# Power law inflation with electromagnetism

## Abstract

We generalize Ringström’s global future causal stability results (Ringström 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 (M{sup n+1},g{sup -hat}, ϕ{sup -hat}) considered by Ringström (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 Ringström (2009) [11]) we focus on pairs of relatively scaled open sets U{sub R{sub 0}}⊂U{sub 4R{sub 0}} on an initial slice of (M{sup n+1},g{sup -hat}), and if we choose a set of perturbed data which on U{sub 4R{sub 0}} is sufficiently close to that of (M{sup n+1},g{sup -hat},ϕ{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,ϕ,A) of this data via the Einstein–Maxwell-scalar field equations, all causal geodesics emanating from U{sub R{sub 0}} are future complete (just as in (M{sup n+1},g{sup -hat})). We also verify that, in a certain sense, the future asymptotic behaviormore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 22220760

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 334; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; COSMOLOGICAL MODELS; DISTURBANCES; ELECTROMAGNETISM; GENERAL RELATIVITY THEORY; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION THEORY; POTENTIALS; SCALAR FIELDS; SPACE-TIME; STABILITY; TOPOLOGY

### Citation Formats

```
Luo, Xianghui, and Isenberg, James, E-mail: isenberg@uoregon.edu.
```*Power law inflation with electromagnetism*. United States: N. p., 2013.
Web. doi:10.1016/J.AOP.2013.04.009.

```
Luo, Xianghui, & Isenberg, James, E-mail: isenberg@uoregon.edu.
```*Power law inflation with electromagnetism*. United States. doi:10.1016/J.AOP.2013.04.009.

```
Luo, Xianghui, and Isenberg, James, E-mail: isenberg@uoregon.edu. Mon .
"Power law inflation with electromagnetism". United States. doi:10.1016/J.AOP.2013.04.009.
```

```
@article{osti_22220760,
```

title = {Power law inflation with electromagnetism},

author = {Luo, Xianghui and Isenberg, James, E-mail: isenberg@uoregon.edu},

abstractNote = {We generalize Ringström’s global future causal stability results (Ringström 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 (M{sup n+1},g{sup -hat}, ϕ{sup -hat}) considered by Ringström (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 Ringström (2009) [11]) we focus on pairs of relatively scaled open sets U{sub R{sub 0}}⊂U{sub 4R{sub 0}} on an initial slice of (M{sup n+1},g{sup -hat}), and if we choose a set of perturbed data which on U{sub 4R{sub 0}} is sufficiently close to that of (M{sup n+1},g{sup -hat},ϕ{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,ϕ,A) of this data via the Einstein–Maxwell-scalar field equations, all causal geodesics emanating from U{sub R{sub 0}} are future complete (just as in (M{sup n+1},g{sup -hat})). 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 (M{sup n+1},g{sup -hat}, ϕ{sup -hat}, A{sup -hat} = 0). -- Highlights: •We prove stability of expanding solutions of the Einstein–Maxwell-scalar field equations. •All nearby solutions are geodesically complete. •The topology of the initial slice is irrelevant to our stability results.},

doi = {10.1016/J.AOP.2013.04.009},

journal = {Annals of Physics (New York)},

number = ,

volume = 334,

place = {United States},

year = {Mon Jul 15 00:00:00 EDT 2013},

month = {Mon Jul 15 00:00:00 EDT 2013}

}