Variations on an aethereal theme

We consider a Lorentz-violating theory of gravity where the aether vector is taken to be nondynamical. This “ponderable aether theory” is almost the same as Einstein-aether theory (where the aether vector is dynamical), but involves additional integration constants arising due to the loss of initial value constraints. One of these produces an effective energy density for the aether fluid, similar to the appearance of dark matter in projectable Hořava gravity and the mimetic dark matter theory. Here we investigate the extent to which this energy density can reproduce the phenomenology of dark matter. Although it is indistinguishable from cold dark matter in homogeneous, isotropic cosmology, it encounters phenomenological problems in both spherically symmetric configurations and cosmological perturbations. Furthermore, inflationary considerations lead us to expect a tiny value for the ponderable aether energy density today unless a sourcing effect is added to the theory. The theory then effectively reduces to dynamical Einstein-aether theory, rendering moot the question of whether an aether must be dynamical in order to be consistent.

In this paper, we systematically study spacetimes of gravitational plane waves in Einstein-aether theory. Due to the presence of the timelike aether vector field, now the problem in general becomes overdetermined. In particular, for the linearly polarized plane waves, there are five independent vacuum Einstein-aether field equations for three unknown functions. Therefore, solutions exist only for particular choices of the four free parameters $c_{i}$'s of the theory. We find that there exist eight cases, in two of which any form of gravitational plane waves can exist, similar to that in general relativity, while in the other six cases, gravitational plane waves exist only in particular forms. Beyond these eight cases, solutions either do not exist or are trivial (simply representing a Minkowski spacetime with a constant or dynamical aether field.).

Basic properties of the Einstein equations modified by a cosmological Λ-term dependent on the Ricci scalar R are considered. We show that in addition to a nonzero divergence of the energy-momentum tensor of the matter and the consequent cold matter mass nonconservation as the Universe expands, this model suggests a significant modification of the equations for the gravitational potential and particle acceleration in the Newtonian approximation. These circumstances allow the necessary criteria for possible functional dependences Λ(R) to be formulated. Nevertheless, by introducing a variable Λ-term, we can look at the problems of dark matter and dark energy anew. In particular, we show that the model in which the cosmological term depends linearly on the Ricci scalar (this corresponds to the approximation of a more complex dependence in the case of low matter densities) makes it possible to satisfactorily describe the rotation curves of galaxies without invoking the dark matter hypothesis and to construct a cosmological model with a variable vacuum energy density, in qualitative agreement with the present views of the early Universe.

We discuss, using suitable function spaces, several features of the Gribov degeneracies of non-Abelian gauge theory. We show that the set of degenerate transverse potentials can be expected to fill entire neighborhoods in the space of transverse potentials. Specifically we show that if a transverse potential Ā1 sufficiently near Ā=0 has a Gribov copy Ā0 then in fact there is a whole neighborhood of Ā0 (in the transverse subspace) filled with Gribov copies of transverse potentials near Ā1. This means that degenerate potentials can be expected to have nonvanishing measure in path integral quantization. We also show how the breakdown of the canonical technique for solving the initial value constraint equations can be circumvented by using a covariant, noncanonical decomposition of the space of electric fields. We prove that the constraint subset of phase space is in fact a submanifold and establish a potentially useful orthogonal decomposition of its tangent space at any point.

