Astronomy and Astrophysics – Astrophysics
Scientific paper
2005-05-23
Braz.J.Phys. 36 (2006) 566-569
Astronomy and Astrophysics
Astrophysics
7 pages, minor changes, improved discussion. To appear in Braz.J.Phys
Scientific paper
The Starobinsky model predicts a primordial inflation period without the presence of an inflaton field. The modified version of this model predicts a simple time dependence for the Hubble parameter $H(t)$, which decreases slowly between the Planck epoch and the end of the inflation, $H(t)=M_{\rm Pl}-\beta M_{\rm Pl}^2 t$, where $\beta$ is a dimensionless constant to be adjusted from observations. We investigate an inflaton model which has the same time dependence for $H(t)$. A reverse engineered inflaton potential for the time dependence of $H$ is derived. Normalization of the derived inflaton potential is determined by the condition that the observed density fluctuations, $\delta\rho/\rho\approx 10^{-5}$, are created at $\sim 60 e$-folds before the end of inflation. The derived potential indicates an energy (mass) scale, $M_{\rm end}\sim 10^{13} {\rm GeV}$, at the end of inflation. Using the slow roll parameters, which are obtained from this potential, we calculate the spectral index for the scalar modes $n_S$ and the relative amplitude of the tensor to scalar modes $r$. A tensor contribution, $r\simeq 0.13$, and an approximately Harrison-Zeldovich density perturbation spectrum, $n_S \simeq 0.95$, are predicted.
Opher Reuven
Pelinson Ana
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