1. Curvature Perturbations from a Non-minimally Coupled Vector Boson Field Mindaugas Karčiauskas work done with Konstantinos Dimopoulos Mindaugas Karčiauskas work done with Konstantinos Dimopoulos arXiv:0803.3041

2. Density Perturbations and Vector Fields ● Explain the origin of cosmological structure; ● Curvature perturbations – so far only scalar fields have been used; ● No fundamental scalar field has been observed yet; ● In our model we use a vector field to produce density perturbations. ● Explain the origin of cosmological structure; ● Curvature perturbations – so far only scalar fields have been used; ● No fundamental scalar field has been observed yet; ● In our model we use a vector field to produce density perturbations.

3. Vector Fields ● Conformal invariance must be broken; ● Literature of primordial magnetic fields (e.g. Turner, Widrow (1988) ) ● Must preserve isotropy of the Universe; ● Massive oscillating vector field acts as an isotropic pressureless matter, i.e. ; (Dimopoulos (2006)) ● Our model: - mass - Ricci scalar ● Conformal invariance must be broken; ● Literature of primordial magnetic fields (e.g. Turner, Widrow (1988) ) ● Must preserve isotropy of the Universe; ● Massive oscillating vector field acts as an isotropic pressureless matter, i.e. ; (Dimopoulos (2006)) ● Our model: - mass - Ricci scalar

4. Particle Production ● Quasi de Sitter inflation = exponential expansion  ; ● Power spectrum: where ● Scale invariance  when ● WMAP 5   ● Quasi de Sitter inflation = exponential expansion  ; ● Power spectrum: where ● Scale invariance  when ● WMAP 5   Hinshaw et al. (2008)

5. Evolution of the Field ● is a commoving field, the physical field is ; ● Inflation  ● Equation of motion for the field ( ): ● is a commoving field, the physical field is ; ● Inflation  ● Equation of motion for the field ( ):  

6. Evolution of the energy- momentum ● Energy-momentum tensor: ● Energy-momentum tensor:   ( )  

7. I. : II. : I. : II. : Curvaton Mechanism vector field must be subdominant vector field must be subdominant   Vector field oscillates Vector field oscillates   almost as pressureless isotropic matter (Dimopoulos (2006)) small anisotropy small anisotropy & & Vector field Vector field HBB Inflation

8. Constraints ● Curvaton mechanism : ● Curvaton mechanism :   (Lyth, Wands (2004)) SCALAR imprints perturbations imprints perturbations

9. Constraints ● Curvaton mechanism : ● Curvaton decay before BBN; ● Gravitational decay; ● Field must stay sub-plankian; ● Condensate evaporation; ● Curvaton mechanism : ● Curvaton decay before BBN; ● Gravitational decay; ● Field must stay sub-plankian; ● Condensate evaporation;   (Lyth, Wands (2004)) SCALAR imprints perturbations imprints perturbations

10. Conclusions ● Massive Abelian vector field can generate density perturbations; ● Perturbations are of scalar nature; ● Constraints from anisotropy and non- Gaussianity in CMB; ● We have presented an example with non- minimal coupling to gravity ( ); ● Parameter space: ; ● No need for scalar fields at all (eg. inflation). ● Massive Abelian vector field can generate density perturbations; ● Perturbations are of scalar nature; ● Constraints from anisotropy and non- Gaussianity in CMB; ● We have presented an example with non- minimal coupling to gravity ( ); ● Parameter space: ; ● No need for scalar fields at all (eg. inflation). arXiv:0803.3041