Quantum fluctuations of Cosmological Perturbations in Generalized Gravity

Recently, we presented a unified way of analysing classical cosmological perturbation in generalized gravity theories. In this paper, we derive the perturbation spectrums generated from quantum fluctuations again in unified forms. We consider a situation where an accelerated expansion phase of the early universe is realized in a particular generic phase of the generalized gravity. We take the perturbative semiclassical approximation which treats the perturbed parts of the metric and matter fields as quantum mechanical operators. Our generic results include the conventional power-law and exponential inflations in Einstein's gravity as special cases.Comment: 5 pages, revtex, no figure

Unified Analysis of Cosmological Perturbations in Generalized Gravity

In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the scalar field and the scalar curvature in the Lagrangian, thus includes broad classes of generalized gravity theories resulting from recent attempts for the unification. We analyze both the scalar-type mode and the gravitational wave in analogous ways. For both modes the large scale evolutions are characterized by the same conserved quantities which are valid in the Einstein's gravity. This unified and simple treatment is possible due to our proper choice of the gauges, or equivalently gauge invariant combinations.Comment: 4 pages, revtex, no figure

Relativistic Hydrodynamic Cosmological Perturbations

Relativistic cosmological perturbation analyses can be made based on several different fundamental gauge conditions. In the pressureless limit the variables in certain gauge conditions show the correct Newtonian behaviors. Considering the general curvature ($K$) and the cosmological constant ($\Lambda$) in the background medium, the perturbed density in the comoving gauge, and the perturbed velocity and the perturbed potential in the zero-shear gauge show the same behavior as the Newtonian ones in general scales. In the first part, we elaborate these Newtonian correspondences. In the second part, using the identified gauge-invariant variables with correct Newtonian correspondences, we present the relativistic results with general pressures in the background and perturbation. We present the general super-sound-horizon scale solutions of the above mentioned variables valid for general $K$, $\Lambda$, and generally evolving equation of state. We show that, for vanishing $K$, the super-sound-horizon scale evolution is characterised by a conserved variable which is the perturbed three-space curvature in the comoving gauge. We also present equations for the multi-component hydrodynamic situation and for the rotation and gravitational wave.Comment: 16 pages, no figure, To appear in Gen. Rel. Gra

String theoretic axion coupling and the evolution of cosmic structures

We examine the effects of the axion coupling to $R\tilde{R}$ on the evolution of cosmic structures. It is shown that the evolutions of the scalar- and vector-type perturbations are not affected by this axion coupling. However the axion coupling causes an asymmetric evolution of the two polarization states of the tensor-type perturbation, which may lead to a sizable polarization asymmetry in the cosmological gravitational wave if inflation involves a period in which the axion coupling is important. The polarization asymmetry produced during inflation are conserved over the subsequent evolution as long as the scales remain in the large-scale limit, and thus this may lead to an observable trace in the cosmic microwave background radiation.Comment: 10 pages, REVte

COBE constraints on inflation models with a massive non-minimal scalar field

We derive power spectra of the scalar- and tensor-type structures generated in an inflation model based on a massive non-minimally coupled scalar field with the strong coupling assumption. We make analyses in both the original-frame and the conformally transformed Einstein-frame. We derive contributions of both structures to the anisotropy of the cosmic microwave background radiation, and compare the contributions with the four-year COBE-DMR data. Previous study showed that sufficient amount of inflation requires a small coupling parameter. In such a case the spectra become near Zeldovich spectra, and the gravitational wave contribution becomes negligible compared with the scalar-type contribution which is testable in future CMBR experiments.Comment: 4 pages, no figure, To appear in Phys. Rev.

Singularities in scalar-tensor gravity

The analysis of certain singularities in scalar-tensor gravity contained in a recent paper is completed, and situations are pointed out in which these singularities cannot occur.Comment: 6 pages, LaTe

Cosmological Perturbations with Multiple Fluids and Fields

We consider the evolution of perturbed cosmological spacetime with multiple fluids and fields in Einstein gravity. Equations are presented in gauge-ready forms, and are presented in various forms using the curvature (\Phi or \phi_\chi) and isocurvature (S_{(ij)} or \delta \phi_{(ij)}) perturbation variables in the general background with K and \Lambda. We clarify the conditions for conserved curvature and isocurvature perturbations in the large-scale limit. Evolutions of curvature perturbations in many different gauge conditions are analysed extensively. In the multi-field system we present a general solution to the linear order in slow-roll parameters.Comment: 19 pages, 6 figures, revised thoroughly; published version in Class. Quant. Gra

Single electron control in n-type semiconductor quantum dots using non-Abelian holonomies generated by spin orbit coupling

We propose that n-type semiconductor quantum dots with the Rashba and Dresselhaus spin orbit interactions may be used for single electron manipulation through adiabatic transformations between degenerate states. All the energy levels are discrete in quantum dots and possess a double degeneracy due to time reversal symmetryin the presence of the Rashba and/or Dresselhaus spin orbit coupling terms. We find that the presence of double degeneracy does not necessarily give rise to a finite non-Abelian (matrix) Berry phase. We show that a distorted two-dimensional harmonic potential may give rise to non-Abelian Berry phases. The presence of the non-Abelian Berry phase may be tested experimentally by measuring the optical dipole transitions.Comment: accepted in Phys. Rev.

Optical Self Energy in Graphene due to Correlations

In highly correlated systems one can define an optical self energy in analogy to its quasiparticle (QP) self energy counterpart. This quantity provides useful information on the nature of the excitations involved in inelastic scattering processes. Here we calculate the self energy of the intraband optical transitions in graphene originating in the electron-electron interaction (EEI) as well as electron-phonon interaction (EPI). Although optics involves an average over all momenta ($k$) of the charge carriers, the structure in the optical self energy is nevertheless found to mirror mainly that of the corresponding quasiparticles for $k$ equal to or near the Fermi momentum $k_F$. Consequently plasmaronic structures which are associated with momenta near the Dirac point at $k=0$ are not important in the intraband optical response. While the structure of the electron-phonon interaction (EPI) reflects the sharp peaks of the phonon density of states, the excitation spectrum associated with the electron-electron interaction is in comparison structureless and flat and extends over an energy range which scales linearly with the value of the chemical potential. Modulations seen on the edge of the interband optical conductivity as it rises towards its universal background value are traced to structure in the quasiparticle self energies around $k_F$ of the lower Dirac cone associated with the occupied states.Comment: 30 pages, 10 figure

The Fate of the Accelerating Universe

The presently accelerating universe may keep accelerating forever, eventually run into the event horizon problem, and thus be in conflict with the superstring idea. In the other way around, the current accelerating phase as well as the fate of the universe may be swayed by a negative cosmological constant, which dictates a big crunch. Based on the current observational data, in this paper we investigate how large the magnitude of a negative cosmological constant is allowed to be. In addition, for distinguishing the sign of the cosmological constant via observations, we point out that a measure of the evolution of the dark energy equation of state may be a good discriminator. Hopefully future observations will provide much more detailed information about dark energy and thereby indicates the sign of the cosmological constant as well as the fate of the presently accelerating universe.Comment: 16 pages, 5 figures, LaTe