arXiv subjects

Glenn D. Starkman

Publications and source records attributed to Glenn D. Starkman.

At least 55 records · Page 3Linked to original sources

arXiv2018

Nuclides as a liquid phase of $SU(2)_L \times SU(2)_R$ chiral perturbation theory I: emergence of pion-less SU(2) $χ$ PT

The Standard Model of particle physics, augmented with neutrino mixing, is at least very nearly the complete theory of interactions of known particles at energies accessible to Nature on Earth. Candidate effective theories of nuclear structure must therefore reflect SM symmetries, especially the chiral global $SU(2)_L \times SU(2)_R$ symmetry of two-massless-quark QCD. For ground-state nuclei, SU(2) chiral perturbation theory (XPT) enables perturbation in inverse powers of $Λ_{XSB}\simeq 1 GeV$, with analytic operators renormalized to all loop orders. We show that pion-less "Static Chiral Nucleon Liquids" (SXNL) emerge as a liquid phase of SU(2) XPT of protons, neutrons and 3 Nambu-Goldstone boson pions. Far-IR pions decouple from SXNL, simplifying the derivation of saturated nuclear matter and microscopic liquid drops (ground-state nuclides). We trace to the global symmetries of two-massless-quark QCD the power of pion-less SU(2) XPT to capture experimental ground-state properties of certain nuclides with even parity, spin zero, even proton number Z, and neutron number N. We derive the SXNL effective SU(2) XPT Lagrangian, including all order $Λ_{XSB},Λ^0_{XSB}$ operators. These include: all 4-nucleon operators that survive Fierz rearrangement in the non-relativistic limit, and effective Lorentz-vector iso-vector neutral "$ρ$-exchange" operators. SXNL motivate nuclear matter as non-topological solitons at zero pressure: the Nuclear Liquid Drop Model and Bethe-Weizsacker Semi-Empirical Mass Formula emerge in an explicit Thomas-Fermi construction provided in the companion paper. For chosen nuclides, nuclear Density Functional and Skyrme models are justified to order $Λ_{χSB}^0$. We conjecture that inclusion of higher order operators will result in accurate "natural" Skyrme, No-Core-Shell, and neutron star models.

nucl-th↗

arXiv2018

The Limited Accuracy of Linearized Gravity

Standard cosmological models rely on an approximate treatment of gravity, utilizing solutions of the linearized Einstein equations as well as physical approximations. In an era of precision cosmology, we should ask: are these approximate predictions sufficiently accurate for comparison to observations, and can we draw meaningful conclusions about properties of our Universe from them? In this work we examine the accuracy of linearized gravity in the presence of collisionless matter and a cosmological constant utilizing fully general relativistic simulations. We observe the gauge-dependence of corrections to linear theory, and note the amplitude of these corrections. For perturbations whose amplitudes are in line with expectations from the standard $Λ$CDM model, we find that the full, general relativistic metric is well-described by linear theory in Newtonian and harmonic gauges, while the metric in comoving-synchronous gauge is not. For the largest observed structures in our Universe, our results suggest that corrections to linear gravitational theory can reach or surpass the percent-level.

astro-ph.CO↗

arXiv2018

Topology and the suppression of CMB large-angle correlations

To date, no compelling evidence has been found that the universe has non-trivial spatial topology. Meanwhile, anomalies in the observed CMB temperature map, such as the lack of correlations at large angular separations, remain observationally robust. We show that if our universe is flat and has one compact dimension of appropriate size (slab topology), this would suppress large-angle temperature correlations while maintaining a low-$\ell$ angular power spectrum consistent with observations. The optimal length appears to be $1.4$ times the conformal radius of the CMB's last scattering surface ($χ_{rec}$). We construct the probability distribution function of the statistic $S_{1/2}$ using simulated Sachs-Wolf-only skies for each of several values of $L_z/χ_{rec}$. For $L_z\simeq1.4χ_{rec}$ the $p$-value of four standard masked Planck maps is $p\simeq0.15$, compared to $p\lesssim0.003$ for the conventional topologically trivial space. The mean angular power spectrum $\langle C_{\ell} \rangle$ of the $L_z=1.4χ_{rec}$ slab space matches the observed power spectrum at $2\leq\ell\lesssim6$ -- including a substantially suppressed quadrupole $C_2$, a slightly suppressed octopole $C_3$, and unsuppressed higher multipoles. It does not predict other low-$\ell$ CMB anomalies, and does not take account of normally sub-dominant Integrated Sachs Wolfe contributions. An $L_z=1.4χ_{rec}$ slab topology is consistent with published limits from the Planck maps ($L_z\gtrsim1.12χ_{rec}$). It is within the 95% confidence range $1.2\leq L_z/χ_{rec}\leq2.1$ inferred using the covariance-matrix of temperature fluctuations. However, it violates published circles-in-the-sky limits from WMAP and related unpublished limits from Planck ($L_z/χ_{rec}\gtrsim1.9$). We remark on the possibility to satisfy these limits, and "postdict" other large-angle anomalies, with closely related topologies.

