Analytic extensions of Starobinsky model of inflation. (arXiv:2111.09058v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Ivanov_V/0/1/0/all/0/1">Vsevolod R. Ivanov</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Ketov_S/0/1/0/all/0/1">Sergei V. Ketov</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Pozdeeva_E/0/1/0/all/0/1">Ekaterina O. Pozdeeva</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Vernov_S/0/1/0/all/0/1">Sergey Yu. Vernov</a>
We propose several extensions of the Starobinsky model of inflation, which
obey all observational constraints on the inflationary parameters, by demanding
that both the inflaton scalar potential in the Einstein frame and the $F(R)$
gravity function in the Jordan frame have the explicit dependence upon fields
and parameters in terms of elementary functions. All our models are
continuously connected to the original Starobinsky model via changing the
parameters. We modify the Starobinsky $(R+R^2)$ model by adding an $R^3$-term,
an $R^4$-term, and an $R^{3/2}$-term, respectively, and calculate the scalar
potentials, the inflationary observables and the allowed limits on the
deformation parameters in all these cases. We also deform the scalar potential
of the Starobinsky model in the Einstein frame, in powers of
$y=expleft(-sqrt{frac{2}{3}}phi/M_{Pl}right)$, where $phi$ is the
canonical inflaton (scalaron) field, calculate the corresponding $F(R)$ gravity
functions in the two new cases, and find the restrictions on the deformation
parameters in the lowest orders with respect to the variable $y$ that is
physically small during slow-roll inflation.
We propose several extensions of the Starobinsky model of inflation, which
obey all observational constraints on the inflationary parameters, by demanding
that both the inflaton scalar potential in the Einstein frame and the $F(R)$
gravity function in the Jordan frame have the explicit dependence upon fields
and parameters in terms of elementary functions. All our models are
continuously connected to the original Starobinsky model via changing the
parameters. We modify the Starobinsky $(R+R^2)$ model by adding an $R^3$-term,
an $R^4$-term, and an $R^{3/2}$-term, respectively, and calculate the scalar
potentials, the inflationary observables and the allowed limits on the
deformation parameters in all these cases. We also deform the scalar potential
of the Starobinsky model in the Einstein frame, in powers of
$y=expleft(-sqrt{frac{2}{3}}phi/M_{Pl}right)$, where $phi$ is the
canonical inflaton (scalaron) field, calculate the corresponding $F(R)$ gravity
functions in the two new cases, and find the restrictions on the deformation
parameters in the lowest orders with respect to the variable $y$ that is
physically small during slow-roll inflation.
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