Konstantinos Dimopoulos

1
Vector Fields and the
Curvature Perturbation in the Universe
Konstantinos Dimopoulos
Lancaster University
2
Hot Big Bang and Cosmic Inflation

• Hot Early Universe CMB

• On large scales Universe Uniform

• Structure smooth over 100 Mpc Universe m Fractal

3
Hot Big Bang and Cosmic Inflation

• Cosmological Principle The Universe is
  Homogeneous and Isotropic

• Incompatible with Finite Age

• Horizon Problem Uniformity over causally
  disconnected regions

• The CMB appears correlated
• on superhorizon scales
• (in thermal equilibrium at
• preferred reference frame)

• Cosmic Inflation Brief period of superluminal
  expansion of space

• Inflation produces correlations over superhorizon
  distances by expanding an initially causally
  connected region to size larger than the
  observable Universe

4
Hot Big Bang and Cosmic Inflation

• Inflation imposes the Cosmological Principle

• C. Principle no galaxies!

• Where do they come from?

• Inflation Quantum Vacuum

• Quantum fluctuations (virtual particles) of light
  fields exit the Horizon

5
The Inflationary Paradigm

• The Universe undergoes inflation when dominated
  by the potential density of a scalar field
  (called the inflaton field)

A flat direction is required
6
Solving the Flatness Problem

• Flatness Problem
• The Universe appears to
• be spatially flat despite the fact that
  flatness is unstable

• Inflation enlarges the radius
• of curvature to scales much larger than the
  Horizon

7
The end of Inflation
Reheating must occur before BBN
8
Particle Production during Inflation

• Semi-classical method for scalar fieds

• Vacuum boundary condition

9
Particle Production during Inflation
Hawking temperature
10
Particle Production during Inflation
? Scale invariance

• Curvature Perturbation

11
The Inflaton Hypothesis

• The field responsible for the curvature
  perturbation is the same field which drives the
  dynamics of inflation

Tight constraint ? Fine tuning
12
The Curvaton Hypothesis

• The curvaton is a light field

• Realistic candidates include RH-sneutrino,
  orthogonal axion, MSSM flat direction

Curvaton not ad hoc
During inflation the curvatons conribution to
the density is negligible
13
The curvaton mechanism

• After unfreezing the curvaton oscillates around
  its VEV

• Coherent curvaton oscillations correspond to
  pressureless matter which dominates the Universe
  imposing its own curvature perturbation

14
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
  parteners) or string theory (moduli)

• However, no 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 (?CDM)

• Inflationary expansion without scalar fields is
  also possible

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

15
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)

16
Massive Abelian Vector Field

• To retain isotropy the vector field must not
  drive inflation

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

• Vector field can be curvaton if safe domination
  of Universe is possible

Pressureless and Isotropic

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

18
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)
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Particle Production of Vector Fields

• Cases AB vector curvaton subdominant
  statistical anisotropy only

20
Non-minimally coupled Vector Curvaton
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Non-minimally coupled Vector Curvaton

• Longitudinal component

• The vector curvaton can be the cause of
  statistical anisotropy

saturates observational bound
22
Statistical Anisotropy and non-Gaussianity

• Non Gaussianity in vector curvaton scenario

• Non-Gaussianity correlated with statistical
  anisotropy

Smoking gun
23
Conclusions

• A vector field can contribute to the curvature
  perturbation

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

• Hence, when the oscillating vector field
  dominates, it introduces negligible anisotropy
  (Axis of Evil?)

• 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

• Correlation of statistical anisotropy and
  non-Gaussianity in the CMB is the smoking gun for
  the vector curvaton scenario

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

Physical Review D 74 (2006) 083502
hep-ph/0607229
arXiv0806.4680 hep-ph
Physical Review D 76 (2007) 063506 0705.3334
hep-ph
arXiv0809.1055 astro-ph
Journal of High Energy Physics 07 (2008) 119
0803.3041 hep-th