astro-ph.CO↗

arXiv2018

Global $SU(2)_L \otimes$BRST symmetry and its LSS theorem: Ward-Takahashi identities governing Green's functions, on-shell T-Matrix elements, and $V_{eff}$, in the scalar-sector of certain spontaneously broken non-Abelian gauge theories

This work is dedicated to the memory of Raymond Stora (1930-2015). $SU(2)_L$ is the simplest spontaneous symmetry breaking (SSB) non-Abelian gauge theory: a complex scalar doublet $ϕ=\frac{1}{\sqrt{2}}\begin{bmatrix}H+iπ_3-π_2 +iπ_1\end{bmatrix}\equiv\frac{1}{\sqrt{2}}\tilde{H}e^{2i\tilde{t}\cdot\tilde{\vecπ}/ }\begin{bmatrix}10\end{bmatrix}$ and a vector $\vec{W}^μ$. In Landau gauge, $\vec{W}^μ$ is transverse, $\vec{\tildeπ}$ are massless derivatively coupled Nambu-Goldstone bosons (NGB). A global shift symmetry enforces $m^{2}_{\tildeπ}=0$. We observe that on-shell T-matrix elements of physical states $\vec{W}^μ$,$ϕ$ are independent of global $SU(2)_{L}$ transformations, and the associated global current is exactly conserved for amplitudes of physical states. We identify two towers of "1-soft-pion" global Ward-Takahashi Identities (WTI), which govern the $ϕ$-sector, and represent a new global symmetry, $SU(2)_L\otimes$BRST, a symmetry not of the Lagrangian but of the physical states. The first gives relations among 1-$ϕ$-I (but one $W^μ,B^μ$ reducible) off-shell Green's functions, the second governs on-shell T-matrix elements, replacing the Adler self-consistency conditions. These WTI constrain the all-loop-orders scalar-sector effective Lagrangian and guarantee IR finiteness of the theory. These on-shell WTI include a Lee-Stora-Symanzik (LSS) theorem, which enforces the condition $m_π^2=0$ (far stronger than $m_{\tildeπ}^2=0$) and causes all relevant-operator contributions to the effective Lagrangian to vanish exactly. The global $SU(2)_L$ and the BRST transformations commute in $R_ξ$ gauges. With the on-shell T-matrix constraints, the physics therefore has more symmetry than does its BRST invariant Lagrangian. We also show that the statements made above hold for the electroweak sector of the Standard Model bosons.

hep-ph↗

arXiv2018

$U(1)\otimes BRST$ symmetry, of on-shell T-matrix elements and (1-$ϕ$-I) Green's functions, determines the vacuum state of the Abelian Higgs Model from symmetry alone: minimization of the scalar-sector effective potential is unnecessary

The weak-scale $U(1)_{Y}$ Abelian Higgs Model (AHM) is the spontaneous-symmetry-breaking gauge theory of a complex scalar $ϕ= \frac{1}{\sqrt{2}}(H + i π)$ and a vector $A_μ$. Global $U(1)_{Y}\otimes BRST$ symmetry emerges: when it is realized that on-shell T-matrix elements enjoy an extra $U(1)_{Y}$ global symmetry beyond the Lagragian's BRST symmetry. The symmetries co-exist: $U(1)_{Y}$ generators $δ_{U(1)_Y}$ commute with BRST generators s and $[δ_{U(1)_Y},s]{\cal L} = 0$. Two towers of Ward Takahashi identities (WTI), which include all-loop-orders quantum corrections, emerge: a tower of relations among off-shell 1-$ϕ$-I (but 1-$A_μ$-Reducible) Green's functions; another tower of Adler-zero WTI for on-shell T-matrix elements. The T-matrix's LSS theorem forces tadpoles to automatically vanish (equivalently $m^{2}_π = 0$) by symmetry alone. We show that, when the full symmetries of Lorenz gauge AHM are enforced on the scalar-sector effective potential, the vacuum state of the theory is specified/decided by symmetry alone. We use recursive WTI relations among Green's functions to include opeators of dimension $\geq 1$. We express the fully renormalized scalar-sector effective potential in a form which shows explicitly that, for small scalar field values, the gauge-independent vacuum state of the theory $\langle H\rangle_{renormalized} = Z^{1/2}_ϕ\langle H\rangle_{bare}$ is determined by $U(1)_{Y}\otimes BRST$ symmetry alone, without minimizing the effective potential.

