A natural and intuitive way of deriving the standard inflationary ΛCDM cosmological model is by identifying the Type-IIB Kähler modulus with the ΛCDM-inflaton. The -brane interaction is of particular importance because the worldvolume theory on a stack of -branes probing a Calabi-Yau 3-fold is a 4-D supersymmetric gauge theory and the importance of a worldvolume theory derives, via duality-relations, from F-theory compactification by availing ourselves to the heterotic/F-theory duality in eight dimensions. Generally, for a -brane, , there naturally is a -D SYM theory associated with its worldvolume , where the Dirac-Born-Infeld action is given by:

coupled to a Chern-Simons Wess-Zumino term:

the worldvolume pullback, and the corresponding p-orientifold action is:

with the string-coupling given by:

and the pullbacks SUGRA fields to the -brane worldvolume. Thus, we can derive the action:

with:

which yields a 10-D SYM action:

with:

and the non-abelian field strength of the gauge field :

where the gauge covariant derivative is defined by:

giving us the -worldvolume SYM action:

with:

with the potential:

that will figure in the Kähler form that will characterize -brane cosmology. -branes are central not simply because of F-theory compactification due to backreaction and Type-IIB axio-dilaton, but also because the Kähler moduli space induced by the -brane F-theoretic backreaction has a modulus that can naturally be identified with the ΛCDM-inflaton. Thus, inflationary cosmology can be derived, up to isomorphism, from 6D F-theory compactification using the Type-IIB string-theory/11D SUGRA duality upon dimensional reduction to 4D, where the Type-IIB SUGRA action in the string frame is given by:

with:

In light of flux moduli stabilization, this is a natural framework since the Kähler moduli potential apriori allows a Type-IIB-modulus/ΛCDM-inflaton identification. In such a SYM -brane scenario, we have an -flaton model in the Large Volume Scenario that evades the -problem, and periodicity of the modulus is achieved by defluxing the pullback of the -term on the superstring worldsheet. This can be readily seen since the total supersymmetric worldsheet action in conformal gauge:

with:

has modular-invariance. The skeleton of Type-IIB flux compactification on a Calabi-Yau threefold is constructed from a superpotential of the form:

where:

is the Gukov-Vafa-Witten superpotential…

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