Scalar induced gravitational waves from primordial black hole Poisson fluctuations in f(R) gravity

Abstract

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.

Formation of primordial black holes after Starobinsky inflation

“…The stochastic gravitational waves induced by PBH production in the Starobinsky-like gravity were investigated in Ref. [32]. Fine tuning of the parameters in our model is necessary to get the significant enhancement of the power spectrum of scalar perturbations leading to the PBH with masses beyond the Hawking evaporation limit and, hence, the possible PBH dark matter, cf.…”

Primordial black holes in loop quantum cosmology: the effect on the threshold

“…At the same time, they are associated with a plethora of gravitational-wave (GW) signals from black-hole merging events [12][13][14][15][16] up to primordial scalar induced GWs [17][18][19][20][21][22] (for a recent review see [23]). In particular, through the aforementioned GW portal, PBHs can act as well as a novel probe shedding light on the underlying gravity theory [24,25]. Other hints in favor of PBHs can be found here [26].…”

Primordial Black Holes from Volkov–Akulov–Starobinsky Supergravity

“…The resulting GW density is shown in Figure . The induced primordial GW signal caused by scalaron would be a clear signature of PBH, being complementary to another primordial GW signal induced by PBH Poisson fluctuations in Starobinsky gravity [ 49 ] and VAS supergravity, see Ref. [50] also.…”