hep-ph↗

arXiv2018

Global $U(1)_Y$xBRST symmetry and the LSS theorem: Ward-Takahashi identities governing Green's functions, on-shell T-Matrix elements, and the effective potential, in the spontaneously broken extended Abelian Higgs model

The weak-scale U(1) Abelian Higgs Model (AHM) is the simplest spontaneous symmetry breaking (SSB) gauge theory. The extended AHM (E-AHM) adds certain heavy scalars $Φ$ and fermions $ψ$. In Lorenz gauge, these theories have a global U(1) conserved physical current, but no conserved charge. As shown by Kibble, the Goldstone theorem applies, there is a massless derivatively coupled Nambu-Goldstone boson (NGB). Proof of all-loop-orders renormalizability and unitarity is tricky because the BRST-invariant Lagrangian is not U(1) symmetric. Nevertheless, Slavnov-Taylor identities guarantee that on-shell T-matrix elements of physical states are independent of anomaly-free gauge transformations. We observe that they are therefore also independent of the usual anomaly-free U(1) global transformations. It follows that the associated global current, is exactly conserved for amplitudes of physical states. We identify corresponding Ward-Takahashi identities (WTI). In Lorenz gauge, two towers of "1-soft-pion" global WTI govern the scalar-sector, and represent a new global U(1)xBRST symmetry not of the Lagrangian but of the physics. The first gives relations among off-shell Green's functions, the second governs on-shell T-matrix elements, replacing the Adler self-consistency conditions. These WTI constrain the all-loop-orders scalar-sector low-energy effective Lagrangian. Consequently, certain heavy CP-conserving heavy matter representations decouple completely in the $M_{Heavy}^2/m_{Weak}^2 \to \infty$ limit. SSB (E-)AHM physics therefore has more symmetry than does its BRST-invariant Lagrantian. The NGB decouples from the observable particle spectrum in the usual way, when the observable vector absorbs it, as if it were a gauge transformation, hiding both towers of WTI from observable particle physics.

hep-ph↗

arXiv2017

The Linear Point Standard Ruler for galaxy survey data: validation with mock catalogues

Due to late time non-linearities, the location of the acoustic peak in the two-point galaxy correlation function is a redshift-dependent quantity, thus it cannot be simply employed as a cosmological standard ruler. This has motivated the recent proposal of a novel ruler, also located in the Baryon Acoustic Oscillation range of scales of the correlation function, dubbed the "linear point". Unlike the peak, it is insensitive at the $0.5\%$ level to many of the non-linear effects that distort the clustering correlation function and shift the peak. However, this is not enough to make the linear point a useful standard ruler. In addition, we require a model-independent method to estimate its value from real data, avoiding the need to deploy a poorly known non-linear model of the correlation function. In this manuscript, we precisely validate a procedure for model-independent estimation of the linear point. We also identify the optimal set-up to estimate the linear point from the correlation function using galaxy catalogs. The methodology developed here is of general validity, and can be applied to any galaxy correlation-function data. As a working example, we apply this procedure to the LOWZ and CMASS galaxy samples of the Twelfth Data Release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS), for which the estimates of cosmic distances using the linear point have been presented in Anselmi et al. (2017) [1].

astro-ph.CO↗

arXiv2017

The Linear Point: A cleaner cosmological standard ruler

We show how a characteristic length scale imprinted in the galaxy two-point correlation function, dubbed the "linear point", can serve as a comoving cosmological standard ruler. In contrast to the Baryon Acoustic Oscillation peak location, this scale is constant in redshift and is unaffected by non-linear effects to within $0.5$ percent precision. We measure the location of the linear point in the galaxy correlation function of the LOWZ and CMASS samples from the Twelfth Data Release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS) collaboration. We combine our linear-point measurement with cosmic-microwave-background constraints from the Planck satellite to estimate the isotropic-volume distance $D_{V}(z)$, without relying on a model-template or reconstruction method. We find $D_V(0.32)=1264\pm 28$ Mpc and $D_V(0.57)=2056\pm 22$ Mpc respectively, consistent with the quoted values from the BOSS collaboration. This remarkable result suggests that all the distance information contained in the baryon acoustic oscillations can be conveniently compressed into the single length associated with the linear point.

astro-ph.CO↗

arXiv2017

Could 1I/'Oumuamua be macroscopic dark matter?

