Confronting the magnetically-induced holographic composite inflation with observation

We study the observational predictions of the phenomenological anti-de Sitter (AdS)/QCD inspired model, in which the inflaton field emerges in a four-dimensional strongly coupled gauge theory, in which the chiral symmetry breaking occurs through the formation of the quark condensate. Based on a top-down approach of AdS/QCD, using a D7-brane in the background of $N_c$ D3-branes, it has already been shown that chiral symmetry breaking in a magnetic field through the generation of the Higgs vacuum expectation value could be a second-order phase transition, although it was doubted that this scenario could lead to enough inflation. Using an iterative method, we consistently solve for the time-dependent parameters, including the embedding function of the D7-brane and the Hubble parameter of the expanding background. We show that with $N_c\sim 10^7$ and $g_{\rm{}_{UV}}\sim {\rm few}\times 0.1$, the predictions of the inflationary model are consistent with the most stringent constraints placed on the inflationary models by Planck 2018. Although the model is capable of producing a large amount of gravitational waves, $r\simeq 0.01$, the displacement of the canonical mass dimension-1 scalar field remains below the Planck mass, in violation of the Lyth bound.