Cosmodynamics: Energy conditions, Hubble bounds, density bounds, time and distance bounds

We refine and extend a programme initiated by one of the current authors [Science 276 (1997) 88; Phys. Rev. D56 (1997) 7578] advocating the use of the classical energy conditions of general relativity in a cosmological setting to place very general bounds on various cosmological parameters. We show how the energy conditions can be used to bound the Hubble parameter H(z), Omega parameter Omega(z), density rho(z), distance d(z), and lookback time T(z) as (relatively) simple functions of the redshift z, present-epoch Hubble parameter H_0, and present-epoch Omega parameter Omega_0. We compare these results with related observations in the literature, and confront the bounds with the recent supernova data.Comment: 21 pages, 2 figure

Type I superconductivity in the Dirac semimetal PdTe2

The superconductor PdTe$_2$ was recently classified as a Type II Dirac semimetal, and advocated to be an improved platform for topological superconductivity. Here we report magnetic and transport measurements conducted to determine the nature of the superconducting phase. Surprisingly, we find that PdTe$_2$ is a Type I superconductor with $T_c = 1.64$ K and a critical field $\mu_0 H_c (0) = 13.6$ mT. Our crystals also exhibit the intermediate state as demonstrated by the differential paramagnetic effect. For $H > H_c$ we observe superconductivity of the surface sheath. This calls for a close examination of superconductivity in PdTe$_2$ in view of the presence of topological surface states.Comment: 5 page

Tolman wormholes violate the strong energy condition

For an arbitrary Tolman wormhole, unconstrained by symmetry, we shall define the bounce in terms of a three-dimensional edgeless achronal spacelike hypersurface of minimal volume. (Zero trace for the extrinsic curvature plus a "flare-out" condition.) This enables us to severely constrain the geometry of spacetime at and near the bounce and to derive general theorems regarding violations of the energy conditions--theorems that do not involve geodesic averaging but nevertheless apply to situations much more general than the highly symmetric FRW-based subclass of Tolman wormholes. [For example: even under the mildest of hypotheses, the strong energy condition (SEC) must be violated.] Alternatively, one can dispense with the minimal volume condition and define a generic bounce entirely in terms of the motion of test particles (future-pointing timelike geodesics), by looking at the expansion of their timelike geodesic congruences. One re-confirms that the SEC must be violated at or near the bounce. In contrast, it is easy to arrange for all the other standard energy conditions to be satisfied.Comment: 8 pages, ReV-TeX 3.

Riemannian geometry of irrotational vortex acoustics

We consider acoustic propagation in an irrotational vortex, using the technical machinery of differential geometry to investigate the ``acoustic geometry'' that is probed by the sound waves. The acoustic space-time curvature of a constant circulation hydrodynamical vortex leads to deflection of phonons at appreciable distances from the vortex core. The scattering angle for phonon rays is shown to be quadratic in the small quantity $\Gamma/(2\pi cb)$, where $\Gamma$ is the vortex circulation, $c$ the speed of sound, and $b$ the impact parameter.Comment: 4 pages, 2 figures, RevTex4. Discussion of focal length added; to appear in Physical Review Letter

Radionuclide Ionization in Protoplanetary Disks: Calculations of Decay Product Radiative Transfer

We present simple analytic solutions for the ionization rate $\zeta_{\rm{SLR}}$ arising from the decay of short-lived radionuclides (SLRs) within protoplanetary disks. We solve the radiative transfer problem for the decay products within the disk, and thereby allow for the loss of radiation at low disk surface densities; energy loss becomes important outside $R\gtrsim30$ for typical disk masses $M_g=0.04$ M$_\odot$. Previous studies of chemistry/physics in these disks have neglected the impact of ionization by SLRs, and often consider only cosmic rays (CRs), because of the high CR-rate present in the ISM. However, recent work suggests that the flux of CRs present in the circumstellar environment could be substantially reduced by relatively modest stellar winds, resulting in severely modulated CR ionization rates, $\zeta_{\rm{CR}}$, equal to or substantially below that of SLRs ($\zeta_{\rm{SLR}}\lesssim10^{-18}$ s$^{-1}$). We compute the net ionizing particle fluxes and corresponding ionization rates as a function of position within the disk for a variety of disk models. The resulting expressions are especially simple for the case of vertically gaussian disks (frequently assumed in the literature). Finally, we provide a power-law fit to the ionization rate in the midplane as a function of gas disk surface density and time. Depending on location in the disk, the ionization rates by SLRs are typically in the range $\zeta_{\rm{SLR}}\sim(1-10)\times10^{-19}$ s$^{-1}$.Comment: 7 pages, 4 figures, accepted to Ap

