The gravitational potential of a gas of initially randomly distributed primordial black holes (PBH) can induce a stochastic gravitational-wave (GW) background through second-order gravitational effects. This GW background can be abundantly generated in a cosmic era dominated by ultralight primordial black holes, with masses m PBH < 109g. In this work, we consider f(R) gravity as the underlying gravitational theory and we study its effect at the level of the gravitational potential of Poisson distributed primordial black holes. After a general analysis, we focus on the R 2 gravity model. In particular, by requiring that the scalar induced GWs (SIGWs) are not overproduced, we find an upper bound on the abundance of PBHs at formation time ΩPBH,f as a function of their mass, namely that ΩPBH,f < 5.5 × 10-5 (109g/m PBH)1/4, which is 45% tighter than the respective upper bound in general relativity. Afterwards, by considering R 2 gravity as an illustrative case study of an f(R) gravity model, we also set upper bound constraints on its mass parameter M. These mass parameter constraints, however, should not be regarded as physical given the fact that the Cosmic Microwave Background (CMB) constraints on R 2 gravity are quite tight. Finally, we conclude that the portal of SIGWs associated to PBH Poisson fluctuations can act as a novel complementary probe to constrain alternative gravity theories.
The gravitational potential of a gas of initially randomly distributed primordial black holes (PBH) can induce a stochastic gravitational-wave background through second-order gravitational effects. This gravitational-wave background can be abundantly generated in a cosmic era of domination of ultralight primordial black holes, with masses m PBH < 10 9 g, which evaporate before Big Bang Nucleosynthesis. Hence, the condition to avoid overproduction of gravitational waves at PBH evaporation time, can act as a novel method to extract constraints on cosmological models and gravitational theories. We consider f (R) gravity as the underlying gravitational theory and we study its effect at the level of the gravitational potential of Poisson distributed primordial black holes. After the general analysis we focus on Starobinsky R 2 gravity model and we extract strong constraints on the involved mass parameter, denoted as M , as a function of the initial primordial black hole abundance, Ω PBH,f and the black hole mass, m PBH . In particular, one finds that in general 5 × 10 −14 M min M Pl 10 −5 , and only in the extreme possible regime where Ω PBH,f > 10 −3 we get that 10 −5 M min M Pl 10 −1 .
Primordial black hole (PBH) fluctuations can induce a stochastic gravitational wave background at second order, and since this procedure is sensitive to the underlying gravitational theory it can be used as a novel tool to test general relativity and extract constraints on possible modified gravity deviations. We apply this formalism in the framework of f(T) gravity, considering three viable mono-parametric models. In particular, we investigate the induced modifications at the level of the gravitational-wave source, which is encoded in terms of the power spectrum of the PBH gravitational potential, as well as at the level of their propagation, described in terms of the Green function which quantifies the propagator of the tensor perturbations. We find that, within the observationally allowed range of the f(T) model-parameters, the obtained deviations from general relativity, both at the levels of source and propagation, are practically negligible. Hence, we conclude that realistic and viable f(T) theories can safely pass the primordial black hole constraints, which may offer an additional argument in their favor.
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