1I/'Oumuamua, formerly known as A/2017 U1, is a sizable body currently passing through the solar system. It is generally considered to be a rocky asteroid-like object that came from another planetary system in the Milky Way. We point out that 1I/'Oumuamua may instead be a chunk of dark matter, a "macro," possibly as massive as $10^{25}$g if it is of nuclear density. If so, then its passage will have caused measurable deviations in the orbits of Mercury, the Earth and Moon.

astro-ph.GA↗

arXiv2017

General Relativistic Corrections to the Weak Lensing Convergence Power Spectrum

We compute the weak lensing convergence power spectrum, $C^{κκ}(θ)$, in a dust-filled universe using fully non-linear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations by computing the Bardeen (Newtonian) potentials in linearized gravity and utilizing the Born approximation. We find corrections to the angular power spectrum amplitude of order ten percent at very large angular scales, $\ell ~ 2-3$, and percent-level corrections at intermediate angular scales of $\ell ~ 20-30$.

astro-ph.CO↗

arXiv2017

Global $SU(3)_C\times SU(2)_L\times U(1)_Y$ linear sigma model: axial-vector Ward Takahashi identities, and decoupling of certain heavy BSM particles due to the Goldstone theorem

Dedicated to the memory of Raymond Stora (1930-2015). In the $SU(2)_L\times SU(2)_R$ Linear Sigma Model with PCAC, towers of Ward-Takahashi Identities (WTI) have long been known to give relations among 1-Scalar-Particle-Irreducible Green's functions, and among I- Scalar-Particle-Reducible T-Matrix elements, for external scalars (i.e. the Brout-Englert-Higgs scalar and 3 pseudoscalars). We extend these WTI and the resulting relations to the $SU(3)_C\times SU(2)_L\times U(1)_Y$ Linear Sigma Model including the heaviest generation of Standard Model (SM) fermions supplemented with the minimum necessary neutrino content -- right-handed neutrinos and Yukawa-coupling-induced Dirac neutrino mass. We extract powerful constraints on the effective Lagrangian: e.g. showing that they make separate tadpole renormalization unnecessary, and guarantee infra-red finiteness. Crucially, ultra-violet quadratic divergences (UVQD) and all other relevant operators contribute only to $m_π^2$, a Nambu-Goldstone boson (NGB) mass-squared. A WTI between T-Matrix elements (i.e. the Goldstone Theorem) then enforces $ m_π^2=0$ for the true NGB in the spontaneous symmetry breaking mode of the theory. All relevant operator contributions originating to all-loop-orders from virtual scalars, quarks and leptons, vanish identically! Our regularization-scheme-independent results are unchanged by the addition of certain heavy CP-conserving matter, such as originate in certain Beyond the SM models. We demonstrate this with two examples: a heavy singlet real scalar field with $Z_2$ symmetry and no VEV; and a heavy singlet right-handed Type I See-saw Majorana neutrino. Specifically, we prove that these heavy degrees of freedom decouple completely from the low-energy effective Lagrangian, contributing only irrelevant operators after quartic-coupling renormalization.

hep-ph↗

arXiv2017

Primordial Black-Hole and Macroscopic Dark-Matter Constraints with LISA

The detectability of gravitational waves originating from primordial black holes or other large macroscopic dark-matter candidates inspiraling into Sagittarius ${\rm A}^{\!*}$ is investigated. It is shown that LISA should be a formidable machine to detect the stochastic signal from the accumulated collection of such objects that have been gravitationally captured by Sgr$\,{\rm A}^{\!*}$, provided they have masses above $\sim 10^{-20}\,M_{\odot}$. This is especially so, if they are the main component of the dark matter, and the dark-matter density at Sagittarius ${\rm A}^{\!*}$ exceeds its value in the solar-neighborhood. Notably, the window of mass that is unconstrained by various gravitational lensing arguments and observations, $2 \times 10^{20}\,{\rm g} \leq m_{\rm DM} \leq 4 \times 10^{24}\,{\rm g}$, will be accessible. Forecasts are derived for the event rates and signal strengths as a function of dark-matter mass, assuming that the dark-matter candidates are not tidally disrupted during the inspiral. This is certainly the case for primordial black holes, and it shown that it is also very likely the case for candidate objects of nuclear density.

gr-qc↗

arXiv2017

Failures of homogeneous and isotropic cosmologies in Extended Quasi-Dilaton Massive Gravity

