Multi-Field versus Single-Field in the Supergravity Models of Inflation and Primordial Black Holes

Abstract

We review the models unifying inflation and Primordial Black Hole (PBH) formation, which are based on the modified (Starobinsky-type) supergravity. We begin with the basic (Starobinsky) inflationary model of modified gravity and its alpha-attractor-type generalizations for PBH production, and recall how all those single-field models can be embedded into the minimal supergravity. Then, we focus on the effective two-field models arising from the modified (Starobinsky-type) supergravity and compare them to the single-field models under review. Those two-field models describe double inflation whose first stage is driven by Starobinsky’s scalaron and whose second stage is driven by another scalar belonging to the supergravity multiplet. The power spectra are numerically computed, and it is found that the ultra-slow-roll regime gives rise to the enhancement (peak) in the scalar power spectrum leading to an efficient PBH formation. The resulting PBH masses and their density fraction (as part of dark matter) are found to be in agreement with cosmological observations. The PBH-induced gravitational waves, if any, are shown to be detectable by the ground-based and space-based gravitational interferometers under construction.

1D Supergravity FLRW Model of Starobinsky

“…Nowadays, it continues to be a viable inflationary model. The predicted spectral index and tensor-to-scalar ratio, n s ≈ 0.96, r ≈ 0.004, respectively, with M of the order of 10 13 GeV, are in good agreement with current observational data [4][5][6].…”

“…Nevertheless, it continues to be considered, in particular in view of recent results [15]. On the other side, there is no reason why supersymmetry should break at LHC scales; it can be much higher [5]. Inflation can be considered from Planck energy scale [16].…”

“…The connection between f (R) and f (R) is, however, not straightforward, due to auxiliary fields satisfying the rather involved algebraic equations of motion [22]. More general actions depending not only on R, but its supersymmetric covariant derivatives, have been used to properly embed the model of Starobinsky into N = 1, 2 4D supergravity [5,[23][24][25].…”

“…By choosing a specific superpotential, we obtain a model whose bosonic part contains Starobinsky and a massive scalar field. We present numerical solutions to the pure bosonic equations of motion, which exhibit inflation driven by the quadratic curvature term, whereas the scalar field is pushed to the minimum energy state (see [5] for another example of a two-field model, where the effect on inflation of both fields is detailed). In Section 5, we present the Hamiltonian formulation, including bosons and fermions, of the equivalent scalar-'tensor' actions for the two models constructed.…”

Cosmological Formation of (2 + 1)-Dimensional Soliton Structures in Models Possessing Potentials with Local Peaks

“…The considered relief form often occurs in theories of modified multidimensional gravity [24]. In addition, supergravity and string theories produce models with effective potentials which might be locally described by the potential form under consideration [25]. Previously, solitons formation in the models with the same potential of two scalar fields in the (1 + 1)-space-time was considered [26,27], and the first results in the (2 + 1)-models were obtained [28,29].…”