The Curvature Perturbation from Vector Fields the Vector
The Curvature Perturbation from Vector Fields: the Vector Curvaton Case Mindaugas Karčiauskas Dimopoulos, Karčiauskas, Lyth, Rodriguez, Karčiauskas, Dimopoulos, Lyth, JCAP 13 (2009) PRD 80 (2009) Dimopoulos, Karčiauskas, Wagstaff, ar. Xiv: 0907. 1838 Dimopoulos, Karčiauskas, Wagstaff, ar. Xiv: 0909. 0475
Density perturbations ● Primordial curvature perturbation – a unique window to the early Universe; ● Origin of structure <= quantum fluctuations; ● Scalar fields - the simplest case; ● Why vector fields: ● Theoretical side: ● No fundamental scalar field has been discovered; ● The possible contribution from gauge fields is neglected; ● Observational side: Land & Magueijo (2005) ● Axis of Evil: alignment of 2 -4 -8 -16 spherical harmonics of CMB; ● Large cold spot, radio galaxy void;
The Vector Curvaton Scenario ● The energy momentum tensor ( I. Inflation scale invariant spectrum II. Light Vector Field III. Heavy Vector Field vector field oscillations Preasureless isotropic Dimopoulos (2006) matter: IV. Vector Field Decay. onset of the Hot Big Bang ):
Vector Field Perturbations ● Massive vector field => 3 degrees of freedom; ● The power spectra ● The anisotropy parameters of particle production : Parity conserving theories:
Vector Field Perturbations From observations, statistically anisotropic contribution <30%. Statistically isotropic Groeneboom & Eriksen (2009) Statistically anisotropic
The Curvature Perturbation ● The total curvature perturbation ● The curvature perturbation (δN formula) , where ● The anisotropic power spectrum of the curvature perturbation: ● Current observational constraints: Groeneboom & Eriksen (2009) ● Expected from Plank if no detection: Pullen & Kamionkowski (2007) ● For vector field perturbations ● The non-Gaussianity
Non-Minimal Vector Curvaton ●Scale invariance => ● The vector field power spectra: => ● The anisotropy in the power spectrum: ● Non-Gaussianity: 1. Anisotropic 2. Modulation is not subdominant 3. 4. Same preferred direction. 5. Configuration dependent modulation.
Varying Kinetic Function See Jacques’ talk on Wednesday ● At the end of inflation: and ● Scale invariance: 1. 2. ● 2 nd case: ● Small coupling => can be a gauge field; ● Richest phenomenology; .
At the end of inflation Light vector field Heavy vector field Anisotropic Isotropic particle production
The Anisotropic Case, ● The anisotropy in the power spectrum: ● The non-Gaussianity: 1. Anisotropic 2. Modulation is not subdominant 3. 4. Same preferred direction ● The parameter space 5. Configuration dependent modulation &
The Isotropic Case, ● No scalar fields needed! ● Standard predictions of the curvaton mechanism: ● The parameter space:
Conclusions ● Vector fields can affect or even generate the curvature perturbation; ● If anisotropic particle production ( 1. Anisotropic and . 2. Modulation is not subdominant 3. , where 4. Same preferred direction . 5. Configuration dependent modulation. ● If isotropic particle => no need for production scalar fields ● Two examples: 1. 2. ):
Dimopoulos, Karčiauskas, Lyth, Rodriguez, Karčiauskas, Dimopoulos, Lyth, JCAP 13 (2009) PRD 80 (2009) Dimopoulos, Karčiauskas, Wagstaff, ar. Xiv: 0907. 1838 Dimopoulos, Karčiauskas, Wagstaff, ar. Xiv: 0909. 0475
Anisotropy Parameters ● Anisotropy in the particle production of the vector field: ● Statistical anisotropy in the curvature perturbation:
Isotropic Random Fields with Statistical Anisotropy - preferred direction
Present Observational Constrains ● The power spectrum of the curvature perturbation: & almost scale invariant; ● Non-Gaussianity from WMAP 5 (Komatsu et. al. (2008)):
δN formalism ● To calculate we use formalism (Sasaki, Stewart (1996); Lyth, Malik, Sasaki (2005)); ● Recently in was generalized to include vector field perturbations (Dimopoulos, Lyth, Rodriguez (2008)): where , , etc.
Estimation of ● For subdominant contribution can be estimated on a fairly general grounds; ● All calculations were done in the limit ● Assuming that one can show
Difficulties with Vector Fields ● Excessive large scale anisotropy The energy momentum tensor ( ● No particle production Massless U(1) vector fields are conformally invariant ):
Avoiding excessive anisotropy ● Orthogonal triad of vector fields Ford (1989) ● Large number of identical vector fields Golovnev, Mukhanov, Vanchurin (2008) ● Modulation of scalar field dynamics Yokoyama, Soda (2008) ● Vector curvaton; Dimopoulos (2006)
Particle Production ● Massless U(1) vector field is conformally invariant no particle => production; ● A known problem in primordial magnetic fields literature; ● Braking conformal invariance: ● Add a potential, e. g. ● Modify kinetic term, e. g.
Stability of the Model ● Two suspected instabilities for longitudinal mode: 1. Ghost; 2. Horizon crossing; 3. Zero mass; 1. Ghost: ● Only for subhorizon modes: ● Initially no particles & weak coupling; 2. Horizon crossing: ● Exact solution: Independent constants:
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