One-loop correction to the enhanced curvature perturbation with local-type non-Gaussianity for the formation of primordial black holes

As one of the promising candidates of cold dark matter (DM), primordial black holes (PBHs) were formed due to the collapse of over-densed regions generated by the enhanced curvature perturbations during the radiation-dominated era. The enhanced curvature perturbations are expected to be non-Gaussian in some relevant inflation models and hence the higher-order loop corrections to the curvature power spectrum might be non-negligible as well as altering the abundance of PBHs. In this paper, we calculate the one-loop correction to the curvature power spectrum with local-type non-Gaussianities characterizing by $F_{\mathrm{NL}}$ and $G_{\mathrm{NL}}$ standing for the quadratic and cubic non-Gaussian parameters, respectively. Requiring that the one-loop correction be subdominant, we find a perturbativity condition, namely $|2cAF_{\mathrm{NL}}^2+6AG_{\mathrm{NL}}|\ll 1$, where $c$ is a constant coefficient which can be explicitly calculated in the given model and $A$ denotes the variance of Gaussian part of enhanced curvature perturbation, and such a perturbativity condition can provide a stringent constraint on the relevant inflation models for the formation of PBHs.Comment: 6 pages, 5 figure

Full analysis of the scalar-induced gravitational waves for the curvature perturbation with local-type non-Gaussianities

Primordial black holes (PBHs) are supposed to form through the gravitational collapse of regions with large density fluctuations. The formation of PBHs inevitably leads to the emission of scalar-induced gravitational wave (SIGW) signals, offering a unique opportunity to test the hypothesis of PBHs as a constituent of dark matter (DM). Previous studies have calculated the energy spectrum of SIGWs in local-type non-Gaussian models, primarily considering the contributions from the $F_{\mathrm{NL}}$-order or the $G_{\mathrm{NL}}$-order while neglecting connected diagrams. In this study, we extend the previous work by (i) considering the full contribution of non-Gaussian diagrams up to the $G_{\mathrm{NL}}$-order; (ii) deriving the generic scaling of the SIGW energy spectrum in the infrared region. We derive semi-analytical results applicable to arbitrary primordial power spectra and numerically evaluate the energy spectrum of SIGWs for a log-normal power spectrum.Comment: 21 pages, 2 figure

Safety and efficacy of etomidate and propofol anesthesia in elderly patients undergoing gastroscopy: A double-blind randomized clinical study

The aim of the present study is to compare the safety, efficacy and cost effectiveness of anesthetic regimens by compound, using etomidate and propofol in elderly patients undergoing gastroscopy. A total of 200 volunteers (65–79 years of age) scheduled for gastroscopy under anesthesia were randomly divided into the following groups: P, propofol (1.5–2.0 mg/kg); E, etomidate (0.15-0.2 mg/kg); P+E, propofol (0.75–1 mg/kg) followed by etomidate (0.075-0.1 mg/kg); and E+P, etomidate (0.075-0.01 mg/kg) followed by propofol (0.75–1 mg/kg). Vital signs and bispectral index were monitored at different time points. Complications, induction and examination time, anesthesia duration, and recovery and discharge time were recorded. At the end of the procedure, the satisfaction of patients, endoscopists and the anesthetist were evaluated. The recovery (6.1±1.2 h) and discharge times (24.8±2.8 h) in group E were significantly longer compared with groups P, P+E and E+P (P<0.05). The occurrence of injection pain in group P+E was significantly higher compared with the other three groups (P<0.05). In addition, the incidence of myoclonus and post-operative nausea and vomiting were significantly higher in group P+E compared with the other three groups (P<0.05). There was no statistical difference among the four groups with regards to the patients' immediate, post-procedure satisfaction (P>0.05). Furthermore, there was no difference in the satisfaction of anesthesia, as evaluated by the anesthetist and endoscopist, among the four groups (P>0.05). The present study demonstrates that anesthesia for gastroscopy in elderly patients can be safely and effectively accomplished using a drug regimen that combines propofol with etomidate. The combined use of propofol and etomidate has unique characteristics which improve hemodynamic stability, cause minimal respiratory depression and less side effects, provide rapid return to full activity and result in high levels of satisfaction