A scaling invariance of k-inflation background equations allows parameter redefinitions that normalize the curvature perturbation spectrum at the CMB pivot scale without altering its shape.
Rolling Tachyon in Brane World Cosmology from Superstring Field Theory
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The pressureless tachyonic matter recently found in superstring field theory has an over-abundance problem in cosmology. We argue that this problem is naturally solved in the brane inflationary scenario if almost all of the tachyon energy is drained (via its coupling to the inflaton and matter fields) to heating the universe, while the rest of the tachyon energy goes to a network of cosmic strings (lower-dimensional BPS D-branes) produced during the tachyon rolling at the end of inflation.
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A scaling invariance of the perturbations in $k$-inflation models
A scaling invariance of k-inflation background equations allows parameter redefinitions that normalize the curvature perturbation spectrum at the CMB pivot scale without altering its shape.