Primordial Black Holes as a Probe of the Early Universe and a Varying Gravitational Constant

Abstract

We discuss recent developments in the study of primordial black holes, focussing particularly on their formation and quantum evaporation. Such studies can place important constraints on models of the early Universe. An especially interesting development has been the realization that such constraints may be severely modified if the value of the gravitational "constant" G varies with cosmological epoch, a possibility which arises in many scenarios for the early Universe. The nature of the modification depends upon whether the value of G near a black hole maintains the value it had at its formation epoch (corresponding to gravitational memory) or whether it tracks the background cosmological value. This is still uncertain but we discuss various approaches which might help to resolve the issue.

Early universe models from noncommutative geometry

“…We discuss how the running of the gravitational parameters of the model influences the behavior of the evaporation of primordial black holes by Hawking radiation. While the type of effects that we see in this model, which depend on the presence of variable effective gravitational and cosmological constants, are qualitatively similar to scenarios of negative gravity in the early universe previously analyzed in theoretical cosmology ( [5], [6], [11], [24], [25], [26], [35], [36], [37], [39], [40], [41], [43], [48]), the mechanism that produces these effects in the noncommutative geometry model is substantially different from those described in these earlier references, which makes the quantitative behavior also different and distinguishable from other models. In fact, most of the effects we investigate in this paper depend directly on the expression of the coefficients of the gravitational and bosonic terms in the asymptotic expansion of the spectral action in terms of the Yukawa parameters of the underlying particle physics model.…”

“…They originate from the collapse of overdense regions, as well as from other mechanisms such as phase transitions in the early universe, cosmic loops and strings, or inflationary reheating. The consequences on primordial black holes of the running of the gravitational constant in the early universe have been analyzed, for example, in [11]. In models where the gravitational constant in the early universe may be different from the value it has in the modern universe, PBHs, whose existence is conjectured but has not been presently confirmed, are seen as a possible source of information about the changing gravitational constant.…”

Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology

“…In [26], therefore, a different viewpoint on the effective gravitational and cosmological constant in the asymptotic expansion of the spectral action in the NCG models is proposed, and a possible early universe model is investigated, which only covers the epochs in between the unification and the electroweak eras, a period which is expected to include the inflationary epoch. It is shown that, if one considers an effective action where the gravitational and cosmological constant are allowed to run according to the RGE flow of the coefficients (2.6) through the expressions (2.5) and with the assigned boundary conditions at unification, then one recovers many of the scenarios predicted by other models with variable gravitational and cosmological constant, as [10], [17], [22], and several different mechanism for inflation, with predictions about parameters such as the spectral index and tensor-to-scalar ratio.…”

“…However, there are cosmological models that include the possibility of a much more drastic variability of the gravitational parameters in the very early universe, including in particular the inflationary epoch. Scenarios with variable gravitational constant had been considered early on in Jordan-Brans-Dicke gravity, where the variability happens through the non-minimal coupling of gravity to a scalar field, and more recently within other modified gravity models, and in terms of RGE running [21], as well as in the context of primordial black holes with gravitational memory (see for instance [5], or the recent [10] and references therein). Similarly, a variable cosmological constant plays a role in various models (see for example [6], [20], [25], [33]).…”

Accretion of radiation and rotating primordial black holes

“…In order to understand the exact effect of angular momentum parameter on the rate of accretion in the radiation dominated era, we have numerically plotted the variation of mass with change in the angular momentum parameter a for a particular PBH formed at t = 10 −22 sec having accretion efficiency 0.5 in Figure 1. In our analysis, we assume that the initial mass (M i ) of PBHs to be of the same as that of the horizon mass [25,26]. One can see from Figure-1 that the rate of accretion decreases with increase in angular momentum parameter.…”