Presentation is loading. Please wait.

Presentation is loading. Please wait.

The Curvature Perturbation from Vector Fields: the Vector Curvaton Case Mindaugas Karčiauskas Dimopoulos, Karčiauskas, Lyth, Rodriguez, JCAP 13 (2009)

Similar presentations


Presentation on theme: "The Curvature Perturbation from Vector Fields: the Vector Curvaton Case Mindaugas Karčiauskas Dimopoulos, Karčiauskas, Lyth, Rodriguez, JCAP 13 (2009)"— Presentation transcript:

1 The Curvature Perturbation from Vector Fields: the Vector Curvaton Case Mindaugas Karčiauskas Dimopoulos, Karčiauskas, Lyth, Rodriguez, JCAP 13 (2009) Karčiauskas, Dimopoulos, Lyth, PRD 80 (2009) Dimopoulos, Karčiauskas, Wagstaff, arXiv:0907.1838 Dimopoulos, Karčiauskas, Wagstaff, arXiv:0909.0475 Dimopoulos, Karčiauskas, Lyth, Rodriguez, JCAP 13 (2009) Karčiauskas, Dimopoulos, Lyth, PRD 80 (2009) Dimopoulos, Karčiauskas, Wagstaff, arXiv:0907.1838 Dimopoulos, Karčiauskas, Wagstaff, arXiv:0909.0475

2 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: ● Axis of Evil: alignment of 2-4-8-16 spherical harmonics of CMB; ● Large cold spot, radio galaxy void; ● 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: ● Axis of Evil: alignment of 2-4-8-16 spherical harmonics of CMB; ● Large cold spot, radio galaxy void; Land & Magueijo (2005)

3 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 matter: IV.Vector Field Decay. onset of the Hot Big Bang ● The energy momentum tensor ( ): I.Inflation scale invariant spectrum II.Light Vector Field III.Heavy Vector Field vector field oscillations Preasureless isotropic matter: IV.Vector Field Decay. onset of the Hot Big Bang Dimopoulos (2006)

4 Vector Field Perturbations ● Massive => 3 degrees of vector field freedom; ● The power spectra ● The anisotropy parameters of particle production : ● Massive => 3 degrees of vector field freedom; ● The power spectra ● The anisotropy parameters of particle production : Parity conser- ving theories:

5 Vector Field Perturbations Statistically isotropic Statistically anisotropic From observations, statistically anisotropic contribution <30%. Groeneboom & Eriksen (2009)

6 The Curvature Perturbation ● The total curvature perturbation ● The curvature perturbation (δN formula), where ● The anisotropic power spectrum of the curvature perturbation: ● For vector field perturbations ● The non-Gaussianity ● The total curvature perturbation ● The curvature perturbation (δN formula), where ● The anisotropic power spectrum of the curvature perturbation: ● For vector field perturbations ● The non-Gaussianity ● Current observational constraints: ● Expected from Plank if no detection: ● Current observational constraints: ● Expected from Plank if no detection: Pullen & Kamionkowski (2007) Groeneboom & Eriksen (2009)

7 ● The vector field power spectra: ● The anisotropy in the power spectrum: ● Non-Gaussianity: ● The vector field power spectra: ● The anisotropy in the power spectrum: ● Non-Gaussianity: Non-Minimal Vector Curvaton ● Scale invariance => => 1. Anisotropic 2. Modulation is not subdominant 3. 4. Same preferred direction. 5. Configuration dependent modulation. 1. Anisotropic 2. Modulation is not subdominant 3. 4. Same preferred direction. 5. Configuration dependent modulation.

