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Register a new userThe reconstruction of tachyon inflationary potentials
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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 $w_{re}=2/3$.
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We derive the reconstruction formulae for the inflation model with the non-minimal derivative coupling term. If reconstructing the potential from the tensor-to-scalar ratio, we could obtain the potential without using the high friction limit. As an example, we reconstruct the potential from the parametrization $r=8alpha/(N+beta)^{gamma}$, which is a general form of the $alpha$-attractor. The reconstructed potential has the same asymptotic behavior as the T- and E-model if we choose $gamma=2$ and $alphall1$. We also discuss the constraints from the reheating phase preceding the radiation domination by assuming the parameter $w_{re}$ of state equation during reheating is a constant. The scale of big-bang nucleosynthesis could put a up limit on $n_s$ if $w_{re}=2/3$ and a low limit on $n_s$ if $w_{re}=1/6$.
We study inflationary models with a Gauss-Bonnet term to reconstruct the scalar field potentials and the Gauss-Bonnet coupling functions from the observable quantities. Using the observationally favored relations for both $n_s$ and $r$, we derive the expressions for both the scalar field potentials and the coupling functions. The implication of the blue-tilted spectrum, $n_t>0$, of the primordial tensor fluctuations is discussed for the reconstructed configurations of the scalar field potential and the Gauss-Bonnet coupling.
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.
For the constant-roll tachyon inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts and the tensor to scalar ratio up to the first order by using the method of Bessel function approximation. The derived $n_s-r$ results for the constant-roll inflation are also compared with the observations, we find that only one constant-roll inflation is consistent with the observations and observations constrain the constant-roll inflation to be slow-roll inflation. The tachyon potential is also reconstructed for the constant-roll inflation which is consistent with the observations.
Within the framework of tachyon inflation, we consider different steep potentials and check their viability in light of the Planck 2015 data. We see that in this scenario, the inverse power-law potential $V(phi)=V_{0}(phi/phi_{0})^{-n}$ with $n=2$ leads to the power-law inflation with the scale factor $a(t)propto t^{q}$ where $q>1$, while with $n<2$, it gives rise to the intermediate inflation with the scale factor $a(t)proptoexpleft(At^{f}right)$ where $A>0$ and $0<f<1$. We find that, although the inverse power-law potential with $nleq 2$ is completely ruled out by the Planck 2015 data, the result of this potential for $n>2$ can be compatible with the 95% CL region of Planck 2015 TT, TE, EE+lowP data. We further conclude that the exponential potential $V(phi)=V_{0}e^{-phi/phi_{0}}$, the inverse $cosh$ potential $V(phi)=V_{0}/cosh(phi/phi_{0})$, and the mutated exponential potential $V(phi)=V_{0}left[1+(n-1)^{-(n-1)}(phi/phi_{0})^{n}right]e^{-phi/phi_{0}}$ with $n=4$, can be consistent with the 95% CL region of Planck 2015 TT, TE, EE+lowP data. Moreover, using the $r-n_s$ constraints on the model parameters, we also estimate the running of the scalar spectral index $dn_{s}/dln k$ and the local non-Gaussianity parameter $f_{{rm NL}}^{{rm local}}$. We find that the lower and upper bounds evaluated for these observables are compatible with the Planck 2015 results.
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