Self-tracking solutions for asymptotic scalar fields

A bstract We explore the dynamics of pure scalar fields rolling on an exponential potential in the absence of any additional background fluid and demonstrate the existence of self-tracking solutions in which the self-perturbations of the scalar field act as an effective radiation background. The validity of these solutions is demonstrated through both analytic techniques and numerical simulations using $$ \mathcal{C}\textrm{osmo}\mathcal{L}\textrm{attice} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> <mml:mtext>osmo</mml:mtext> <mml:mi>L</mml:mi> <mml:mtext>attice</mml:mtext> </mml:math> . We discuss applications to string cosmologies with significant trans-Planckian field excursions between inflation and BBN, including the required initial level of scalar perturbations to avoid overshoot.