What is the amplitude of the Gravitational Waves background expected in the Starobinsky model ?. (arXiv:1909.08014v3 [astro-ph.CO] UPDATED)

<a href="http://arxiv.org/find/astro-ph/1/au:+Renzi_F/0/1/0/all/0/1">Fabrizio Renzi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Shokri_M/0/1/0/all/0/1">Mehdi Shokri</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Melchiorri_A/0/1/0/all/0/1">Alessandro Melchiorri</a>

The inflationary model proposed by Starobinski in 1979 predicts an amplitude

of the spectrum of primordial gravitational waves, parametrized by the tensor

to scalar ratio, of $r=0.0037$ in case of a scalar spectral index of

$n_S=0.965$. This amplitude is currently used as a target value in the design

of future CMB experiments with the ultimate goal of measuring it at more than

five standard deviations. Here we evaluate how stable are the predictions of

the Starobinski model on $r$ considering the experimental uncertainties on

$n_S$ and the assumption of $Lambda$CDM. We also consider inflationary models

where the $R^2$ term in Starobinsky action is generalized to a $R^{2p}$ term

with index $p$ close to unity. We found that current data place a lower limit

of $r>0.0013$ at $95 %$ C.L. for the classic Starobinski model, and predict

also a running of the scalar index different from zero at more than three

standard deviation in the range $dn/dlnk=-0.0006_{-0.0001}^{+0.0002}$. A level

of gravitational waves of $rsim0.001$ is therefore possible in the Starobinski

scenario and it will not be clearly detectable by future CMB missions as

LiteBIRD and CMB-S4. When assuming a more general $R^{2p}$ inflation we found

no expected lower limit on $r$, and a running consistent with zero. We found

that current data are able to place a tight constraints on the index of

$R^{2p}$ models at $95%$ C.L. i.e. $p= 0.99^{+0.02}_{-0.03}$.

The inflationary model proposed by Starobinski in 1979 predicts an amplitude

of the spectrum of primordial gravitational waves, parametrized by the tensor

to scalar ratio, of $r=0.0037$ in case of a scalar spectral index of

$n_S=0.965$. This amplitude is currently used as a target value in the design

of future CMB experiments with the ultimate goal of measuring it at more than

five standard deviations. Here we evaluate how stable are the predictions of

the Starobinski model on $r$ considering the experimental uncertainties on

$n_S$ and the assumption of $Lambda$CDM. We also consider inflationary models

where the $R^2$ term in Starobinsky action is generalized to a $R^{2p}$ term

with index $p$ close to unity. We found that current data place a lower limit

of $r>0.0013$ at $95 %$ C.L. for the classic Starobinski model, and predict

also a running of the scalar index different from zero at more than three

standard deviation in the range $dn/dlnk=-0.0006_{-0.0001}^{+0.0002}$. A level

of gravitational waves of $rsim0.001$ is therefore possible in the Starobinski

scenario and it will not be clearly detectable by future CMB missions as

LiteBIRD and CMB-S4. When assuming a more general $R^{2p}$ inflation we found

no expected lower limit on $r$, and a running consistent with zero. We found

that current data are able to place a tight constraints on the index of

$R^{2p}$ models at $95%$ C.L. i.e. $p= 0.99^{+0.02}_{-0.03}$.

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