Annals of physics

THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

Quintom Cosmology: theoretical implications and observations

We present distance measurements to 71 high redshift type Ia supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color light-curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands. Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshift. With this data set, we have built a Hubble diagram extending to z = 1, with all distance measurements involving at least two bands. Systematic uncertainties are evaluated making use of the multiband photometry obtained at CFHT. Cosmological fits to this first year SNLS Hubble diagram give the following results: {Omega}{sub M} = 0.263 {+-} 0.042 (stat) {+-} 0.032 (sys) for a flat {Lambda}CDM model; and w = -1.023 {+-} 0.090 (stat) {+-} 0.054 (sys) for a flat cosmology with constant equation of state w when combined with the constraint from the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations.

The Supernova Legacy Survey: Measurement of Omega_m, Omega_l and w from the First Year Data Set

Advances in physics

Self-consistent solutions to the nonlinear spinor field equations in general relativity are studied for the case of Bianchi type-I (BI) space-time. It is shown that, for some special type of nonlinearity the model provides a regular solution, but this singularity-free solution is attained at the cost of breaking the dominant energy condition in the Hawking-Penrose theorem. It is also shown that the introduction of a $\ensuremath{\Lambda}$ term in the Lagrangian generates oscillations of the BI model, which is not the case in the absence of a $\ensuremath{\Lambda}$ term. Moreover, for the linear spinor field, the $\ensuremath{\Lambda}$ term provides oscillatory solutions, which are regular everywhere, without violating the dominant energy condition.

Spinor field in a Bianchi type-I universe: Regular solutions

We consider a self-consistent system of interacting spinor and scalar fields within the framework of a Bianchi type-I (BI) cosmological model filled with perfect fluid. The interacting term in the Lagrangian is chosen in the form of derivative coupling, i.e., ${\mathcal{L}}_{\mathrm{int}}=(\ensuremath{\lambda}/2){\ensuremath{\varphi}}_{,\ensuremath{\alpha}}{\ensuremath{\varphi}}^{,\ensuremath{\alpha}}F.$ Here F is a power or trigonometric function of the invariants I and/or J constructed from bilinear spinor forms $S=\overline{\ensuremath{\psi}}\ensuremath{\psi}$ and $P=i\overline{\ensuremath{\psi}}{\ensuremath{\gamma}}^{5}\ensuremath{\psi}.$ Self-consistent solutions to the spinor, scalar, and BI gravitational field equations are obtained. The problems of an initial singularity and the asymptotically isotropization process of the initially anisotropic space-time are studied. The role of the cosmological constant $(\ensuremath{\Lambda}$ term) in the evolution of a BI Universe is studied. It is shown that a positive $\ensuremath{\Lambda}$ generates an oscillatory mode of expansion of the BI model, whereas if F in ${\mathcal{L}}_{\mathrm{int}}$ is chosen to be a trigonometric function of its arguments, there exists a nonexponential mode of evolution even with a negative $\ensuremath{\Lambda}.$ It is shown also that for a suitable choice of problem parameters the present model allows regular solutions without a broken dominant energy condition.

Bianchi type I cosmology with scalar and spinor fields

We consider a self-consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy given by a cosmological constant. The perfect fluid is chosen to be the one obeying either the usual equation of state, i.e., p = ζ, with ζ ∊ [0, 1] or a van der Waals equation of state. Role of the Λ term in the evolution of the BI Universe has been studied.

https://wwwinfo.jinr.ru/~bijan/my_papers/lambda_ass_06.pdf

Anisotropic Cosmological Models with a Perfect Fluid and a Λ Term

We consider a self consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., p = ξe, with ζ∉[0, 1] whereas, the dark energy is considered to be obeying a quintessence-like equation of state. The modification of the ordinary quintessence lies in the fact that its pressure becomes positive if the (dark) energy density exceeds some critical value. Exact solutions to the corresponding Einstein equations are obtained. The model in consideration gives rise to a Universe which is spatially finite. Depending on the choice of problem parameters the Universe is either close with a space-time singularity, or an open one which is oscillatory, regular and infinite in time.

https://wwwinfo.jinr.ru/~bijan/my_papers/ijtp_osc.pdf

Anisotropic Cosmological Models with Perfect Fluid and Dark Energy Reexamined

In this paper we study the evolution of the dark energy parameter within the scope of a spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and dark energy by revisiting the recent results (Amirhashchi et al. in Chin. Phys. Lett. 28:039801, 2011a). To prevail the deterministic solution we select the scale factor $a(t) = \sqrt{t^{n}e^{t}}$
 which generates a time-dependent deceleration parameter (DP), representing a model which generates a transition of the universe from the early decelerating phase to the recent accelerating phase. We consider the two cases of an interacting and non-interacting two-fluid (barotropic and dark energy) scenario and obtained general results. The cosmic jerk parameter in our derived model is also found to be in good agreement with the recent data of astrophysical observations under the suitable condition. The physical aspects of the models and the stability of the corresponding solutions are also discussed.

Bijan Saha

Papers

Spinor field in a Bianchi type-I universe: Regular solutions

Bianchi type I cosmology with scalar and spinor fields

Anisotropic Cosmological Models with a Perfect Fluid and a Λ Term

Anisotropic Cosmological Models with Perfect Fluid and Dark Energy Reexamined

Two-Fluid Scenario for Dark Energy Models in an FRW Universe-Revisited