8 ● 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: and. ● Scale invariance: 1. 2. ● 2 nd case: ● Small coupling => can be a gauge field; ● Richest phenomenology; Varying Kinetic Function See Jacques’ talk on Wednesday

9 Anisotropic particle production Anisotropic particle production Isotropic particle production Isotropic particle production Light vector field Light vector field Heavy vector field Heavy vector field At the end of inflation

10 ● The anisotropy in the power spectrum: ● The non-Gaussianity: ● The parameter space & ● The anisotropy in the power spectrum: ● The non-Gaussianity: ● The parameter space & The Anisotropic Case, 1. Anisotropic 2. Modulation is not subdominant 3. 4. Same preferred direction 5. Configuration dependent modulation 1. Anisotropic 2. Modulation is not subdominant 3. 4. Same preferred direction 5. Configuration dependent modulation

11 ● No scalar fields needed! ● Standard predictions of the curvaton mechanism: ● The parameter space: ● No scalar fields needed! ● Standard predictions of the curvaton mechanism: ● The parameter space: The Isotropic Case,

12 ● Vector fields can affect or even generate the curvature perturbation; ● If anisotropic particle production ( ): ● If isotropic particle => no need for production scalar fields ● Two examples: 1. 2. ● Vector fields can affect or even generate the curvature perturbation; ● If anisotropic particle production ( ): ● If isotropic particle => no need for production scalar fields ● Two examples: 1. 2. Conclusions 1. Anisotropic and. 2. Modulation is not subdominant 3., where 4. Same preferred direction. 5. Configuration dependent modulation. 1. Anisotropic and. 2. Modulation is not subdominant 3., where 4. Same preferred direction. 5. Configuration dependent modulation.

13 Dimopoulos, Karčiauskas, Lyth, Rodriguez, JCAP 13 (2009) Karčiauskas, Dimopoulos, Lyth, PRD 80 (2009) Dimopoulos, Karčiauskas, Wagstaff, arXiv:0907.1838 Dimopoulos, Karčiauskas, Wagstaff, arXiv:0909.0475 Dimopoulos, Karčiauskas, Lyth, Rodriguez, JCAP 13 (2009) Karčiauskas, Dimopoulos, Lyth, PRD 80 (2009) Dimopoulos, Karčiauskas, Wagstaff, arXiv:0907.1838 Dimopoulos, Karčiauskas, Wagstaff, arXiv:0909.0475

14

15 Anisotropy Parameters ● Anisotropy in the particle production of the vector field: ● Statistical anisotropy in the curvature perturbation: ● Anisotropy in the particle production of the vector field: ● Statistical anisotropy in the curvature perturbation:

16 Random Fields with Statistical Anisotropy Isotropic - preferred direction

17 Present Observational Constrains ● The power spectrum of the curvature perturbation: & almost scale invariant; ● Non-Gaussianity from WMAP5 (Komatsu et. al. (2008)) : ● The power spectrum of the curvature perturbation: & almost scale invariant; ● Non-Gaussianity from WMAP5 (Komatsu et. al. (2008)) :

18 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. ● 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.

19

20 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 that ● For subdominant contribution can be estimated on a fairly general grounds; ● All calculations were done in the limit ● Assuming that one can show that

21 Difficulties with Vector Fields ● Excessive large scale anisotropy The energy momentum tensor ( ): ● No particle production Massless U(1) vector fields are conformally invariant ● Excessive large scale anisotropy The energy momentum tensor ( ): ● No particle production Massless U(1) vector fields are conformally invariant

22 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) ● 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)

23 Particle Production ● Massless U(1) vector no particle field is conformally => production; invariant ● A known problem in primordial magnetic fields literature; ● Braking conformal invariance: ● Add a potential, e.g. ● Modify kinetic term, e.g. ● Massless U(1) vector no particle field is conformally => production; invariant ● A known problem in primordial magnetic fields literature; ● Braking conformal invariance: ● Add a potential, e.g. ● Modify kinetic term, e.g.

24 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: ● 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:


Download ppt "The Curvature Perturbation from Vector Fields: the Vector Curvaton Case Mindaugas Karčiauskas Dimopoulos, Karčiauskas, Lyth, Rodriguez, JCAP 13 (2009)"

Similar presentations


Ads by Google