We analyze the Extended Quasi-Dilaton Massive Gravity model around a Friedmann-Lemaître-Robertson-Walker cosmological background. We present a careful stability analysis of asymptotic fixed points. We find that the traditional fixed point cannot be approached dynamically, except from a perfectly fine-tuned initial condition involving both the quasi-dilaton and the Hubble parameter. A less-well examined fixed-point solution, where the time derivative of the 0-th Stückelberg field vanishes $\dotϕ^0=0$, encounters no such difficulty, and the fixed point is an attractor in some finite region of initial conditions. We examine the question of the presence of a Boulware-Deser ghost in the theory. We show that the additional constraint which generically allows for the elimination of the Boulware-Deser mode is only present under special initial conditions. We find that the only possibility corresponds to the traditional fixed point and the initial conditions are the same fine-tuned conditions that allow the fixed point to be approached dynamically.

astro-ph.CO↗

arXiv2017

A cosmologically motivated reference formulation of numerical relativity

The application of numerical relativity to cosmological spacetimes is providing new insights into the behavior of Einstein's equations, beyond common approximations. In order for simulations to be performed as accurately and efficiently as possible, we investigate a novel formulation of Einstein's equations. This formulation evolves differences from a "reference" solution describing the dominant behavior of the spacetime, which mitigates error due to both truncation and approximate finite difference calculations. We find that the error in solutions obtained using the reference formulation can be smaller by an order of magnitude or more, with the level of improvement depending on how well the reference solution approximates the exact solution.

gr-qc↗

arXiv2017

Beating non-linearities: improving the Baryon Acoustic Oscillations with the linear point

We propose a new way of looking at the Baryon Acoustic Oscillations in the Large Scale Structure clustering correlation function. We identify a scale s_LP that has two fundamental features: its position is insensitive to non-linear gravity, redshift space distortions, and scale-dependent bias at the 0.5% level; it is geometrical, i.e. independent of the power spectrum of the primordial density fluctuation parameters. These two properties together make s_LP, called the "linear point", an excellent cosmological standard ruler. The linear point is also appealing because it is easily identified irrespectively of how non-linearities distort the correlation function. Finally, the correlation function amplitude at s_LP is similarly insensitive to non-linear corrections to within a few percent. Hence, exploiting the particular Baryon features in the correlation function, we propose three new estimators for growth measurements. A preliminary analysis of s_LP in current data is encouraging.

astro-ph.CO↗

arXiv2016

Reconsidering seismological constraints on the available parameter space of macroscopic dark matter

Using lunar seismological data, constraints have been proposed on the available parameter space of macroscopic dark matter (macros). We show that actual limits are considerably weaker by considering in greater detail the mechanism through which macro impacts generate detectable seismic waves, which have wavelengths considerably longer than the diameter of the macro. We show that the portion of the macro parameter space that can be ruled out by current seismological evidence is considerably smaller than previously reported, and specifically that candidates with greater than or equal to nuclear density are not excluded by lunar seismology.

astro-ph.CO↗

arXiv2016

CMB-S4 Science Book, First Edition

This book lays out the scientific goals to be addressed by the next-generation ground-based cosmic microwave background experiment, CMB-S4, envisioned to consist of dedicated telescopes at the South Pole, the high Chilean Atacama plateau and possibly a northern hemisphere site, all equipped with new superconducting cameras. CMB-S4 will dramatically advance cosmological studies by crossing critical thresholds in the search for the B-mode polarization signature of primordial gravitational waves, in the determination of the number and masses of the neutrinos, in the search for evidence of new light relics, in constraining the nature of dark energy, and in testing general relativity on large scales.

astro-ph.CO↗

arXiv2016

Observable Deviations from Homogeneity in an Inhomogeneous Universe

How does inhomogeneity affect our interpretation of cosmological observations? It has long been wondered to what extent the observable properties of an inhomogeneous universe differ from those of a corresponding Friedman-Lemaitre-Robertson-Walker (FLRW) model, and how the inhomogeneities affect that correspondence. Here, we use numerical relativity to study the behavior of light beams traversing an inhomogeneous universe and construct the resulting Hubble diagrams. The universe that emerges exhibits an average FLRW behavior, but inhomogeneous structures contribute to deviations in observables across the observer's sky. We also investigate the relationship between angular diameter distance and the angular extent of a source, finding deviations that grow with source redshift. These departures from FLRW are important path-dependent effects with implications for using real observables in an inhomogeneous universe such as our own.

astro-ph.CO↗