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There are large classes of inflationary models, particularly popular in the context of string theory and braneworld approaches to inflation, in which the ratio of linearized tensor-to-scalar metric fluctuations is very small. In such models, however, gravitational waves produced by scalar modes cannot be neglected. We derive the lower bound on the tensor-to-scalar ratio by considering the back-reaction of the scalar perturbations as a source of gravitational waves. These results show that no cosmological model that is compatible with a metric scalar amplitude of ≈10^-5 can have a ratio of the tensor-to-scalar power spectra less than ≈10^-8 at recombination and that higher-order terms leads to logarithmic growth for r during radiation domination. Our lower bound also applies to non-inflationary models which produce an almost scale-invariant spectrum of coherent super-Hubble scale metric fluctuations.

The new formal analogy between superfluid systems and cosmology, which emerges by taking into account the back-reaction of the vacuum to the quanta of sound waves,¹ enables us to put forward some common features between these two different areas of physics. We find the condition that allows us to justify a General Relativity (GR) derivation of the hydrodynamical equation for the superfluid in a four-dimensional space whose metric is the Unruh one.² Furthermore, we show how, in the particular case taken into account, our hydrodynamical equation can be deduced within a four-dimensional space from the wave equation of a massless scalar field.

We take the viewpoint that the physically acceptable solutions of the Lorentz–Dirac equation for radiation back-reaction are actually determined by a second-order equation of motion, the self-force being given as a function of spacetime location and velocity. We propose three different methods to obtain this self-force function. For two example systems, we determine the second-order equation of motion exactly in the non-relativistic regime via each of these three methods, leading to the same result. We reveal that, for both systems considered, back-reaction induces a damping proportional to velocity and, in addition, it decreases the effect of the external force.

A new analogy between superfluid systems and cosmology is here presented, which relies strongly on the following ingredient: the back-reaction of the vacuum to the quanta of sound waves. We show how the presence of thermal phonons, the excitations above the quantum vacuum for T > 0, enable us to deduce an hydrodynamical equation formally similar to the one obtained for a perfect fluid in a Universe obeying the Friedmann–Robertson–Walker metric.

By considering the back-reaction of the spacetime through the spherically symmetric quantum fluctuations of the background metric, Kazakov and Solodukhin removed the singularity of the Schwarzschild black hole. This regular Schwarzschild black hole has a spherical central region with a radius of the order of the Planck length. On the other hand, due to the positively accelerating expansion of the Universe, it seems that there exists a universal repulsive force known as dark energy. In the framework of quantum field theories, the quintessence field is a candidate model for investigating and modeling dark energy. Accordingly, by taking into account the quintessential matter field in the background of the Schwarzschild black hole, Kiselev gained the metric of this black hole surrounded by quintessence. By combining these two above ideas, in this study, we consider the quantum-corrected Schwarzschild black hole surrounded by quintessence to investigate null and time-like geodesics structure. Generally, this study points out that black holes are quantum-gravitational objects. We will show that the accelerated expansion of the Universe, instead of dark energy, happens because of the presence of quantum effects in this setup. Also, due to the presence of the central Planck-size sphere, the regular black hole has been possessed a shifting over radial coordinate in its inner structure.

A new general framework for studying relativistic spherical accretion of a self-gravitating fluid onto a central black hole is introduced in stationary coordinates for an observer at infinity. The important feature of gravitational back-reaction due to a self-gravitating fluid on the metric is included in the model. The model is solved numerically for the most simple case of a polytropic fluid and compared to analytical solutions, and the implications of these findings are discussed. Finally, the model is focused on the accretion of a relativistic Fermi gas and the implications this might have on the rapid growth of supermassive black holes in the early universe.