The Quaternionic Quantum Mechanics

A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form $\frac{1}{c^2}\frac{\partial^2\psi_0}{\partial t^2} - \nabla^2\psi_0+2(\frac{m_0}{\hbar})\frac{\partial\psi_0}{\partial t}+(\frac{m_0c}{\hbar})^2\psi_0=0$. This reduces to the massless Klein-Gordon equation, if we replace $\frac{\partial}{\partial t}\to\frac{\partial}{\partial t}+\frac{m_0c^2}{\hbar}$. For a plane wave solution the angular frequency is complex and is given by $\vec{\omega}_\pm=i\frac{m_0c^2}{\hbar}\pm c\vec{k}$, where $\vec{k}$ is the propagation constant vector. This equation is in agreement with the Einstein energy-momentum formula. The spin of the particle is obtained from the interaction of the particle with the photon field.Comment: 13 Latex pages, no figure

The Equivalence between Different Dark (Matter) Energy Scenarios

We have shown that the phenomenological models with a cosmological constant of the type $\Lambda=\beta(\frac{\ddot R}{R})$ and $\Lambda=3\alpha H^2$, where $R$ is the scale factor of the universe and $H$ is the Hubble constant, are equivalent to a quintessence model with a scalar ($\phi$) potential of the form $V\propto \phi^{-n}, n$ = constant. The equation of state of the cosmic fluid is described by these parameters ($\alpha, \beta, n$) only. The equation of state of the cosmic fluid (dark energy) can be determined by any of these parameters. The actual amount of dark energy will define the equation of state of the cosmic fluid. All of the three forms can give rise to cosmic acceleration depending the amount of dark energy in the universe

Viscous Dark Energy Models with Variable G and Lambda

We consider a cosmological model with bulk viscosity ($\eta$) and variable cosmological $(\Lambda\propto \rho^{-\alpha}, \alpha=\rm const.$) and gravitational ($G$) constants. The model exhibits many interesting cosmological features. Inflation proceeds du to the presence of bulk viscosity and dark energy without requiring the equation of state $p=-\rho$. During the inflationary era the energy density ($\rho$) does not remain constant, as in the de-Sitter type. Moreover, the cosmological and gravitational constants increase exponentially with time, whereas the energy density and viscosity decrease exponentially with time. The rate of mass creation during inflation is found to be very huge suggesting that all matter in the universe was created during inflation.Comment: 6 Latex page

A mass-extended 't Hooft-Nobbenhuis complex transformations and their consequences

We have extended the 't Hooft-Nobbenhuis complex transformations to include mass. Under these new transformations, Schrodinger, Dirac, Klein-Gordon and Einstein general relativity equations are invariant. The non invariance of the cosmological constant in Einstein field equations dictates it to vanish thus solving the longstanding cosmological constant problem.Comment: 6 LateX pages, no figure