Muon spin rotation study of the topological superconductor SrxBi2Se3

We report transverse-field (TF) muon spin rotation experiments on single crystals of the topological superconductor Sr$_x$Bi$_2$Se$_3$ with nominal concentrations $x=0.15$ and $0.18$ ($T_c \sim 3$ K). The TF spectra ($B= 10$ mT), measured after cooling to below $T_c$ in field, did not show any additional damping of the muon precession signal due to the flux line lattice within the experimental uncertainty. This puts a lower bound on the magnetic penetration depth $\lambda \geq 2.3 ~\mu$m. However, when we induce disorder in the vortex lattice by changing the magnetic field below $T_c$ a sizeable damping rate is obtained for $T \rightarrow 0$. The data provide microscopic evidence for a superconducting volume fraction of $\sim 70~ \%$ in the $x=0.18$ crystal and thus bulk superconductivity.Comment: 6 pages, includes 4 figure

Fundamental limitations on "warp drive" spacetimes

"Warp drive" spacetimes are useful as "gedanken-experiments" that force us to confront the foundations of general relativity, and among other things, to precisely formulate the notion of "superluminal" communication. We verify the non-perturbative violation of the classical energy conditions of the Alcubierre and Natario warp drive spacetimes and apply linearized gravity to the weak-field warp drive, testing the energy conditions to first and second order of the non-relativistic warp-bubble velocity. We are primarily interested in a secondary feature of the warp drive that has not previously been remarked upon, if it could be built, the warp drive would be an example of a "reaction-less drive". For both the Alcubierre and Natario warp drives we find that the occurrence of significant energy condition violations is not just a high-speed effect, but that the violations persist even at arbitrarily low speeds. An interesting feature of this construction is that it is now meaningful to place a finite mass spaceship at the center of the warp bubble, and compare the warp field energy with the mass-energy of the spaceship. There is no hope of doing this in Alcubierre's original version of the warp-field, since by definition the point in the center of the warp bubble moves on a geodesic and is "massless". That is, in Alcubierre's original formalism and in the Natario formalism the spaceship is always treated as a test particle, while in the linearized theory we can treat the spaceship as a finite mass object. For both the Alcubierre and Natario warp drives we find that even at low speeds the net (negative) energy stored in the warp fields must be a significant fraction of the mass of the spaceship.Comment: 18 pages, Revtex4. V2: one reference added, some clarifying comments and discussion, no physics changes, accepted for publication in Classical and Quantum Gravit

The Hubble series: Convergence properties and redshift variables

In cosmography, cosmokinetics, and cosmology it is quite common to encounter physical quantities expanded as a Taylor series in the cosmological redshift z. Perhaps the most well-known exemplar of this phenomenon is the Hubble relation between distance and redshift. However, we now have considerable high-z data available, for instance we have supernova data at least back to redshift z=1.75. This opens up the theoretical question as to whether or not the Hubble series (or more generally any series expansion based on the z-redshift) actually converges for large redshift? Based on a combination of mathematical and physical reasoning, we argue that the radius of convergence of any series expansion in z is less than or equal to 1, and that z-based expansions must break down for z>1, corresponding to a universe less than half its current size. Furthermore, we shall argue on theoretical grounds for the utility of an improved parameterization y=z/(1+z). In terms of the y-redshift we again argue that the radius of convergence of any series expansion in y is less than or equal to 1, so that y-based expansions are likely to be good all the way back to the big bang y=1, but that y-based expansions must break down for y<-1, now corresponding to a universe more than twice its current size.Comment: 15 pages, 2 figures, accepted for publication in Classical and Quantum Gravit