Congruence lattices of semilattices

The main result of this paper is that the class of congruence lattices of semilattices satisfies no nontrivial lattice identities. It is also shown that the class of subalgebra lattices of semilattices satisfies no nontrivial lattice identities. As a consequence it is shown that if V is a semigroup variety all of whose congruence lattices satisfy some fixed nontrivial lattice identity, then all the members of V are groups with exponent dividing a fixed finite number

Chain Inflation in the Landscape: "Bubble Bubble Toil and Trouble"

In the model of Chain Inflation, a sequential chain of coupled scalar fields drives inflation. We consider a multidimensional potential with a large number of bowls, or local minima, separated by energy barriers: inflation takes place as the system tunnels from the highest energy bowl to another bowl of lower energy, and so on until it reaches the zero energy ground state. Such a scenario can be motivated by the many vacua in the stringy landscape, and our model can apply to other multidimensional potentials. The ''graceful exit'' problem of Old Inflation is resolved since reheating is easily achieved at each stage. Coupling between the fields is crucial to the scenario. The model is quite generic and succeeds for natural couplings and parameters. Chain inflation succeeds for a wide variety of energy scales -- for potentials ranging from 10MeV scale inflation to $10^{16}$ GeV scale inflation.Comment: 31 pages, 3 figures, one reference adde

Dark matter and the first stars: a new phase of stellar evolution

A mechanism is identified whereby dark matter (DM) in protostellar halos dramatically alters the current theoretical framework for the formation of the first stars. Heat from neutralino DM annihilation is shown to overwhelm any cooling mechanism, consequently impeding the star formation process and possibly leading to a new stellar phase. A "dark star'' may result: a giant ($\gtrsim 1$ AU) hydrogen-helium star powered by DM annihilation instead of nuclear fusion. Observational consequences are discussed.Comment: 5 pages, 2 figures; replaced with accepted versio

Determining Dark Matter properties with a XENONnT/LZ signal and LHC-Run3 mono-jet searches

We develop a method to forecast the outcome of the LHC Run 3 based on the hypothetical detection of $\mathcal{O}(100)$ signal events at XENONnT. Our method relies on a systematic classification of renormalisable single-mediator models for dark matter-quark interactions, and is valid for dark matter candidates of spin less than or equal to one. Applying our method to simulated data, we find that at the end of the LHC Run 3 only two mutually exclusive scenarios would be compatible with the detection of $\mathcal{O}(100)$ signal events at XENONnT. In a first scenario, the energy distribution of the signal events is featureless, as for canonical spin-independent interactions. In this case, if a mono-jet signal is detected at the LHC, dark matter must have spin 1/2 and interact with nucleons through a unique velocity-dependent operator. If a mono-jet signal is not detected, dark matter interacts with nucleons through canonical spin-independent interactions. In a second scenario, the spectral distribution of the signal events exhibits a bump at non zero recoil energies. In this second case, a mono-jet signal can be detected at the LHC Run 3, dark matter must have spin 1/2 and interact with nucleons through a unique momentum-dependent operator. We therefore conclude that the observation of $\mathcal{O}(100)$ signal events at XENONnT combined with the detection, or the lack of detection, of a mono-jet signal at the LHC Run 3 would significantly narrow the range of possible dark matter-nucleon interactions. As we argued above, it can also provide key information on the dark matter particle spin.Comment: 17 pages, 8 figures, updated operator coefficients and figures, version accepted by PR

MACHOs, White Dwarfs, and the Age of the Universe

(Abridged Abstract) A favored interpretation of recent microlensing measurements towards the Large Magellanic Cloud implies that a large fraction (i.e. 10--50%) of the mass of the galactic halo is composed of white dwarfs. We compare model white dwarf luminosity functions to the data from the observational surveys in order to determine a lower bound on the age of any substantial white dwarf halo population (and hence possibly on the age of the Universe). We compare various theoretical white dwarf luminosity functions, in which we vary hese three parameters, with the abovementioned survey results. From this comparison, we conclude that if white dwarfs do indeed constitute more than 10% of the local halo mass density, then the Universe must be at least 10 Gyr old for our most extreme allowed values of the parameters. When we use cooling curves that account for chemical fractionation and more likely values of the IMF and the bolometric correction, we find tighter limits: a white dwarf MACHO fraction of 10% (30%) requires a minimum age of 14 Gyr (15.5 Gyr). Our analysis also indicates that the halo white dwarfs almost certainly have helium-dominated atmospheres.Comment: Final version accepted for publication, straight TeX formate, 6 figs, 22 page

On an easy transition from operator dynamics to generating functionals by Clifford algebras

Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that opposite Clifford algebras have to be used also. Based on this mathematics, we give a fully Clifford algebraic account on generating functionals, which is thereby geometric. The field operators are shown to be Clifford and opposite Clifford maps. This picture relying on geometry does not need positivity in principle. Furthermore, we propose a transition from operator dynamics to corresponding generating functionals, which is based on the algebraic techniques. As a calculational benefit, this transition is considerable short compared to standard ones. The transition is not injective (unique) and depends additionally on the choice of an ordering. We obtain a direct and constructive connection between orderings and the explicit form of the functional Hamiltonian. These orderings depend on the propagator of the theory and thus on the ground state. This is invisible in path integral formulations. The method is demonstrated within two examples, a non-linear spinor field theory and spinor QED. Antisymmetrized and normal-ordered functional equations are derived in both cases.Comment: 23p., 76kB, plain LaTeX, [email protected]

Fluid Interpretation of Cardassian Expansion

A fluid interpretation of Cardassian expansion is developed. Here, the Friedmann equation takes the form $H^2 = g(\rho_M)$ where $\rho_M$ contains only matter and radiation (no vacuum). The function g(\rhom) returns to the usual 8\pi\rhom/(3 m_{pl}^2) during the early history of the universe, but takes a different form that drives an accelerated expansion after a redshift $z \sim 1$. One possible interpretation of this function (and of the right hand side of Einstein's equations) is that it describes a fluid with total energy density \rho_{tot} = {3 m_{pl}^2 \over 8 \pi} g(\rhom) = \rhom + \rho_K containing not only matter density (mass times number density) but also interaction terms $\rho_K$. These interaction terms give rise to an effective negative pressure which drives cosmological acceleration. These interactions may be due to interacting dark matter, e.g. with a fifth force between particles $F \sim r^{\alpha -1}$. Such interactions may be intrinsically four dimensional or may result from higher dimensional physics. A fully relativistic fluid model is developed here, with conservation of energy, momentum, and particle number. A modified Poisson's equation is derived. A study of fluctuations in the early universe is presented, although a fully relativistic treatment of the perturbations including gauge choice is as yet incomplete.Comment: 25 pages, 1 figure. Replaced with published version. Title changed in journa

Chemical Abundance Constraints on White Dwarfs as Halo Dark Matter

We examine the chemical abundance constraints on a population of white dwarfs in the Halo of our Galaxy. We are motivated by microlensing evidence for massive compact halo objects (Machos) in the Galactic Halo, but our work constrains white dwarfs in the Halo regardless of what the Machos are. We focus on the composition of the material that would be ejected as the white dwarfs are formed; abundance patterns in the ejecta strongly constrain white dwarf production scenarios. Using both analytical and numerical chemical evolution models, we confirm that very strong constraints come from Galactic Pop II and extragalactic carbon abundances. We also point out that depending on the stellar model, significant nitrogen is produced rather than carbon. The combined constraints from C and N give $\Omega_{WD} h < 2 \times 10^{-4}$ from comparison with the low C and N abundances in the Ly$\alpha$ forest. We note, however, that these results are subject to uncertainties regarding the nucleosynthesis of low-metallicity stars. We thus investigate additional constraints from D and $^4$He, finding that these light elements can be kept within observational limits only for \Omega_{WD} \la 0.003 and for a white dwarf progenitor initial mass function sharply peaked at low mass (2$M_\odot$). Finally, we consider a Galactic wind, which is required to remove the ejecta accompanying white dwarf production from the galaxy. We show that such a wind can be driven by Type Ia supernovae arising from the white dwarfs themselves, but these supernovae also lead to unacceptably large abundances of iron. We conclude that abundance constraints exclude white dwarfs as Machos. (abridged)Comment: Written in AASTeX, 26 pages plus 4 ps figure

Chloroquine-resistant Plasmodium falciparum malaria in the Kavango region of Namibia

The sensitivity to chloroquine of Plasmodium falciparum from the Kavango region of Namibia was determined by a 24-hour test in vitro. Twenty-six Isolates were successfully tested, of which 11 were resistant to a low degree, schizogony being inhibited at 8 pmollwell. The results of the Dill-Glazko test for the presence of 4-amlnoquinolines in urine indicate that chloroquine is not Widely used in the area

Inflating with the QCD Axion

We show that the QCD axion can drive inflation via a series of tunneling events. For axion models with a softly broken $Z_N$ symmetry, the axion potential has a series of $N$ local minima and may be modeled by a tilted cosine. Chain inflation results along this tilted cosine: the field tunnels from an initial minimum near the top of the potential through a series of ever lower minima to the bottom. This results in sufficient inflation and reheating. QCD axions, potentially detectable in current searches, may thus simultaneously solve problems in particle physics and provide inflation.Comment: 5 pages, 1 figure, revised for submission to PR