Constraining primordial black hole masses through f(R) gravity scalarons in Big Bang Nucleosynthesis

Abstract

Big Bang Nucleosynthesis (BBN) is a strong probe for constraining new physics including gravitation. f(R) gravity theory is an interesting alternative to general relativity which introduces additional degrees of freedom known as scalarons. In this work we demonstrate the existence of black hole solutions in f(R) gravity and develop a relation between scalaron mass and black hole mass. We have used observed bound on the freezeout temperature to constrain scalaron mass range by modifying the cosmic expansion rate at the BBN epoch. The mass range of primordial black holes (PBHs) which are astrophysical dark matter candidates is deduced. The range of scalaron mass which does not spoil the BBN era is found to be 10-16–104 eV for both relativistic and non-relativistic scalarons. The window 10-16–10-14 eV of scalaron mass obtained from solar system constraint on PPN parameter is compatible with the BBN bound derived in this work. The PBH mass range is obtained as 106–10-14 M ⊙. Scalarons constrained by BBN are also eligible to accommodate axion like dark matter particles. The problem of ultra-light PBHs (M ≤ 10-24 M ⊙) not constrained by the present study of BBN is still open. Estimation of deuterium (D) fraction and relative D+3He abundance in the f(R) gravity scenario shows that the BBN history mimics that of general relativity. While the PBH mass range is eligible for non-baryonic dark matter, the BBN bounded scalarons provide with an independent strong field test of f(R) gravity. The PBH mass range obtained in the study is discussed in relation to future astronomical measurements.

Big Bang Nucleosynthesis with f(R) Gravity Scalarons and Astrophysical Consequences

“…where m ψ and T represent scalaron mass and temperature, respectively, and ζ(ν) and Γ(ν) represent Riemann zeta function and gamma function for a number ν, respectively. It has been found earlier that the scalaron density parameter is independent of scalaron mass in the relativistic case (Talukdar et al 2024). Therefore, the BBN calculation cannot be used for constraining scalaron mass for the relativistic case.…”

“…-, where T H is the Hawking temperature of a black hole (see Kalita 2020 for details of such calculations). The scalaron mass (m ψ ) is found to be inversely proportional to the black hole mass (M), and in natural units, c = 1 = h, it is given by (Talukdar et al 2024),…”

“…It has been found that for nonrelativistic scalarons the scalaron density parameter is dependent on scalaron mass (see below), and therefore, it is possible to constrain scalaron mass by using the density parameter in the BBN code. Assuming scalarons to be in thermal equilibrium with radiation and applying Bose-Einstein statistics in the radiation era, the scalaron mass density has been obtained as (Talukdar et al 2024)…”

“…where N is the number of effective relativistic degrees of freedom and is expressed as We have considered scalaron mass in the range (1 − 10 5 ) eV. This mass range is enclosed by (10 −16 − 10 5 ) eV, which was obtained earlier from the observed shift of freeze-out temperature (Talukdar et al 2024). In this work, the higher end of scalaron mass is considered for obtaining the lower bound on the PBH mass (see Equation (3)).…”