Inflation plays a central role in our current understanding of the universe. According to the standard viewpoint, the homogeneous and isotropic mode of the inflaton field drove an early phase of nearly exponential expansion of the universe, while the quantum fluctuations (uncertainties) of the other modes gave rise to the seeds of cosmic structure. However, if we accept that the accelerated expansion led the universe into an essentially homogeneous and isotropic space-time, with the state of all the matter fields in their vacuum (except for the zero mode of the inflaton field), we can not escape the conclusion that the state of the universe as a whole would remain always homogeneous and isotropic. It was recently proposed in [A. Perez, H. Sahlmann and D.Sudarsky, "On the quantum origin of the seeds of cosmic structure," Class. Quant. Grav. 23, -2354 (2006)] that a collapse (representing physics beyond the established paradigm, and presumably associated with a quantum-gravity effectà la Penrose) of the state function of the inflaton field might be the missing element, and thus would be responsible for the emergence of the primordial inhomogeneities. Here we will discuss a formalism that relies strongly on quantum field theory on curved space-times, and within which we can implement a detailed description of such a process. The picture that emerges clarifies many aspects of the problem, and is conceptually quite transparent. Nonetheless, we will find that the results lead us to argue that the resulting picture is not fully compatible with a purely geometric description of space-time. * Electronic address: alberto.diez@fisica.ugto.mx † Electronic address: sudarsky@nucleares.unam.mx 2317

We study the evolution of a massive scalar field surrounding a Schwarzschild black hole and find configurations that can survive for arbitrarily long times, provided the black hole or the scalar field mass is small enough. In particular, both ultralight scalar field dark matter around supermassive black holes and axionlike scalar fields around primordial black holes can survive for cosmological times. Moreover, these results are quite generic in the sense that fairly arbitrary initial data evolve, at late times, as a combination of those long-lived configurations.

Classical scalar fields have been proposed as possible candidates for the dark matter component of the universe. Given the fact that super-massive black holes seem to exist at the center of most galaxies, in order to be a viable candidate for the dark matter halo a scalar field configuration should be stable in the presence of a central black hole, or at least be able to survive for cosmological time-scales. In the present work we consider a scalar field as a test field on a Schwarzschild background, and study under which conditions one can obtain long-lived configurations. We present a detailed study of the Klein-Gordon equation in the Schwarzschild spacetime, both from an analytical and numerical point of view, and show that indeed there exist quasi-stationary solutions that can remain surrounding a black hole for large time-scales.Comment: 34 pages, 13 figure

We present new, fully nonlinear numerical solutions to the static, spherically symmetric Einstein-Klein-Gordon system for a collection of an arbitrary odd number N of complex scalar fields with an internal U (N) symmetry and no self-interactions. These solutions, which we dub ℓ-boson stars, are parametrized by an angular momentum number ℓ = (N − 1)/2, an excitation number n, and a continuous parameter representing the amplitude of the fields. They are regular at every point and possess a finite total mass. For ℓ = 0 the standard spherically symmetric boson stars are recovered. We determine their generalizations for ℓ > 0, and show that they give rise to a large class of new static configurations which might have a much larger compactness ratio than ℓ = 0 stars.