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

The Curvature Perturbation from Vector Fields: the Vector Curvaton Case

The Curvature Perturbation from Vector Fields: the Vector Curvaton Case

Mindaugas KarčiauskasMindaugas Karčiauskas

Dimopoulos, Karčiauskas, Lyth, Rodriguez, JCAP 13

(2009)

Karčiauskas, Dimopoulos, Lyth, PRD 80 (2009)

Dimopoulos, Karčiauskas, Wagstaff,

arXiv:0907.1838


arXiv:0909.0475


(2009)



arXiv:0907.1838


arXiv:0909.0475

Density perturbationsDensity 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)Land & Magueijo (2005)

The Vector Curvaton Scenario

The Vector Curvaton Scenario

● The energy momentum tensor ( ):

I. Inflationscale invariant spectrum

II. Light Vector Field

III. Heavy Vector Fieldvector field oscillationsPreasureless isotropic matter:

IV. Vector Field Decay.onset of the Hot Big Bang

● The energy momentum tensor ( ):

I. Inflationscale invariant spectrum

II. Light Vector Field

III. Heavy Vector Fieldvector field oscillationsPreasureless isotropic matter:

IV. Vector Field Decay.onset of the Hot Big Bang

Dimopoulos (2006)Dimopoulos (2006)

Vector Field PerturbationsVector 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:

Parity conser-ving

theories:

Vector Field PerturbationsVector Field Perturbations

Statistically isotropicStatistically isotropic

Statistically anisotropicStatistically anisotropic

From observations, statistically anisotropic contribution <30%.From observations, statistically anisotropic contribution <30%.

Groeneboom & Eriksen (2009)Groeneboom & Eriksen (2009)

The Curvature Perturbation

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)Pullen & Kamionkowski (2007)

Groeneboom & Eriksen (2009)Groeneboom & Eriksen (2009)

● The vector field power spectra:

● The anisotropy in the power spectrum:

● Non-Gaussianity:

● The vector field power spectra:


● Non-Gaussianity:

Non-Minimal Vector Curvaton

Non-Minimal Vector Curvaton

●Scale invariance =>

=>=>

1. Anisotropic

2. Modulation is not subdominant

3.

4. Same preferred direction.

5. Configuration dependent modulation.

1. Anisotropic


3.

4. Same preferred direction.


● At the end of inflation: and .

● Scale invariance:

1. 2.

● 2nd case:

● Small coupling => can be a gauge field;

● Richest phenomenology;

● At the end of inflation: and .

● Scale invariance:

1. 2.

● 2nd case:

● Small coupling => can be a gauge field;

● Richest phenomenology;

Varying Kinetic FunctionVarying Kinetic FunctionSee Jacques’ talk on Wednesday

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 inflationAt the end of inflation


● The non-Gaussianity:

● The parameter space

&


● The non-Gaussianity:

● The parameter space

&

The Anisotropic Case,

The Anisotropic Case,

1. Anisotropic


3.

4. Same preferred direction

5. Configuration dependent modulation

1. Anisotropic


3.

4. Same preferred direction

5. Configuration dependent modulation

● 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,The Isotropic Case,

● 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.

ConclusionsConclusions

1. Anisotropic and .


3. , where

4. Same preferred direction .


1. Anisotropic and .


3. , where

4. Same preferred direction .



(2009)



arXiv:0907.1838


arXiv:0909.0475


(2009)



arXiv:0907.1838


arXiv:0909.0475

Anisotropy ParametersAnisotropy 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:

Random Fields with Statistical

Anisotropy

Random Fields with Statistical

Anisotropy

IsotropicIsotropic

- preferred direction- preferred direction

Present Observational Constrains

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)):

δN formalismδN 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.

Estimation of 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

Difficulties with Vector Fields

Difficulties with Vector Fields

● Excessive large scale anisotropyThe energy momentum tensor ( ):

● No particle productionMassless U(1) vector fields are conformally

invariant

● Excessive large scale anisotropyThe energy momentum tensor ( ):

● No particle productionMassless U(1) vector fields are conformally

invariant

Avoiding excessive anisotropyAvoiding 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)

Particle ProductionParticle 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.

Stability of the ModelStability 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:

Documents

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