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Vector Curvaton

without istabilities

Konstantinos Dimopoulos

Lancaster University

Work done with M. Karciauskas and J.M. Wagstaff

0907.1838, 0909.0475

e.g. inflation due to geometry: gravity ( - inflation)Scalar vs Vector Fields

- Scalar fields employed to address many open issues: inflationary paradigm, dark energy (quintessence) baryogenesis (Affleck-Dine)

- Scalar fields are ubiquitous in theories beyond the standard model such as Supersymmetry (scalar partners) or string theory (moduli)

- However,no fundamental scalar field has ever been observed

- Designing models using unobserved scalar fields undermines their predictability and falsifiability, despite the recent precision data

- The latest theoretical developments (string landscape) offer too much freedom for model-building

- Can we do Cosmology without scalar fields?

- Some topics are OK:

Baryogenesis

, Dark Matter

, Dark Energy (ΛCDM)

- Inflation without fundamental scalar fields is also possible:

- However, to date,no mechanism for the generation of the curvature/density perturbation without a scalar field exists

l=5 in galactic coordinates

l=5 in preferred frame

Why not Vector Fields?- Inflation homogenizes Vector Fields

- To affect / generate the curvature perturbation a Vector Field needs to (nearly) dominate the Universe

- Homogeneous Vector Field = in general anisotropic

- Basic Problem:the generatation of a large-scale anisotropy is in conflict with CMB observations

- However, An oscillating massive vector field can avoid excessive large-scale anisotropy

- Also, some weak large-scale anisotropy might be present in the CMB (“Axis of Evil”):

Massive vector field:

Abelian vector field:

Equations of motion:

Flat FRW metric:

Inflation homogenises the vector field:

& Klein-Gordon

Massive Abelian Vector FieldRenormalisable

- To retain isotropy the vector field must not drive inflation

Vector Inflation [Golovnev et al. (2008)] uses 100s of vector fields

&

- Eq. of motion:

harmonic oscillations

Vector Curvaton- Safe domination of Universe required

[KD, PRD 74 (2006) 083502]

Pressureless

and Isotropic

- Vector field domination can occur without introducing significant anisotropy. The curvature perturbation is imposed at domination

Mass term not enough no scale invariance

(e.g. , , or )

- Typically, introduce Xterm :

- Find eq. of motion for vector field perturbations:

Fourier transform:

Promote to operator:

Polarization

vectors:

Canonical quantization:

Particle Production of Vector Fields- Breakdown of conformality of massless vector field is necessary

Conformal Invariance: vector field does not couple to metric

(virtual particles not pulled outside Horizon during inflation)

Solve with vacuum boundary conditions:

&

Lorentz boost factor:

from frame with

- Obtain power spectra:

expansion = isotropic

- Case A:

parity violating

- Case B:

parity conserving (most generic)

isotropic particle production

- Case C:

- Statistical Anisotropy: anisotropic patterns in CMB

Observations: weak bound

- Vector Curvaton = solely responsible for only in Case C

Groeneboom and Eriksen (2009)

- Cases A&B: vector curvaton = subdominant: statistical anisotropy only

(Parity conserving)

- Case B: Vector curvaton contribution to must be subdominant

- Possible instabilities:

Himmetoglu, Contaldi and Peloso (2009)

Exact solution found with no pathologies

KD, Karciauskas, Lyth and Rodriguez (2009)

Scale invariance if:

&

Non-minimal coupling to GravityKD & Karciauskas

(2008)

- The vector curvaton can cause statistical anisotropy only

- Longitudinal component unstable at horizon crossng

- Longitudinal component = ghost when subhorizon

Interactions with other fields = negligible

Subhorizon for limited time (from Planck length to Horizon)

Negative energy subdominant to inflation energy

Motivates model even if vector field is not gauge boson

at Horizon exit

-1 ± 3

- If gauge boson then (weakly coupled during inflation)

- In supergravity = gauge kinetic function (holomorphic)

-4

- Kahler corrections to the scalar potential result in masses:

- Fast-rolling scalar fields cause significant variation to

It is natural to expect during inflation

- Paticle production anisotropic (Case B) if:

6

1< < 10

- Vector Curvaton can be naturally realised in SUGRA, without

- Paticle production isotropic (Case C) if:

<

Vector Curvaton without instabilitiesKD (2007)

- Maxwell kinetic term does not suffer from instabilities (ghost-free)

Scale invariance:

No need for fundamental scalar field

The vector field can act as a curvaton if, after inflation, its mass becomes: ( zero VEV: vacuum = Lorentz invariant )Conclusions

- Vetor Curvaton: the only known mechanism which can form the curvature perturbation without fundamntal scalar fields

- In this case, the vector field undergoes rapid harmonic oscillations during which it acts as a pressureless isotropic fluid

- Hence, the vector field introduces negligible anisotropy at domination

- If particle production is isotropic then the vector curvaton can alone generate the curvature perturbation in the Universe

- If particle production is anisotropic then the vector curvaton can give rise to statistical anisotropy, potentially observable by Planck

- A Massive Abelian vector curvaton with a Maxwell kinetic term & varying kinetic function and mass can generate isotropic (anisotropic) perturbations if heavy (light) by end of inflation without giving rise to any instabilities (e.g. ghosts)

- The challenge is to obtain candidates in theories beyond the standard model, which can play the role of the vector curvaton

0907.1838

0909.0475

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