No Arabic abstract
We calculate the one-loop corrections from inflationary gravitons to the electromagnetic fields of a point charge and a point magnetic dipole on a locally de Sitter space background. Results are obtained both for an observer at rest in co-moving coordinates, whose physical distance from the sources increases with the expanding universe, and for an observer at rest in static coordinates, whose physical distance from the sources is constant. The fields of both sources show the de Sitter analogs of the fractional $G/r^2$ corrections which occur in flat space, but there are also some fractional $G H^2$ corrections due to the scattering of virtual photons from the vast ensemble of infrared gravitons produced by inflation. The co-moving observer perceives the magnitude of the point charge to increase linearly with co-moving time and logarithmically with the co-moving position, however, the magnetic dipole shows only a negative logarithmic spatial variation. The static observer perceives no secular change of the point charge but he does report a secular enhancement of the magnetic dipole moment.
We include the single graviton loop contribution to the linearized Einstein equation. Explicit results are obtained for one loop corrections to the propagation of gravitational radiation. Although suppressed by a minuscule loop-counting parameter, these corrections are enhanced by the square of the number of inflationary e-foldings. One consequence is that perturbation theory breaks down for a very long epoch of primordial inflation. Another consequence is that the one loop correction to the tensor power spectrum might be observable, in the far future, after the full development of 21cm cosmology.
We derive a lower bound on the field excursion for the tachyon inflation, which is determined by the amplitude of the scalar perturbation and the number of $e$-folds before the end of inflation. Using the relation between the observables like $n_s$ and $r$ with the slow-roll parameters, we reconstruct three classes of tachyon potentials. The model parameters are determined from the observations before the potentials are reconstructed, and the observations prefer the concave potential. We also discuss the constraints from the reheating phase preceding the radiation domination for the three classes of models by assuming the equation of state parameter $w_{re}$ during reheating is a constant. Depending on the model parameters and the value of $w_{re}$, the constraints on $N_{re}$ and $T_{re}$ are different. As $n_s$ increases, the allowed reheating epoch becomes longer for $w_{re}=-1/3$, 0 and $1/6$ while the allowed reheating epoch becomes shorter for $w_{re}=2/3$.
The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of quantum field models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameters values. The scalar electrodynamics inflationary scenario thus obtained are seen to be in good agreement with the most recent observational data.
We show that the ghost degrees of freedom of Einstein gravity with a Weyl term can be eliminated by a simple mechanism that invokes local Lorentz symmetry breaking. We demonstrate how the mechanism works in a cosmological setting. The presence of the Weyl term forces a redefinition of the quantum vacuum state of the tensor perturbations. As a consequence the amplitude of their spectrum blows up when the Lorentz-violating scale becomes comparable to the Hubble radius. Such a behaviour is in sharp contrast to what happens in standard Weyl gravity where the gravitational ghosts smoothly damp out the spectrum of primordial gravitational waves.
The BICEP2 collaboration has recently released data showing that the scalar-to-tensor ratio $r$ is much larger than expected. The immediate consequence, in the context of $f(R)$ gravity, is that the Starobinsky model of inflation is ruled out since it predicts a value of $r$ much smaller than what is observed. Of course, the BICEP2 data need verification, especially from Planck with which there is some tension, therefore any conclusion seems premature. However, it is interesting to ask what would be the functional form of $f(R)$ in the case when the value of $r$ is different from the one predicted by the Starobinsky model. In this paper, we show how to determine the form of $f(R)$, once the slow-roll parameters are known with some accuracy. The striking result is that, for given values of the scalar spectral index $n_{S}$ and $r$, the effective Lagrangian has the form $f(R)=R^{zeta}$, where $zeta=2-varepsilon$ and $|varepsilon|ll 1$. Therefore, it appears that the inflationary phase of the Universe is best described by a $R^{2}$ theory, with a small deviation that, as we show, can be obtained by quantum corrections.