The inflationary account for the emergence of the seeds of cosmic structure falls short of actually explaining the generation of primordial anisotropies and inhomogeneities. This description starts from a symmetric background, and invokes symmetric dynamics, so it cannot explain asymmetries. To generate asymmetries, we present an application of the continuous spontaneous localization model of wave function collapse in the context of inflation. This modification of quantum dynamics introduces a stochastic nonunitary component to the evolution of the inflaton field perturbations. This leads to passage from a homogeneous and isotropic stage to another, where the quantum uncertainties in the initial state of inflation transmute into the primordial inhomogeneities and anisotropies. We show, by proper choice of the collapse-generating operator, that it is possible to achieve compatibility with the precise observations of the cosmic microwave background radiation.

As previously proposed in Simpson and Visser [ J. Cosmol. Astropart. Phys. 02 (2019) 042], Mazza et al. [ J. Cosmol. Astropart. Phys. 04 (2021) 082], Franzin et al. [ J. Cosmol. Astropart. Phys. 07 (2021) 036], and Lobo et al. [ Phys. Rev. D 103, 084052 (2021), the “black bounce” spacetimes are an interesting type of globally regular modifications of the ordinary black holes (such as the Kerr-Newman geometry and its particular cases) which generically contain a spacetime singularity (usually of the curvature type) at their center. To transforms a static, spherically symmetric and asymptotically flat black hole (SSS-AF-BH) geometry regular everywhere except its center of symmetry $r=0$ (where $r$ stands for the “areal radius” of the two-dimensional spheres of symmetry) and with (outer) event horizon at $r=r_h>0$, into a black bounce spacetime, is to simply replace $r$ with $\sqrt{{\rho }^2+a^2}$ and $dr$ with $d\rho$, being $\rho$ a new radial coordinate, and $a$ is some real constant nonzero. As long as $r_h=\sqrt{{\rho }_h^2+a^2}>|a|$, the result is a globally regular (or singularity-free) black hole spacetime (called black bounce) where the singularity that occurs in the ordinary SSS-AF-BH geometry at $r=0$ now in the transformed geometry turns into a regular spacetime region determined by the two-dimensional spheres of symmetry of radius $|a|$, while the areal radius $\sqrt{{\rho }^2+a^2}$ always remains positive for all $\rho \in (-\infty ,\infty )$ and has a minimum at $\rho =0$ given by $|a|$. Hence, in the transformed spacetime, the areal radius has a minimum, decreasing before and increasing after this minimum (defining two SSS-AF regions that bounce). In this work we will present several black-bounces exact solutions of General Relativity. Among them is a novel type of black-bounce solution, which in contrast to the Simpson-Visser type {[Simpson and Visser, J. Cosmol. Astropart. Phys. 02 (2019) 042], [Mazza et al., J. Cosmol. Astropart. Phys. 04 (2021) 082], [Franzin et al., J. Cosmol. Astropart. Phys. 07 (2021) 036], [Lobo et al., Phys. Rev. D 103, 084052 (2021)]}, does not have the Ellis wormhole metric as a particular case. The source of these solutions is linear superposition of phantom scalar fields and nonlinear electromagnetic fields.

In this paper, we present an exact solution for ($3+1$)-dimensional Einstein-scalar-Gauss-Bonnet theory (EsGB) in electrovacuum. The solution is characterized by only one parameter, $Q$, which in general can be associated with the electromagnetic field and the scalar field. We show that the solution corresponds to a charged wormhole with a throat at the region $r=|Q|$ and is also supported by a real scalar field having a positive kinetic term. We show that the solution belongs to the most general class of solutions known as Ellis wormholes but without the need for “exotic matter” or a phantom scalar field.

In this work the first exact asymptotically flat static and spherically symmetric black hole solution for ($3+1$)-dimensional extended scalar-tensor-Gauss-Bonnet theory is presented, with a model of nonlinear electrodynamics—which reduces to Maxwell’s theory in the weak field limit and satisfies the weak energy condition—as a source. The solution has a nonzero magnetic charge, and scalar hair, which turns out to be dependent of the magnetic charge. It is characterized by the Arnowitt-Deser-Misner mass $m$ and the magnetic charge $q$. Depending on the range of these parameters, the solution describes black holes with different structure. In the case $m\ge 0$ and $q\ge 0$, it shares many of the characteristics of the Schwarzschild solution. For $m>0$ and $q<0$, it is akin to the Reissner-Nordström metric. In the case $m=0$, it represents a purely magnetic black hole.

We present a novel, exact, traversable wormhole (T-WH) solution for ($3+1$)-dimensional Einstein-scalar-Gauss-Bonnet theory (EsGB) coupled to a power-Maxwell nonlinear electrodynamics (NLED). The solution is characterized by two parameters, ${\mathcal{Q}}_{\mathrm{e}}$ and ${\mathcal{Q}}_{\mathcal{S}}$, associated respectively with the electromagnetic field and the scalar field. We show that for ${\mathcal{Q}}_{\mathrm{e}}^2-{\mathcal{Q}}_{\mathcal{S}}>0$ the solution can be interpreted as a traversable wormhole. In the general case, with nonvanishing electromagnetic field, the scalar-Gauss-Bonnet term (sGB) is the only responsible for the negative energy density necessary for the traversability. In the limiting case of vanishing electromagnetic field, the scalar field becomes a phantom one keeping the WH throat open and in this case the Ellis WH solution [ J. Math. Phys. (N.Y.) 14, 104 (1973); Gen. Relativ. Gravit. 10, 105 (1979)] is recovered.