Abstract:
We investigate interacting dark energy models in the framework of fractal cosmology. We discuss a fractal FRW universe filled with the dark energy and dark matter which interact with each other. We obtain the equation for the relative density of dark matter and dark energy and the deceleration parameter. This model demonstrates new types of evolution, which are not common to cosmological models with this type of interaction.

Abstract:
Recent observations of near supernova show that the acceleration expansion of Universe decreases. This phenomenon is called the transient acceleration. In the second part of work we consider the 3-component Universe composed of a scalar field, interacting with the dark matter on the agegraphic dark energy background. We show that the transient acceleration appears in frame of such a model. The obtained results agree with the latest cosmological observations, namely, the 557 SNIa sample (Union2) was released by the Supernova Cosmology Project (SCP) Collaboration.

Abstract:
The hyperfine structure (HFS) of a bound electron is modified by the self-interaction of the electron with its own radiation field. This effect is known as the self-energy correction. In this work, we discuss the evaluation of higher-order self-energy corrections to the HFS of bound P states. These are expressed in a semi-analytic expansion involving powers of Zalpha and ln(Zalpha), where Z is the nuclear charge number and alpha is the fine-structure constant. We find that the correction of relative order alpha (Zalpha)^2 involves only a single logarithm ln(Zalpha) for P_1/2 states [but no term of order alpha (Zalpha)^2 ln^2(Zalpha), whereas for P_3/2 states, even the single logarithm vanishes. By a Foldy-Wouthuysen transformation, we identify a nuclear-spin dependent correction to the electron's transition current, which contributes to the HFS of P states. A comparison of the obtained analytic results to a numerical approach is made.

Abstract:
The hyperfine structure (hfs) and the g factor of a bound electron are caused by external magnetic fields. For the hfs, the magnetic field is due to the nuclear spin. A uniform-in-space and constant-in-time magnetic field is used to probe the bound-electron g factor. The self-energy corrections to these effects are more difficult to evaluate than those to the Lamb shift. Here, we describe a numerical approach for both effects in the notoriously problematic regime of hydrogen-like bound systems with low nuclear charge numbers. The calculation is nonperturbative in the binding Coulomb field. Accurate numerical values for the remainder functions are provided for 2P states and for nS states with n=1,2,3.

Abstract:
A high-precision numerical calculation is reported for the self-energy correction to the hyperfine splitting and to the bound-electron g factor in hydrogenlike ions with low nuclear charge numbers. The binding nuclear Coulomb field is treated to all orders, and the nonperturbative remainder beyond the known $Z\alpha$-expansion coefficients is determined. For the $^3{\rm He}^+$ ion, the nonperturbative remainder yields a contribution of -450 Hz to the normalized difference of the 1S and 2S hyperfine-structure intervals, to be compared with the experimental uncertainty of 71 Hz and with the theoretical error of 50 Hz due to other contributions. In the case of the g factor, the calculation provides the most stringent test of equivalence of the perturbative and nonperturbative approaches reported so far in the bound-state QED calculations.

Abstract:
State-dependent quantum electrodynamic corrections are evaluated for the hyperfine splitting of nS states for arbitrary principal quantum number n. The calculations comprise both the self-energy and the vacuum-polarization correction of order alpha(Z alpha)^2 E_F and the recoil correction of order (Z alpha)^2 (m/M) E_F. Higher-order corrections are summarized and partly reevaluated as well. Accurate predictions for hydrogen hyperfine splitting intervals of nS states with n=2,...,8 are presented. The results obtained are important due to steady progress in hydrogen spectroscopy for transitions involving highly excited S states.

Abstract:
The accurate determination of atomic masses and the high-precision measurement of the bound-electron g factor are prerequisites for the determination of the electron mass, which is one of the fundamental constants of nature. In the 2002 CODATA adjustment [P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 77, 1 (2005)], the values of the electron mass and the electron-proton mass ratio are mainly based on g factor measurements in combination with atomic mass measurements. In this paper, we briefly discuss the prospects for obtaining other fundamental information from bound-electron g factor measurements, we present some details of a recent investigation of two-loop binding corrections to the g factor, and we also investigate the radiative corrections in the limit of highly excited Rydberg S states with a long lifetime, where the g factor might be explored using a double resonance experiment.

Abstract:
The kinematics and dynamic interpretation of the cosmological expansion is reviewed in a widely accessible manner with emphasis on the acceleration aspect. Virtually all the approaches that can in principle account for the accelerated expansion of the Universe are reviewed, including dark energy as an item in the energy budget of the Universe; modified Einstein equations; and, on a fundamentally new level, the use of the holographic principle.

Abstract:
Agegraphic dark energy, has been recently proposed, based on the so-called Karolyhazy uncertainty relation, which arises from quantum mechanics together with general relativity. In the first part of the article we study the original agegraphic dark energy model by including the interaction between agegraphic dark energy and pressureless (dark) matter. The phase space analysis was made and the critical points were found, one of which is the attractor corresponding to an accelerated expanding Universe. Recent observations of near supernova show that the acceleration of Universe decreases. This phenomenon is called the transient acceleration. In the second part of Article we consider the 3-component Universe composed of a scalar field, interacting with the dark matter on the agegraphic dark energy background. We show that the transient acceleration appears in frame of such a model. The obtained results agree with the observations.

Abstract:
Within a systematic approach based on the dimensionally regularized nonrelativistic quantum electrodynamics, we derive the complete result for the two-loop correction to order $(\alpha/\pi)^2 (Z \alpha)^4$ for the $g$ factor of an electron bound in an $nS$ state of a hydrogenlike ion. The results obtained significantly improve the accuracy of the theoretical predictions for the hydrogenlike carbon and oxygen ions and influence the value of the electron mass inferred from $g$ factor measurements.