On the Vacuum Structure of the N=4 Conformal Supergravity

Abstract

We consider N=4 conformal supergravity with an arbitrary holomorphic function of the complex scalar S which parametrizes the SU(1,1)/U(1) coset. Assuming non-vanishings vevs for S and the scalars in a symmetric matrix Eij of the 10¯ of SU(4) R-symmetry group, we determine the vacuum structure of the theory. We find that the possible vacua are classified by the number of zero eigenvalues of the scalar matrix and the spacetime is either Minkowski, de Sitter, or anti-de Sitter. We determine the spectrum of the scalar fluctuations and we find that it contains tachyonic states which, however, can be removed by appropriate choice of the unspecified at the supergravity level holomorphic function. Finally, we also establish that S-supersymmetry is always broken whereas Q-supersymmetry exists only on flat Minkowski spacetime.

Constraints on the curvature power spectrum from primordial black hole evaporation

“…This scenario in the realistic framework of the inflationary attractors has been examined in Ref. [25]. In this case we find that…”

“…Actually, it is the low mass window, M • M , the most promising one for explaining the dark matter in the galaxies, according to the current observational constraints. Several inflation models that achieve the required P R (k) enhancement have been proposed the last years [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] putting forward new ideas and elaborating further earlier works [28][29][30][31][32][33]. The shape of the P R (k) at small scales is mainly constrained at a scale k • where the abundance of relic PBHs maximizes.…”