cosmology. Here, considering angular distribution of Type Ia supernovae (SN) within the Pantheon compilation and working within flat $Λ$CDM cosmology, we observe a correlation between higher $H_0$ and the CMB dipole direction, confirming our previous results for strongly-lensed quasars \cite{Krishnan:2021dyb}. Concretely, we record a $\sim 1$ km/s/Mpc variation in $H_0$ at antipodal points on the sky within the Pantheon sample, which is evident in the Low $z$ subsample ($z \lesssim 0.075$) and gets enhanced by higher redshift SN. Our work raises the possibility that we may be at the precision required to probe anisotropic Hubble expansions, while providing a concrete prediction for future inferences of $H_0$.

astro-ph.CO↗

arXiv2022

$H_0$ as a Universal FLRW Diagnostic

We reverse the logic behind the apparent existence of $H_0$-tension, to design diagnostics for cosmological models. The basic idea is that the non-constancy of $H_0$ inferred from observations at different redshifts is a null hypothesis test for models within the FLRW paradigm -- if $H_0$ runs, the model is wrong. Depending on the kind of observational data, the most suitable form of the diagnostic can vary. As examples, we present two $H_0$ diagnostics that are adapted to two different BAO observables. We use these and the corresponding BAO data to Gaussian reconstruct the running of $H_0$ in flat $Λ$CDM with Planck values for the model parameters. For flat $Λ$CDM when the radiation contribution can be neglected, with comoving distance data, the diagnostic is a simple hypergeometric function. Possible late time deviations from the FLRW paradigm can also be accommodated, by simply keeping track of the (potentially anisotropic) sky variation of the diagnostic.

astro-ph.CO↗

arXiv2021

Interpreting the Bulk Page Curve: A Vestige of Locality on Holographic Screens

Areas of extremal surfaces anchored to sub-regions on screens in Minkowski space satisfy various entanglement entropy inequalities. In 2+1 dimensions where the arguments are simplest, we demonstrate (a) monogamy of mutual information, (b) various versions of (strong) subadditivity, (c) various inequalities involving the entanglement of purification, as well as (e) reflection inequality and (f) Araki-Lieb inequality. Just as in AdS, Linden-Winter and the tower of Cadney-Linden-Winter inequalities are satisfied trivially. All of these are purely geometric (and therefore unambiguous) statements, and we expect them to hold semi-classically when $G_N \rightarrow 0$. The results of arXiv:2103.17253 suggest that it is unlikely that there is non-analyticity at $G_N=0$. These observations have relevance for the Page phase transition in flat space black holes observed with respect to a screen in arXiv:2005.02993 and arXiv:2006.06872. In particular, they constitute a Lorentzian argument that these extremal surface transitions are indeed phase transitions of $some$ suitably defined entanglement entropy associated to $subregions$ on the screen.

hep-th↗

arXiv2021

Does Hubble Tension Signal a Breakdown in FLRW Cosmology?

The tension between early and late Universe probes of the Hubble constant has motivated various new FLRW cosmologies. Here, we reanalyse the Hubble tension with a recent age of the Universe constraint. This allows us to restrict attention to matter and a dark energy sector that we treat without assuming a specific model. Assuming analyticity of the Hubble parameter $H(z)$, and a generic low redshift modification to flat $Λ$CDM, we find that low redshift data ($z \lesssim 2.5$) and well-motivated priors only permit a dark energy sector close to the cosmological constant $Λ$. This restriction rules out late Universe modifications within FLRW. We show that early Universe physics that alters the sound horizon can yield an upper limit of $H_0 \sim 71 \pm 1$ km/s/Mpc. Since various local determinations may be converging to $H_0 \sim 73$ km/s/Mpc, a breakdown of the FLRW framework is a plausible resolution. We outline how future data, in particular strongly lensed quasar data, could also provide further confirmations of such a resolution.

astro-ph.CO↗

arXiv2021

Dirichlet Baths and the Not-so-Fine-Grained Page Curve

We present a doubly holographic prescription for computing entanglement entropy on a gravitating brane. It involves a Ryu-Takayanagi surface with a Dirichlet anchoring condition. In braneworld cosmology, a related approach was used previously in arXiv:2007.06551. There, the prescription naturally computed a co-moving entanglement entropy, and was argued to resolve the information paradox for a black hole living in the cosmology. In this paper, we show that the Dirichlet prescription leads to reasonable results, when applied to a recently studied wedge holography set up with a gravitating bath. The nature of the information paradox and its resolution in our Dirichlet problem have a natural understanding in terms of the strength of gravity on the two branes and at the anchoring location. By sliding the anchor to the defect, we demonstrate that the limit where gravity decouples from the anchor is continuous -- in other words, as far as island physics is considered, weak gravity on the anchor is identical to no gravity. The weak and (moderately) strong gravity regions on the brane are separated by a "Dirichlet wall". We find an intricate interplay between various extremal surfaces, with an island coming to the rescue whenever there is an information paradox. This is despite the presence of massless gravitons in the spectrum. The overall physics is consistent with the slogan that gravity becomes "more holographic", as it gets stronger. Our observations strengthen the case that the conventional Page curve is indeed of significance, when discussing the information paradox in flat space. We work in high enough dimensions so that the graviton is non-trivial, and our results are in line with the previous discussions on gravitating baths in arXiv:2005.02993 and arXiv:2007.06551.

hep-th↗

arXiv2021

A Large-$N$ Phase Transition in a Finite Lattice Gauge Theory

We consider gauge theories of non-Abelian $finite$ groups, and discuss the 1+1 dimensional lattice gauge theory of the permutation group $S_N$ as an illustrative example. The partition function at finite $N$ can be written explicitly in a compact form using properties of $S_N$ conjugacy classes. A natural large-$N$ limit exists with a new 't Hooft coupling, $λ=g^2 \log N$. We identify a Gross-Witten-Wadia-like phase transition at infinite $N$, at $λ=2$. It is first order. An analogue of the string tension can be computed from the Wilson loop expectation value, and it jumps from zero to a finite value. We view this as a type of large-$N$ (de-)confinement transition. Our holographic motivations for considering such theories are briefly discussed.

hep-th↗

arXiv2021

Running Hubble Tension and a H0 Diagnostic

Hubble tension is routinely presented as a mismatch between the Hubble constant $H_0$ determined locally and a value inferred from the flat $Λ$CDM cosmology. In essence, the tension boils down to a disagreement between two numbers. Here, assuming the tension is cosmological in origin, we predict that within flat $Λ$CDM there should be other inferred values of $H_0$, and that a "running of $H_0$ with redshift" can be expected. These additional determinations of $H_0$ may be traced to a difference between the effective equation of state (EoS) of the Universe within the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology framework and the current standard model. We introduce a diagnostic that flags such a running of $H_0$.

astro-ph.CO↗