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.
