arXiv subjects

Latham Boyle

Publications and source records attributed to Latham Boyle.

At least 37 records · Page 2Linked to original sources

arXiv2022

Gravitational entropy and the flatness, homogeneity and isotropy puzzles

We suggest a new explanation for the observed large scale flatness, homogeneity and isotropy of the universe. The basic ingredients are elementary and well-known, namely Einstein's theory of gravity and Hawking's method of computing gravitational entropy. The new twist is provided by the boundary conditions we recently proposed for "big bang" type singularities dominated by conformal matter, enforcing $CPT$ symmetry and analyticity. Here, we show that, besides allowing us to describe the big bang, these boundary conditions allow new gravitational instantons, enabling us to calculate the gravitational entropy of cosmologies which include radiation, dark energy and space curvature of either sign. We find the gravitational entropy of these universes, $S_g \sim S_Λ^{1/ 4} S_r$, where $S_Λ$ is the famous de Sitter entropy and $S_r$ is the total entropy in radiation. To the extent that $S_g$ exceeds $S_Λ$, the most probable universe is flat. By analysing the perturbations about our new instantons, we argue it is also homogeneous and isotropic on large scales.

hep-th↗

arXiv2021

Two-Sheeted Universe, Analyticity and the Arrow of Time

Our universe seems to be radiation dominated at early times, and vacuum energy dominated at late times. When we consider the maximal analytic extension of this spacetime, its symmetries and complex analytic properties suggest a picture in which spacetime has two sheets, exchanged by an isometry which, in turn, picks a preferred (CPT-symmetric) vacuum state for quantum fields on the spacetime. Previously (arXiv:1803.08928, arXiv:1803.08930), we showed how this line of thought provides new explanations for dark matter, the matter-antimatter asymmetry, the absence of primordial vector and tensor perturbations, and the {\it phase} of the primordial scalar perturbations; and additional testable predictions. In this paper, we develop this picture in several respects and, in particular, point out that it also provides a new explanation for why the thermodynamic arrow of time points away from the bang.

hep-th↗

arXiv2020

The standard model, the Pati-Salam model, and "Jordan geometry"

We argue that the ordinary commutative-and-associative algebra of spacetime coordinates (familiar from general relativity) should perhaps be replaced, not by a noncommutative algebra (as in noncommutative geometry), but rather by a Jordan algebra (leading to a framework which we term "Jordan geometry"). We present the Jordan algebra (and representation) that most nearly describes the standard model of particle physics, and we explain that it actually describes a certain (phenomenologically viable) extension of the standard model: by three right-handed (sterile) neutrinos, a complex scalar field $φ$, and a $U(1)_{B-L}$ gauge boson which is Higgsed by $φ$. We then note a natural extension of this construction, which describes the $SU(4)\times SU(2)_{L}\times SU(2)_{R}$ Pati-Salam model. Finally, we discuss a simple and natural Jordan generalization of the exterior algebra of differential forms.

hep-th↗

arXiv2019

Conformal Quasicrystals and Holography

Recent studies of holographic tensor network models defined on regular tessellations of hyperbolic space have not yet addressed the underlying discrete geometry of the boundary. We show that the boundary degrees of freedom naturally live on a novel structure, a conformal quasicrystal, that provides a discrete model of conformal geometry. We introduce and construct a class of one-dimensional conformal quasicrystals, and discuss a higher-dimensional example (related to the Penrose tiling). Our construction permits discretizations of conformal field theories that preserve an infinite discrete subgroup of the global conformal group at the cost of lattice periodicity.