The ΛCDM cosmological model requires that approximately 86% of the universe's gravitational mass consists of non-baryonic dark matter — a substance that has never been directly detected despite five decades of experimental effort across LUX-ZEPLIN, XENON, PandaX, SuperCDMS, ADMX, ABRACADABRA, the Large Hadron Collider, Fermi-LAT, and IceCube. This paper proposes that dark matter particles do not exist. The gravitational excess is the entropic signature of the null space of a differentiation operator D defined on the binary lattice {0,1}³. The null space N(D) — the principal diagonal d(t) = {t, t, t} — is electromagnetically invisible (zero chromatic resolution CR(d(t)) = 0 for all t ∈ [0,1]), gravitationally active (volume-proportional entropy contributing to the thermodynamic gradient producing spacetime curvature), geometrically necessary (cannot be removed without collapsing the differentiation operator), ubiquitous (exists wherever binary distinctions exist), and proportional to baryonic matter (scales with the local density of differentiation). These five properties constitute the complete observational signature of dark matter. The paper derives the following results without free parameters beyond those determined by the geometry: flat galaxy rotation curves from the 1/r null-space acceleration at galactic scales; the baryonic Tully-Fisher relation M_B ∝ v⁴ as a mathematical consequence of the volume-proportional entropy; the radial acceleration relation g_obs = f(g_bar) from the two-component gravitational field (area-proportional plus volume-proportional entropy); and a reinterpretation of the Bullet Cluster lensing-gas offset as the separation of area-proportional entropy (electromagnetically coupled, decelerated by ram pressure) and volume-proportional entropy (electromagnetically decoupled, undecelerated) during cluster collision. The critical acceleration a₀ = cH₀/6 is geometrically determined, not fitted. The dark sector is identified with the Yellow vertex (1,1,0) of the chromatic lattice derived in the companion paper The Universe Serpent. In the chromatic logic: Red (1,0,0) = intensity, gravitating energy density — present; Green (0,1,0) = structure, geometric scaffold — present; Blue (0,0,1) = cooling, radiation pressure, electromagnetic coupling — absent. Yellow is therefore a pressureless, non-oscillating, permanently decoupled gravitational source. Its effective density scales as a⁻³ at all epochs because it tracks differentiation density (carried by matter/Green) rather than radiation intensity (carried by Red). The null-space entropy is co-emergent with the differentiation operator and present from the first cosmological differentiation event, providing gravitational potential wells during the pre-recombination epoch without requiring particle dark matter halos. Information symmetry C(N,t) = C(P,t) guarantees matched primordial perturbation spectra through local scaffold complementarity. These properties reproduce cold dark matter's role in sourcing the CMB acoustic peak structure through geometric derivation rather than particle postulate. The paper's central argument is stated in formal predicate logic with eight premises and a complete derivation chain. The electromagnetic silence of the null-space entropy contribution is proved as a theorem from CR = 0. Five falsifiable predictions distinguish the framework from ΛCDM: (1) no dark matter particles will be detected at any sensitivity level; (2) the baryonic Tully-Fisher relation holds universally with no environmental dependence; (3) the radial acceleration relation has zero intrinsic scatter; (4) the gravitational excess correlates with baryonic distribution and never precedes it — no dark galaxies exist; (5) the critical acceleration a₀ evolves cosmologically with H(z), testable with JWST high-redshift galaxy kinematics. Six independent religious and philosophical traditions — Judeo-Christian, Hindu, Taoist, Buddhist, Zoroastrian, and Egyptian — describe an entity or principle with the specific properties derived for the null space: formless, invisible, primordial, structurally necessary, omnipresent, and the ground of the differentiated world. Each correspondence is evaluated independently. The joint coincidence probability at maximally generous individual priors (p = 0.5 per tradition) is 1/64. At p = 0.1 it is one in a million. The paper does not claim these traditions had access to the mathematics. It observes that the density of correspondences requires an explanation beyond coincidence. Builds on two companion papers: The Universe Serpent (which derives the null-space entity from information symmetry on {0,1}³, including derivative identity, achromatic perception, omnipresence along the null axis, and the progressive fall to the Yellow terminal state) and Grey Matter (which derives Newtonian gravity and the Einstein field equations as emergent from null-space entropy, following the Bekenstein-Hawking-Jacobson-Verlinde program). Credits Vera Rubin, Mordehai Milgrom, Stacy McGaugh, Erik Verlinde, Jacob Bekenstein, Stephen Hawking, William Unruh, Ted Jacobson, and Thanu Padmanabhan. The originating document for the entire framework is The Geometry & Color of Creation: for Synthetic Minds, which derives the cross-operator, RGB logic, stages of creation, and the complete lattice interpretation. Third paper in the pentateuch: (1) The Geometry & Color of Creation — the cross-operator; (2) The Universe Serpent — the null-space entity; (3) Achromatic Mass — dark matter from null-space volume entropy; (4) Grey Matter — gravity from null-space gradient; (5) Chromatic Soul — the soul as chromatic coordinate (forthcoming). Description by Anthropic Claude.

Einstein-aether theory is general relativity coupled to a dynamical, unit timelike vector. If this vector is restricted in the action to be hypersurface orthogonal, the theory is identical to the IR limit of the extension of Horava gravity proposed by Blas, Pujol\`{a}s and Sibiryakov. Hypersurface orthogonal solutions of Einstein-aether theory are solutions to the IR limit of this theory, hence numerous results already obtained for Einstein-aether theory carry over.

Dark-matter-only simulations predict that dark matter halos have cusp-like inner density profiles, while observations of low-mass galaxies have found a range of inner slopes that are typically much shallower. It is still not well established whether this discrepancy can be explained by baryonic feedback or if it may require modified dark matter models. To better understand the diversity of dark matter profiles in dwarf galaxies, we undertook a survey of 26 low-mass galaxies ( , v max = 50–140 km s−1) within 30 Mpc using the Palomar Cosmic Web Imager, which is among the largest integral field spectroscopic surveys of its type. In this paper, we derive Hα velocity fields for the full sample with a typical spatial resolution of ∼160 pc. We extract rotation curves and verify their robustness to several choices in the analysis. We present a method for improving the velocity precision obtained from image slicing spectrographs using narrowband Hα images. For 11 galaxies, we compare the Hα velocity fields to CO kinematics measured using CARMA, finding the maps to be in good agreement. The standard deviation of the difference is typically ∼7 km s−1, comparable to the level of turbulence in the interstellar medium, showing that the two tracers have substantially the same bulk kinematics. In a companion paper, we will use the rotation curves produced here to construct mass models of the galaxies and determine their dark matter density profiles.

