[en] Inflationary models with power-law potentials are starting to be severely constrained by the recent measurements of Cosmic Microwave Background anisotropies provided by the Planck Satellite and by the BICEP2 telescope. In particular, models with power-law potentials $V\left(\phi \right)\propto {\phi }^n$ with $n\ge 2$ are strongly disfavored by present data since they predict a sizable contribution of gravitational waves with a tensor/scalar ratio of $r\sim 0.15$ that is at odds with current limits. A non-minimal coupling to gravity has been proposed as a physical mechanism to lower the predictions for $r$. In this paper we further investigate the issue, presenting constraints on non-minimal couplings from current CMB data under the assumption of power-law potentials. We found that models with $n>2$ show a statistically significant indication (above 95% C.L.) for a non minimal coupling. Non minimal coupling is also preferred by models with $n<2$ albeit just at about 68% C.L. Interestingly, all the models considered show a non-zero running of the spectral index, $n_{\mathrm{run}}$, consistent with the 2018 Planck release value of $-0.007\pm 0.0068$. We point out how future accurate measurement of $n_{\mathrm{run}}$ would be necessary to significantly constraint these models and eventually rule out some or all of them. The combination of Planck data with the Bicep/Keck dataset strengthen these considerations.

[en] One of the important problems with the existence of weak gravity conjecture (WGC) is the violation of the cosmic censorship. Such a cosmic phenomena is important and consistent in general relativity. It means that for a charged black hole in four dimensions and in the normal state, the WGC cannot hold due to the violation of the weak cosmic censorship conjecture (WCCC). But in this paper, in order to eliminate such a violation, we try to consider RN black hole at two cases, with quintessence, quintessence and cloud of strings in asymptotically flat and non-asymptotically flat. By using such metric background and applying restrictions on its parameters, we show that there will be a good compatibility between WGC and WCCC. Here, we can also see that quintessence case has less freedom in establishing compatibility than quintessence and cloud of strings. Because in the second case, the number of parameters is more and there is a degree of freedom to better establish the compatibility of two theories. Also, here we explain charged black hole in presence of quintessence and cloud of string for Q > M and use some interesting figures we show the corresponding the black hole has an event horizon.

[en] Highlights: • We considered a non-minimal coupling inflationary model in the context of the constant-roll idea which was investigated by the first-order formalism. • We attempted to find the hidden symmetries behind the model by the Lie symmetry method. • We supplied this aim using the symmetry features of the Heun function. • We showed that the hidden symmetries of the nonminimal constant-roll inflation in the cases of power-law and exponential couplings are characterized as a generalized form of $sl(2,R)$ and $su(1,1)$ algebra, respectively. In the present work, we consider the non-minimal coupling inflationary model in the context of the constant-roll idea which is investigated by the first-order formalism. We attempt to find the hidden symmetries behind the model by the Lie symmetry method. We supply this aim by using the symmetry features of the Heun function instead of Killing vector approach. We show that the hidden symmetries of the non-minimal constant-roll inflation in the cases of power-law and exponential couplings are characterized as a generalized form of $sl(2,R)$ and $su(1,1)$ algebra,