hep-th↗

arXiv2018

CPT-Symmetric Universe

We propose that the state of the universe does {\it not} spontaneously violate CPT. Instead, the universe after the big bang is the CPT image of the universe before it, both classically and quantum mechanically. The pre- and post-bang epochs comprise a universe/anti-universe pair, emerging from nothing directly into a hot, radiation-dominated era. CPT symmetry selects a unique QFT vacuum state on such a spacetime, providing a new interpretation of the cosmological baryon asymmetry, as well as a remarkably economical explanation for the cosmological dark matter. Requiring only the standard three-generation model of particle physics (with right-handed neutrinos), a $\mathbb{Z}_2$ symmetry suffices to render one of the right-handed neutrinos stable. We calculate its abundance from first principles: matching the observed dark matter density requires its mass to be $4.8\times10^{8}~{\rm GeV}$. Several other testable predictions follow: (i) the three light neutrinos are Majorana and allow neutrinoless double $β$ decay; (ii) the lightest neutrino is massless; and (iii) there are no primordial long-wavelength gravitational waves. We mention connections to the strong CP problem and the arrow of time.

hep-ph↗

arXiv2018

A new algebraic structure in the standard model of particle physics

We introduce a new formulation of the real-spectral-triple formalism in non-commutative geometry (NCG): we explain its mathematical advantages and its success in capturing the structure of the standard model of particle physics. The idea, in brief, is to represent $A$ (the algebra of differential forms on some possibly-noncommutative space) on $H$ (the Hilbert space of spinors on that space), and to reinterpret this representation as a simple super-algebra $B=A\oplus H$ with even part $A$ and odd part $H$. $B$ is the fundamental object in our approach: we show that (nearly) all of the basic axioms and assumptions of the traditional real-spectral-triple formalism of NCG are elegantly recovered from the simple requirement that $B$ should be a differential graded $\ast$-algebra (or "$\ast$-DGA"). Moreover, this requirement also yields other, new, geometrical constraints. When we apply our formalism to the NCG traditionally used to describe the standard model of particle physics, we find that these new constraints are physically meaningful and phenomenologically correct. In particular, these new constraints provide a novel interpretation of electroweak symmetry breaking that is geometric rather than dynamical. This formalism is more restrictive than effective field theory, and so explains more about the observed structure of the standard model, and offers more guidance about physics beyond the standard model.

hep-th↗

arXiv2016

Reflection Quasilattices and the Maximal Quasilattice

We introduce the concept of a {\it reflection quasilattice}, the quasiperiodic generalization of a Bravais lattice with irreducible reflection symmetry. Among their applications, reflection quasilattices are the reciprocal (i.e. Bragg diffraction) lattices for quasicrystals and quasicrystal tilings, such as Penrose tilings, with irreducible reflection symmetry and discrete scale invariance. In a follow-up paper, we will show that reflection quasilattices can be used to generate tilings in real space with properties analogous to those in Penrose tilings, but with different symmetries and in various dimensions. Here we explain that reflection quasilattices only exist in dimensions two, three and four, and we prove that there is a unique reflection quasilattice in dimension four: the "maximal reflection quasilattice" in terms of dimensionality and symmetry. Unlike crystallographic Bravais lattices, all reflection quasilattices are invariant under rescaling by certain discrete scale factors. We tabulate the complete set of scale factors for all reflection quasilattices in dimension $d>2$, and for all those with quadratic irrational scale factors in $d=2$.

math-ph↗

arXiv2016

Symmetric Satellite Swarms and Choreographic Crystals

In this paper, we introduce a natural dynamical analogue of crystalline order, which we call choreographic order. In an ordinary (static) crystal, a high degree of symmetry may be achieved through a careful arrangement of the fundamental repeated elements. In the dynamical analogue, a high degree of symmetry may be achieved by having the fundamental elements perform a carefully choreographed dance. For starters, we show how to construct and classify all symmetric satellite constellations. Then we explain how to generalize these ideas to construct and classify choreographic crystals more broadly. We introduce a quantity, called the "choreography" of a given configuration. We discuss the possibility that some (naturally occurring or artificial) many-body or condensed-matter systems may exhibit choreographic order, and suggest natural experimental signatures that could be used to identify and characterize such systems.

