Power law inflation with electromagnetism

We generalize Ringstrom's global future causal stability results (Ringstrom 2009) [11] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein-Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (Mn+1, (g) over cap, (phi) over cap) considered by Ringstrom (2009) in [11] are solutions of the Einstein-Maxwell-scalar field system (with exponential potential) as well as of the Einstein-scalar field system (with the same exponential potential), we consider (nonlinear) perturbations of initial data sets of these spacetimes which include electromagnetic perturbations as well as gravitational and scalar perturbations. We show that if (as in Ringstrom (2009) [11]) we focus on pairs of relatively scaled open sets U-R0 subset of U-4R0 on an initial slice of (Mn+1, (g) over cap and if we choose a set of perturbed data which on U-4R0 is sufficiently close to that of (Mn+1, (g) over cap, (phi) over cap, (A) over cap = 0), then in the maximal globally hyperbolic spacetime development (Mn+1, g, phi, A) of this data via the Einstein-Maxwell-scalar field equations, all causal geodesics emanating from U-R0 are future complete (just as in (Mn+1, (g) over cap)). We also verify that, in a certain sense, the future asymptotic behavior of the fields in the spacetime developments of the perturbed data sets does not differ significantly from the future asymptotic behavior of (Mn+1, (g) over cap, (phi) over cap, (A) over cap = 0). (c) 2013 Elsevier Inc. All rights reserved.