Gravitational Collapse in the Post-Inflationary Universe

Abstract

The Universe may pass through an effectively matter-dominated epoch between inflation and Big Bang Nucleosynthesis during which gravitationally bound structures can form on subhorizon scales. In particular, the inflaton field can collapse into inflaton halos, forming "large scale" structure in the very early universe. We combine N-body simulations with high-resolution zoom-in regions in which the non-relativistic Schrödinger-Poisson equations are used to resolve the detailed, wavelike structure of inflaton halos. Solitonic cores form inside them, matching structure formation simulations with axion-like particles in the late-time universe. We denote these objects inflaton stars, by analogy with boson stars. Based on a semi-analytic formalism we compute their overall mass distribution which shows that some regions will reach overdensities of 10 15 if the early matterdominated epoch lasts for 20 e-folds. The radii of the most massive inflaton stars can shrink below the Schwarzschild radius, suggesting that they could form primordial black holes prior to thermalization.

Primordial Black Holes in Matter-Dominated Eras: the Role of Accretion

“…We will show that, under the spherical symmetry assumption, PBHs may form by post-collapse accretion onto pre-existing matter overdensities, might them be self-gravitating clouds or bounded clumps e.g. inflaton stars [16][17][18][19][20]. We will also show that PBHs may efficiently accrete and increase their initial mass by various orders of magnitude during the matter-dominated era, provided the geometry of the accretion flow is spherical.…”

“…This case may describe both the dynamics during the standard matterdominated phase, as well as the dynamics during an early matter-dominated phase when the universe is filled by a scalar field (inflaton or modulus), but the size of the collapsed cloud is such that quantum effects play no role and no bosonic soliton is formed. Subsequently, we will analyse accretion onto overdense solitonic stars in the case in which, for instance, the early matter-dominated phase is the one immediately after inflation [16][17][18][19][20]. In both cases, we assume that no PBHs have formed from the collapse of the initial overdensity.…”

“…In such a case the Compton wavelength of the inflaton ∼ 1/m (m being the mass of the inflaton) is comparable to, or larger than, the typical size of the collapsed object. In such a case, the formation of PBHs may occur from accretion onto inflaton stars, which are localized lumps of boson energy density held together by the competing forces of gravity, self-interactions and gradient energy [16][17][18][19][20], and may form during the post-inflation early matter-dominated phase and before reheating. In the following, we will assume that the initial overdensity produced by the scalar field inhomogeneity is not so large to give rise directly to a PBH, but instead it forms a solitonic core.…”

“…At this stage the universe is filled by the classical inflaton field and by its quanta whose fluctuations are gradually re-entering the horizon. They may give rise, upon collapse, to bounded structures [16][17][18][19][20] and eventually to PBHs [21,22]. This early matter-dominated phase ends when the inflaton decays and reheats the universe, starting the radiationdominated phase.…”

A Faster Growth of Perturbations in an Early Matter Dominated Epoch: Primordial Black Holes and Gravitational Waves

“…On the other hand, though, any deviation from spherical symmetry will tend to virialise the collapsing system, avoiding the formation of a horizon. We defer a detailed numerical study of the formation of PBHs and microhalos, along the lines of [39][40][41][42][43][44], to a future work. In the present paper, we will provide simple estimates to exhibit the potentially rich phenomenology.…”