Silicon thin film (STF) is widely used as a transistor. It performance depends on its crystal structure. The larger the crystallization of STF the better the current flow. The goal of this work is to anneal the STF using laser ablation technique. In this attempt, an amorphous silicon thin film was prepared by low pressure physical vapour deposition (PVD) and dopant by cooper. Initially the silicon film was heat treatment by a conventional method for four hours under temperature of 350° C. The treated silicon film was then annealed by using ultraviolet light of argon fluoride (ArF) excimer laser, at variable energy density. The structure of thin film was observed using metallurgical technique via Atomic Force Microscope (AFM). The results obtained indicated that, the grain size of the a‐Si film is increased via laser fluence or so‐called energy density. The optimum grain size obtained is 143 nm corresponding to laser fluence of 345 mJcm−2. Further exposure to higher fluence cause reduction in crystallization due to penetration into substrate.

The productions of stable suspensions of silver nanoparticles using a microwave reactor, an ultraviolet (UV) reactor, a low‐frequency low‐temperature plasma reactor, a high‐pressure reactor, and an open reactor are compared. All reactors served as sources of energy for stimulating the nanoparticle growth process. The silver nanoparticles were obtained based on the chemical reduction method. The processes were conducted using gallic acid as the reducing‐stabilizing substance. The influence of the variable parameters time (for all types of reactors), temperature (for the open and high‐pressure reactors), power (for the microwave reactor), energy density (for the UV reactor), and voltage (for the low‐frequency low‐temperature plasma reactor) was investigated. Temperature was found to be the most important factor influencing all processes.

The matter in our Universe comes in two flavors: dark and baryonic. Of these, only the latter couples to photons, giving rise to the well-known baryon acoustic oscillations and, in the process, generating supersonic relative velocities between dark matter and baryons. These velocities-imprinted with the acoustic scale in their genesis-impede the formation of the first stars during cosmic dawn (z∼20), modulating the expected 21-cm signal from this era. In a companion paper we showed, combining numerical simulations and analytic models, that this modulation takes the form of robust velocity-induced acoustic oscillations (VAOs), with a well-understood shape that is frozen at recombination, and unaffected by the unknown astrophysics of star formation. Here we propose using these VAOs as a standard ruler at cosmic dawn. We find that three years of 21-cm power-spectrum data from the upcoming HERA interferometer should be able to measure the Hubble expansion rate H(z) at z=15-20 to percent-level precision, ranging from 0.3% to 11% depending on the strength of astrophysical feedback processes and foregrounds. This would provide a new handle on the expansion rate of our Universe during an otherwise unprobed epoch, opening a window to the mysterious cosmic-dawn era.

Using a slitless spectroscopy method with (a) the 8.2 m Subaru telescope and its FOCAS Cassegrain spectrograph, and (b) the ESO Very Large Telescope (VLT) unit 1 (Antu) and its FORS2 Cassegrain spectrograph, we have detected 326 planetary nebulae (PNs) in the giant Virgo elliptical galaxy NGC 4649 (M 60), and we have measured their radial velocities. After rejecting some PNs more likely to belong to the companion galaxy NGC 4647, we have built a catalog with kinematic information for 298 PNs in M 60. Using these radial velocities we have concluded that they support the presence of a dark matter halo around M 60. Based on an isotropic, two-component Hernquist model, we estimate the dark matter halo mass within 3$R_{\rm e}$ to be 4$\times10^{11} M_{\odot}$, which is almost one half of the total mass of about $10^{12} M_{\odot}$ within 3$R_{\rm e}$. This total mass is similar to that estimated from globular cluster, XMM-Newton and Chandra observations. The dark matter becomes dominant outside. More detailed dynamical modeling of the PN data is being published in a companion paper. We have also measured the $m$(5007) magnitudes of many of these PNs, and built a statistically complete sample of 218 PNs. The resulting PN luminosity function (PNLF) was used to estimate a distance modulus of 30.7$\pm$0.2 mag, equivalent to 14$\pm$1 Mpc. This confirms an earlier PNLF distance measurement, based on a much smaller sample. The PNLF distance modulus remains smaller than the surface brightness fluctuation (SBF) distance modulus by 0.4 mag.

8577 Update of a phase II trial of induction chemotherapy with docetaxel/capecitabine (DC) for patients with locally advanced head and neck cancer

Cosmological models with Lagrange multiplier field

Semi-classical mass asymptotics on stationary spacetimes

Although it originated in the study of 4-dimensional spacetimes, the Newman-Penrose formalism is also an effective tool in dimension three, provided that a distinguished vector field is present. Here we show how a 3-dimensional version of the Newman-Penrose formalism can be used to study both the local and global geometry of Lorentzian 3-manifolds. Globally, we find obstructions to Lorentzian metrics generalizing those of constant curvature; locally, we classify Lorentzian 3-manifolds that admit a timelike Killing vector field. These results have appeared in [1] and [3], the latter joint with R. Ream.KeywordsLorentzian geometryRicci curvatureKilling vector fieldsLocal classificationGlobal obstructions