cond-mat.other↗

arXiv2015

On testing and extending the inflationary consistency relation for tensor modes

If observations confirm BICEP2's claim of a tensor-scalar ratio $r\approx 0.2$ on CMB scales, then the inflationary consistency relation $n_{t}=-r/8$ predicts a small negative value for the tensor spectral index $n_t$. We show that future CMB polarization experiments should be able to confirm this prediction at several sigma. We also show how to properly extend the consistency relation to solar system scales, where the primordial gravitational wave density $Ω_{gw}$ could be measured by proposed experiments such as the Big Bang Observer. This would provide a far more stringent test of the consistency relation and access much more detailed information about the early universe.

astro-ph.CO↗

arXiv2015

Non-Associative Geometry and the Spectral Action Principle

Chamseddine and Connes have argued that the action for Einstein gravity, coupled to the SU(3)\times SU(2)\times U(1) standard model of particle physics, may be elegantly recast as the "spectral action" on a certain "non-commutative geometry." In this paper, we show how this formalism may be extended to "non-associative geometries," and explain the motivations for doing so. As a guiding illustration, we present the simplest non-associative geometry (based on the octonions) and evaluate its spectral action: it describes Einstein gravity coupled to a G_2 gauge theory, with 8 Dirac fermions (which transform as a singlet and a septuplet under G_2). This is just the simplest example: in a forthcoming paper we show how to construct more realistic models that include Higgs fields, spontaneous symmetry breaking and fermion masses.

hep-th↗

arXiv2015

Rethinking Connes' approach to the standard model of particle physics via non-commutative geometry

Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation of this framework that is: (i) simpler and more unified in its axioms, and (ii) allows the Lagrangian for the standard model of particle physics (coupled to Einstein gravity) to be specified in a way that is tighter and more explanatory than the traditional algorithm based on effective field theory. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Applying this perspective to the NCG traditionally used to describe the standard model we find, instead, an extension of the standard model by an extra $U(1)_{B-L}$ gauge symmetry, and a single extra complex scalar field $σ$, which is a singlet under $SU(3)_{C}\times SU(2)_{L}\times U(1)_{Y}$, but has $B-L=2$. This field has cosmological implications, and offers a new solution to the discrepancy between the observed Higgs mass and the NCG prediction.

hep-th↗

arXiv2014

Non-Commutative Geometry, Non-Associative Geometry and the Standard Model of Particle Physics

Connes' notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking reinterepretation of the standard model of particle physics, coupled to Einstein gravity. We suggest a simple reformulation with two key mathematical advantages: (i) it unifies many of the traditional NCG axioms into a single one; and (ii) it immediately generalizes from non-commutative to non-associative geometry. Remarkably, it also resolves a long-standing problem plaguing the NCG construction of the standard model, by precisely eliminating from the action the collection of 7 unwanted terms that previously had to be removed by an extra, non-geometric, assumption. With this problem solved, the NCG algorithm for constructing the standard model action is tighter and more explanatory than the traditional one based on effective field theory.

hep-th↗

arXiv2014

On quantifying and resolving the BICEP2/Planck tension over gravitational waves

The recent BICEP2 measurement of primordial gravity waves (r = 0.2^{+0.07}_{-0.05}) appears to be in tension with the upper limit from WMAP (r<0.13 at 95% CL) and Planck (r<0.11 at 95% CL). We carefully quantify the level of tension and show that it is very significant (around 0.1% unlikely) when the observed deficit of large-scale temperature power is taken into account. We show that measurements of TE and EE power spectra in the near future will discriminate between the hypotheses that this tension is either a statistical fluke, or a sign of new physics. We also discuss extensions of the standard cosmological model that relieve the tension, and some novel ways to constrain them.

