Yeuk-Kwan E. Cheung

Big-Bounce Genesis

Ernest Rutherford Physics Building, McGill University,3600 rue University, Montreal, QC H3A 2T8, Canada(Dated: March 25, 2014)We report on the possibility to use dark matter mass and its interaction cross section as a smokinggun signal of the existence of a big bounce at the early stage in the evolution of our currently observeduniverse. A model independent study of dark matter production in the contraction and expansionphasesof the bounce universe reveals a newvenue for achieving the observed relic abundance in whicha significantly smaller amount of dark matter–compared to the standard cosmology–is produced andsurvives until today, diluted only by the cosmic expansion since the radiation dominated era. OnceDM mass and its interaction strength with ordinary matter are determined by experiments, thisalternative route becomes a signature of the bounce universe scenario.

Direct dark matter searches—Test of the Big Bounce Cosmology

We consider the possibility of using dark matter particles mass and its interaction cross section as a smoking gun signal of the existence of a Big Bounce at the early stage in the evolution of our currently observed universe. A study of dark matter production in the pre-bounce contraction and the post bounce expansion epochs of this universe reveals a new venue for achieving the observed relic abundance of our present universe. Specifically, it predicts a characteristic relation governing a dark matter mass and interaction cross section and a factor of 1/2 in thermally averaged cross section, as compared to the non-thermal production in standard cosmology, is needed for creating enough dark matter particle to satisfy the currently observed relic abundance because dark matter is being created during the pre-bounce contraction, in addition to the post-bounce expansion. As the production rate is lower than the Hubble expansion rate information of the bounce universe evolution is preserved. Therefore once the value of dark matter mass and interaction cross section are obtained by direct detection in laboratories, this alternative route becomes a signature prediction of the bounce universe scenario. This leads us to consider a scalar dark matter candidate, which if it is light, has important implications on dark matter searches.

Nonplanar on-shell diagrams and leading singularities of scattering amplitudes

Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto–Cachazo–Feng–Witten (BCFW) decomposable on-shell diagram process a rational top form if and only if the algebraic ideal comprised the geometrical constraints are shifted linearly during successive BCFW integrations. With a proper geometric interpretation of the constraints in the Grassmannian manifold, the rational top form integration contours can thus be obtained, and understood, in a straightforward way. All rational top form integrands of arbitrary higher loops leading singularities can therefore be derived recursively, as long as the corresponding on-shell diagram is BCFW decomposable.

A differential operator for integrating one-loop scattering equations

A bstractWe propose a differential operator for computing the residues associated with a class of meromorphic n-forms that frequently appear in the Cachazo-He-Yuan form of the scattering amplitudes. This differential operator is conjectured to be uniquely determined by the local duality theorem and the intersection number of the divisors in the n-form. We use the operator to evaluate the one-loop integrand of Yang-Mills theory from their generalized CHY formulae. The method can reduce the complexity of the calculation. In addition, the expression for the 1-loop four-point Yang-Mills integrand obtained in our approach has a clear correspondence with the Q-cut results.

Effective action for cosmological scalar fields at finite temperature

A bstractScalar fields appear in many theories beyond the Standard Model of particle physics. In the early universe, they are exposed to extreme conditions, including high temperature and rapid cosmic expansion. Understanding their behavior in this environment is crucial to understand the implications for cosmology. We calculate the finite temperature effective action for the field expectation value in two particularly important cases, for damped oscillations near the ground state and for scalar fields with a flat potential. We find that the behavior in both cases can in good approximation be described by a complex valued effective potential that yields Markovian equations of motion. Near the potential minimum, we recover the solution to the well-known Langevin equation. For large field values we find a very different behavior, and our result for the damping coefficient differs from the expressions frequently used in the literature. We illustrate our results in a simple scalar model, for which we give analytic approximations for the effective potential and damping coefficient. We also provide various expressions for loop integrals at finite temperature that are useful for future calculations in other models.

