analysis of r p inflationary model as p geqslant 2

• DOI: 10.1007/s10773-018-3809-0
• Publication Date: 2018-01-01
• Authors: Lei-Hua Liu
• Keywords: Cosmology and Nongalactic Astrophysics (astro-ph.CO); 0103 physical sciences; FOS: Physical sciences; General Relativity and Quantum Cosmology (gr-qc); 01 natural sciences; General Relativity and Quantum Cosmology; Astrophysics - Cosmology and Nongalactic Astrophysics

We study the $R^p$ inflationary model of [Muller:1989rp] for $p>2$ using the result of Ref. [Motohashi:2014tra]. After reproducing the observable quantities: the power spectral index $n_s$, its corresponding running $��=\frac{dn_s}{d\ln(k)}$ and the tensor to scalar ration $r$ in terms of e-folding number $N$ and $p$, we show that $R^p$ inflation model is still alive as $p$ is from $2$ to $2.02$. In this range, our calculation confirms that $n_s$ and $r$ agree with observations and $��$ is of order $10^{-4}$ which needs more precise observational constraints. We find that, as the value of $p$ increases, all $n_s$, $r$ and $|��|$ decrease. However, the precise interdependence between these observables is such that this class of models can in principle be tested by the next generation of dedicated satellite CMB probes.<br/>14 pages, 4 figures, some places are correcting<br/>