astro-ph.CO↗

arXiv2013

The Minimal Dimensionless Standard Model (MDSM) and its Cosmology

Consider the minimal renormalizable extension of the Standard Model with purely dimensionless couplings, successful electroweak symmetry breaking (via the Coleman-Weinberg mechanism) and a see-saw mechanism for neutrino mass: we will call this the Minimal Dimensionless Standard Model (MDSM). In fact, 3 closely related models fit the bill: MDSM_1, MDSM_2 and MDSM_3. We analyze the theoretical and observational constraints on these models. We argue that, when they are minimally coupled to gravity, they can accomplish several important cosmological tasks (inflation, dark matter, leptogenesis) in a way that is economical, predictive and tightly woven into the fabric of known physics. One of the models (MDSM_3), which includes an extra U(1)_{B-L} gauge symmetry, seems particularly promising.

hep-ph↗

arXiv2013

Pulsar timing arrays as imaging gravitational wave telescopes: angular resolution and source (de)confusion

Pulsar timing arrays (PTAs) will be sensitive to a finite number of gravitational wave (GW) "point" sources (e.g. supermassive black hole binaries). N quiet pulsars with accurately known distances d_{pulsar} can characterize up to 2N/7 distant chirping sources per frequency bin Δf_{gw}=1/T, and localize them with "diffraction limited" precision δθ\gtrsim (1/SNR)(λ_{gw}/d_{pulsar}). Even if the pulsar distances are poorly known, a PTA with F frequency bins can still characterize up to (2N/7)[1-(1/2F)] sources per bin, and the quasi-singular pattern of timing residuals in the vicinity of a GW source still allows the source to be localized quasi-topologically within roughly the smallest quadrilateral of quiet pulsars that encircles it on the sky, down to a limiting resolution δθ\gtrsim (1/SNR) \sqrt{λ_{gw}/d_{pulsar}}. PTAs may be unconfused, even at the lowest frequencies, with matched filtering always appropriate.

astro-ph.HE↗

arXiv2011

Light Loop Echoes and Blinking Black Holes

Radiation emitted near a black hole reaches the observer by multiple paths; and when this radiation varies in time, the time-delays between the various paths generate a "blinking" effect in the observed light curve L(t) or its auto-correlation function xi(T)= . For the particularly important "face-on" configuration (in which the hole is viewed roughly along its spin axis, while the emission comes roughly from its equatorial plane -- e.g. from the inner edge of its accretion disk, or from the violent flash of a nearby/infalling star) we calculate the blinking in detail by computing the time delay Delta t_{j}(r,a) and magnification mu_{j}(r,a) of the jth path (j=1,2,3,...), relative to the primary path (j=0), as a function of the emission radius r and black hole spin 0<a/M<1. The particular geometry and symmetry of the nearly-face-on configuration enhances and "protects" the blinking signal, making it more detectable and more independent of certain astrophysical and observational details. The effect can be surprisingly strong: e.g. for radiation from the innermost stable circular orbit ("ISCO") of a black hole of critical spin (a_{crit}/M = 0.853), the j=1,2,3 fluxes are, respectively, 27%, 2% and 0.1% of the j=0 flux.

astro-ph.HE↗

arXiv2010

Testing Inflation: A Bootstrap Approach

We note that the essential idea of inflation, that the universe underwent a brief period of accelerated expansion followed by a long period of decelerated expansion, can be encapsulated in a "closure condition" which relates the amount of accelerated expansion during inflation to the amount of decelerated expansion afterward. We present a protocol for systematically testing the validity of this condition observationally.

astro-ph↗

arXiv2010

The general theory of porcupines, perfect and imperfect

Porcupines are networks of gravitational wave detectors in which the detectors and the distances between them are short relative to the gravitational wavelengths of interest. Perfect porcupines are special configurations whose sensitivity to a gravitational plane wave is independent of the propagation direction or polarization of the wave. I develop the theory of porcupines, including the optimal estimator \hat{h}^{ij} for the gravitational wave field; useful formulae for the spin-averaged and rotationally-averaged SNR^{2}; and a simple derivation of the properties of perfect porcupines. I apply these results to the interesting class of ``simple'' porcupines, and mention some open problems.

gr-qc↗