%0 Journal Article 
%A Medina Reus, Elena Blanca
%A Álvarez Galindo, Gabriel
%T Adaptive asymptotic solutions of infationary models in the Hamilton-Jacobi formalism: application to T-models
%D 2024
%@ 1029-8479
%U http://hdl.handle.net/10498/33513
%X We develop a method to compute the slow-roll expansion for the Hubble parameter
in infationary models in a fat Friedmann-Lemaître-Robertson-Walker spacetime that is
applicable to a wide class of potentials including monomial, polynomial, or rational functions
of the infaton, as well as polynomial or rational functions of the exponential of the infaton.
The method, formulated within the Hamilton-Jacobi formalism, adapts the form of the slow roll expansion to the analytic form of the infationary potential, thus allowing a consistent
order-by-order computation amenable to Padé summation. Using T-models as an example, we
show that Padé summation extends the domain of validity of this adapted slow-roll expansion
to the end of infation. Likewise, Padé summation extends the domain of validity of kinetic dominance asymptotic expansions of the Hubble parameter into the fast-roll regime, where
they can be matched to the aforesaid Padé-summed slow-roll expansions. This matching in
turn determines the relation between the expansions for the number N of e-folds and allows
us to compute the total amount of infation as a function of the initial data or, conversely, to
select initial data that correspond to a fxed total amount of infation. Using the slow-roll
stage expansions, we also derive expansions for the corresponding spectral index ns accurate
to order 1/N^2, and tensor-to-scalar ratio r accurate to order 1/N^3 for these T-models.
%K Cosmology of Theories BSM
%K Cosmological models
%K Supergravity Models
%~ Universidad de Cádiz