A combinatoric shortcut to evaluate CHY-forms

A bstractIn our recent work, we proposed a differential operator for the evaluation of the multi-dimensional residues on isolated (zero-dimensional) poles. In this paper we discuss some new insight on evaluating the (generalized) Cachazo-He-Yuan (CHY) forms of the scattering amplitudes using this differential operator. We introduce a tableau represen-tation for the coefficients appearing in the proposed differential operator. Combining the tableaux with the polynomial form of the scattering equations, the evaluation of the gen-eralized CHY form becomes a simple combinatoric problem. It is thus possible to obtain the coefficients arising in the differential operator in a straightforward way. We present the procedure for a complete solution of the n-gon amplitudes at one-loop level in a generalized CHY form. We also apply our method to fully evaluate the one-loop five-point amplitude in the maximally supersymmetric Yang-Mills theory; the final result is identical to the one obtained by Q-Cut.

Light WIMP searches involving electron scattering

In the present work we examine the possibility for detecting electrons in dark matter searches. These detectors are considered to be the most appropriate for detecting light dark matter particles in the MeV region. We analyze theoretically some key issues involved in such a detection and we perform calculations for the expected rates employing reasonable theoretical models.

Permutation relations of generalized Yangian Invariants, unitarity cuts, and scattering amplitudes

A bstractWe find a permutation relation among the generalized Yangian Invariants — two Yangian Invariants with adjacent external lines exchanged are related by a simple kinematic factor — which is shown to be equivalent to U(1) decoupling and Bern-Carrasco-Johansson (BCJ) relation at the level of maximal helicity violating (MHV) amplitudes. We propose using unitarity cuts to study nonplanar amplitudes and to systematically reconstruct the integrands of nonplanar MHV amplitudes, up to a rational function which vanishes under all possible unitarity cuts. This is made possible with the newly found permutation relations by converting nonplanar on-shell diagrams into planar ones. As explicit examples the construction of one-loop double-trace MHV amplitudes of 4- and 5-point interactions are presented using on-shell diagrams. The kinematic factors and the resultant planar diagrams are carefully dealt with using the unitarity cut conditions. The first next-to-MHV amplitudes are addressed using generalized unitarity cuts. Their leading singularities can be identified as residues of the Grassmanian integrals. These examples also serve to demonstrate the power of the newly found relation of the generalized Yangian Invariants.

No-ghost theorem for the bosonic Nappi-Witten string

We prove a no-ghost theorem for a bosonic string propagating in Nappi-Witten spacetime. This is achieved in two steps. We first demonstrate unitarity for a class of NW/U(1) modules: the norm of any ...

CONSTRAINING THE STRING GAUGE FIELD BY GALAXY ROTATION CURVES AND PERIHELION PRECESSION OF PLANETS

We discuss a cosmological model in which the string gauge field coupled universally to matter gives rise to an extra centripetal force and will have observable signatures on cosmological and astronomical observations. Several tests are performed using data including galaxy rotation curves of 22 spiral galaxies of varied luminosities and sizes and perihelion precessions of planets in the solar system. The rotation curves of the same group of galaxies are independently fit using a dark matter model with the generalized Navarro-Frenk-White (NFW) profile and the string model. A remarkable fit of galaxy rotation curves is achieved using the one-parameter string model as compared to the three-parameter dark matter model with the NFW profile. The average χ2 value of the NFW fit is 9% better than that of the string model at a price of two more free parameters. Furthermore, from the string model, we can give a dynamical explanation for the phenomenological Tully-Fisher relation. We are able to derive a relation between field strength, galaxy size, and luminosity, which can be verified with data from the 22 galaxies. To further test the hypothesis of the universal existence of the string gauge field, we apply our string model to the solar system. Constraint on the magnitude of the string field in the solar system is deduced from the current ranges for any anomalous perihelion precession of planets allowed by the latest observations. The field distribution resembles a dipole field originating from the Sun. The string field strength deduced from the solar system observations is of a similar magnitude as the field strength needed to sustain the rotational speed of the Sun inside the Milky Way. This hypothesis can be tested further by future observations with higher precision.