In this paper, we prove a classification theorem of 4-manifolds according to some conformal invariants, which generalizes the conformally invariant sphere theorem of Chang-Gursky-Yang cite{CGY}. Moreover, it provides a four-dimensional analogue of th
e well-known classification theorem of Schoen-Yau cite{SY2} on 3-manifolds with positive Yamabe invariants.
We propose a model of asymmetric dark matter (DM) where the dark sector is an identical copy of both forces and matter of the standard model (SM) as in the mirror universe models discussed in literature. In addition to being connected by gravity, the
SM and DM sectors are also connected at high temperature by a common set of heavy right-handed Majorana neutrinos via their Yukawa couplings to leptons and Higgs bosons. The lightest nucleon in the dark (mirror) sector is a candidate for dark matter. The out of equilibrium decay of right-handed neutrino produces equal lepton asymmetry in both sectors via resonant leptogenesis which then get converted to baryonic and dark baryonic matter. The dark baryon asymmetry due to higher dark nucleon masses leads to higher dark matter density compared to the familiar baryon density that is observed. The standard model neutrinos in this case acquire masses from the inverse seesaw mechanism. A kinetic mixing between the U(1) gauge fields of the two sectors is introduced to guarantee the success of Big-Bang Nucleosynthesis.
We discuss various aspects of models with long-lived or stable colored particles. In particular we focus on an ideal Quirk model with electroweak neutral heavy (O(TeV)) particles which carry ordinary color and another $ SU(3)$ color with a very low s
cale $Lambda$. We show that contrary to what one might think, such a model is cosmologically consistent and evades many Pitfalls even for very low O(10 eV) $Lambda$ and without assuming a low reheat temperature. We also show that the expected production of Quirks by cosmic rays which are incorporated in heavy Isotopes in Ocean water is consistent with the highly stringent bounds on the latter. This evades a real threat to the Quirk model which would have excluded it regardless of Cosmology. Finally we briefly comment on possible LHC signatures.
We briefly review some recent Cold Dark Matter (CDM) models. Our main focus are charge symmetric models of WIMPs which are not the standard SUSY LSPs (Lightest Supersymmetric Partners). We indicate which experiments are most sensitive to certain aspe
cts of the models. In particular we discuss the manifestations of the new models in neutrino telescopes and other set-ups. We also discuss some direct detection experiments and comment on measuring the direction of recoil ions--which is correlated with the direction of the incoming WIMP. This could yield daily variations providing along with the annual modulation signatures for CDM.
The ongoing experimental efforts in the high energy and high precision communities keep providing evidence for CPT, a fundamental symmetry holding in any local Lorentz invariant theory. We suggest possible interconnections between different CPT viola
ting parameters. Specifically, the very precise test of CPT in the $K^0-bar K^0$ system suggests--though definitely does not imply--that CPT violations in other observable parameters (mass, width, charge, magnetic moments, etc.) are much smaller than the directly measured bounds.
An early phase of theoretical high energy physics in Israel specifically that connected with Yuval Neeman and a small group of my classmates, myself, and several others who worked around him after his return to Israel on the Eight-fold way as seen by me is briefly described.
We consider Wimp annihilations into monochromatic and continuous $gamma$s and the angular distribution of the resulting gammas. We discuss how the WIMP density profile can be reconstructed from the angular dependence of the photon flux.
We propose a new class of R-parity violating extension of MSSM with type II seesaw mechanism for neutrino masses where an unstable gravitino is the dark matter of the Universe. It decays predominantly into three leptons final states, thereby providin
g a natural explanation of the positron excess but no antiproton excess in the PAMELA experiment. The model can explain neutrino masses without invoking any high scale physics while keeping the pre-existing baryon asymmetry of the universe in tact.
Unparticle $U$ with scaling dimension $d_U$ has peculiar thermal properties due to its unique phase space structure. We find that the equation of state parameter $omega_U$, the ratio of pressure to energy density, is given by $1/(2d_U +1)$ providing
a new form of energy in our universe. In an expanding universe, the unparticle energy density $rho_U(T)$ evolves dramatically differently from that for photons. For $d_U >1$, even if $rho_U(T_D)$ at a high decoupling temperature $T_D$ is very small, it is possible to have a large relic density $rho_U(T^0_gamma)$ at present photon temperature $T^0_gamma$, large enough to play the role of dark matter. We calculate $T_D$ and $rho_U(T^0_gamma)$ using photon-unparticle interactions for illustration.
In this paper, we completely classify all compact 4-manifolds with positive isotropic curvature. We show that they are diffeomorphic to $mathbb{S}^4,$ or $mathbb{R}mathbb{P}^4$ or quotients of $mathbb{S}^3times mathbb{R}$ by a cocompact fixed point f
ree subgroup of the isometry group of the standard metric of $mathbb{S}^3times mathbb{R}$, or a connected sum of them.
