Primordial magnetic seeds from string cosmology

1. Primordial magnetic seeds from string cosmology M. Gasperini Bologna September 2005 International conference on The origin and evolution of cosmic magnetism

2. Primordial magnetic seeds: very early (inflationary?) production, fundamental high-energy interactions • Primordial seeds: possible sources for large scale fields (see e.g. M. Giovannini, 2004; Grasso and Rubinstein, 2001) • How to produce them?

3. Most natural mechanism: inflation • even in vacuum, F  0 because of quantum fluctuations • accelerated expansion Ffrozen outside horizon  amplified after re-entry Inflation should produce primordial, large scale e. m. fields (just like it produces scalar “seeds” for the CMB anisotropy) However …

4. Does not work for the Maxwell action minimally • coupled to a conformally flat background: • the canonical action for quantum fluctuations decouples from the geometry: (radiation gauge, ) free, oscillating vacuum solutions insensitive to the cosmological expansion

5. How to avoid this conclusion? • non conformally-flat metric backgrounds • non-conformal couplings to the geometry • non-conformal couplings to other background fields

6. 1 - Non conformally-flat metric backgrounds:modify the geometry, not the Maxwell action • Ex.1: Kasner-like (non isotropic) expansion(K. Lotze, 1990) • Ex.2: direct product of 3 ext. and n internal (dynamical) dimensions e. m. action (radiation gauge, K.K. ansatz) canonical quantum fluctuations amplified by the evolution of the internal geometry (M. Giovannini, 2000)

7. 2 - Non conformal couplings to gravity • Non-minimal couplings to the curvature, ~ RF2 + RA2 terms (Turner and Widrow, 1988; Basset et al, 2000) • Quantum (trace- anomaly) breaking of conformal symmetry (Dolgov, 1993) • Trans-Planckian non-conformal boundary term, ~ M-2∫∂(A2 ∂2 K), M ~ 10-34 eV(Ashoorioon and Mann, 2005)

8. 3 - Non-conformal couplings to other fields • non-minimal coupling to the inflaton (Ratra, 1992) • non-minimal coupling to the axion (Garretson et al, 1992; Brandemberger et al, 1999) • coupling to the dilaton (M. G. , Giovannini and Veneziano, 1995; Lemoine, 1995) • minimal coupling to charged scalar fields (Calzetta et al, 1997; Giovannini and Shaposhnikov, 2000; Davis et al, 2000: Finelli, 2000) • spontaneous breaking of Lorentz symmetry (Bertolami and Mota, 1998) • coupling to metric and matter perturbations (Marklund et al, 2000; 2003; Maroto, 2000; Matarrese et al, 2004; Takahashi et al, 2005) • coupling to gravi-photons (M. G., 2001) • ……..

9. String effective action(tree-level in the loop expansion, lowest order in ’ ) = dimensionally reduced dilaton (including volume internal dimensions) =1 heteroting superstring  = constant parameter =1/2 Type I superstrings canonical quantum fluctuations possibly amplified by the dilaton evolution

10. Difference from other mechanisms: coupling to the dilaton notinvented ad hoc, but prescribed by string theory • The prescribed coupling does not automatically guarantee an efficient seed production • Amplification of fluctuations strongly depends on the details of the dilaton evolution constraints on seed production can be used as constraints on string theory models of the early Universe

11. Typical string cosmology model:the “minimal” pre-big bang scenario • low-energy, dilaton-driven phase: fully determined • string phase: two unknown parameters, duration zs = s / and acceleration, gs / g1 PRE-BIG BANG POST-BIG BANG g1 dilaton coupling g = e/2 gs curvature scale H2 time s 1 dilaton phase string phase standard radiation phase

12. Amplification of e. m. fluctuations: two-parameter spectrum. Energy density  (critical units) : log(,t0) log s 1 • unknown parameters: slope and extension of the high frequency branch. • end-point g(1) : controlled by the string scale, MS / MP ~ 0.1 : r(t0) ~10-4

13. Main constraints on the e. m. spectrum - Homogeneity, and negligible backreaction: (,t) /r(t)< 1 (all times, all scales ) - Efficient (large enough) seed production: model dependent Example: standard galactic dynamo (Turner and Widrow, 1988) • Required seed field: • Required energy density: • Required coherence scale:

14. Heterotic superstring model (=1) Assuming g1=MS/MP ~0.1 ,all conditions satisfied in a wide region of parameter space Efficient seed production(M. G., Giovannini and Veneziano, 1995) long enough string phase, zS > 1010 small enough initial dilaton, gS/g1 < 10-20

15. Independent checks of the string cosmology predictions • Seed production associated to graviton production with related spectrum • e. m. constraints directly affect the shape of the graviton spectrum • Heterotic model (=1):no overlap between seed production and graviton detection (evaded by string models with ≠1) (M. G.,1995)

16. Conclusion • Inflationary production of primordiale seeds: an interesting open problem of contemporary astrophysics. • String cosmology suggests a possible “dilatonic” solution • Consistency of this solution leads to important information on primordial cosmology and Planck/string scale physics