1. Theory and observations
The quantum origin of
cosmic structure:
Theory and observations
Konstantinos Dimopoulos
Lancaster University

2. Hot Big Bang and Cosmic Inflation
Standard Model of Cosmology: Hot Big Bang + Cosmic Inflation
HBB: expansion, CMB, BBN, age
Cosmic inflation: horizon & flatness
Inflation: Brief superluminal expansion in the Early Universe
Universe = large + uniform
Perfect uniformity
 no galaxies!
Deviation from uniformity needed: Primordial Density Perturbation
 evidence of the PDP in the CMB
Sachs-Wolfe effect: CMB redshifted when crossing growing overdensities
Origin of PDP: Inflation again!

3. Particle Production during Inflation
Friedman Equation:
vacuum density domination:
End of inflation:
 change of vacuum
Vacuum states in inflation  populated afterwards
virtual particles real particles
Horizon during inflation Event Horizon of inverted Black Hole
quantum fluctuations classical perturbations

4. Particle Production during Inflation
Standard choice: free scalar field
Perturb:
Fourier Xform:
Equation of motion:
Promote to operator:
Vacuum condition:
before Horizon exit
Solution:

5. Particle Production during Inflation
Superhorizon limit:
Power spectrum:
Light field:
Scale invariance
Hawking temperature

6. Particle Production during Inflation
Classical evolution:
→ Scale
invariance
freezing:
Curvature Perturbation:
same scale
dependence
Spectral
Index:
For light scalar field:
WMAP observations:

7. The Curvature Perturbation
In GR curvature  density: depends on spacetime foliation
Gauge invariant curvature perturbation:
Power spectrum:
WMAP
Bispectrum:
Non-linearity parameter:
equilateral:
WMAP
local:

8. The Inflationary Paradigm
The Universe undergoes inflation when dominated by the potential density of a scalar field (called the inflaton field)
For homogeneous scalar field:
Potential domination:
Slow-Roll:
flat direction required
Inflation end:
Reheating: oscillations correspond to inflaton particles which decay to thermal bath of HBB

9. The Inflaton Hypothesis
The field responsible for the curvature perturbation also drives inflation
Inflaton = light Slow Roll
Inflaton Perturbations
Inflation ends at different times at different locations
Difference between uniform
density and spatial flatness
Spectral index:
Non-Gaussianity:
If non-G observed then
single field inflation killed

10. The Curvaton Hypothesis
The field responsible for the curvature perturbation is other than the inflaton (curvaton )
Lyth & Wands (2002)
The curvaton is a light field
Curvaton = not ad hoc
Realistic candidates include RH-sneutrino, orthogonal axion, MSSM flat direction
Spectral index:
During inflation the curvaton’s contribution to the density is negligible
The curvature perturbation depends on the evolution after inflation

11. The curvaton mechanism
During inflation the curvaton is frozen with
After inflation the curvaton unfreezes when
After unfreezing the curvaton oscillates around its VEV
Oscillations = pressureless matter  curvaton (nearly) dominates the Universe
at different times at
different locations
Afterwards decays to thermal bath of HBB
Non-Gaussianity:
WMAP bound

12. Why not Vector Fields?
Tantalising evidence exists of a preferred direction in the CMB
l=5 in preferred frame
l=5 in galactic coordinates
Impossible to form with scalars
Also, despite their abundance in theories beyond SM, scalar fields are not observed as yet
What if Higgs not found in LHC?
Until recently Vector Fields not considered for particle production
Inflation homogenizes Vector Fields
Homogeneous Vector Field = in general anisotropic
Generation of large-scale anisotropy in conflict with CMB uniformity
Circumvented if Vector Field is subdominant during inflation
Light Vector Fields  conformally invariant  no particle production
 model dependent mechanisms to break conformality

13. Particle Production of Vector Fields
Consider model with suitable breakdown of vector field conformality
Perturb:
Fourier Xform:
Promote to operator:
Polarization
vectors:
Solve with vacuum boundary conditions:
&
Lorentz boost factor:
from frame with
Obtain power spectra:
expansion = isotropic

14. Particle Production of Vector Fields
Case A:
parity violating
Case B:
parity conserving (most generic)
Case C:
isotropic particle production
Statistical Anisotropy: anisotropic patterns in CMB
Groeneboom and Eriksen (2009)
Observations: weak bound
Cases A&B: vector field = subdominant  statistical anisotropy only
Curvature perturbation due to Vector Field alone only in Case C

15. Non-minimal coupling to Gravity
KD & Karciauskas
(2008)
&
Transverse component:
(Parity conserving)
Scale invariance if:
&
Longitudinal component:
Case B: The vector field can generate statistical anisotropy only
Model may suffer from instabilities (ghosts)
Himmetoglu et al. (2009)

16. Varying kinetic function and mass
KD (2007)
Maxwell kinetic term does not suffer from instabilities (ghost-free)
Motivates model even if vector field is not gauge boson
Abelian massive vector field = renormalizable even if not a gauge field
Scale
invariance:
at Horizon exit
KD, Karciauskas, Wagstaff (2009)
Vector field remains light:
Statistical anisotropy only (Case B)
Vector field becomes heavy:
Particle production isotropic (Case C)
No need for fundamental scalar field

17. Vector Curvaton Paradigm
Inflation homogenises the vector field:
&
[KD, PRD 74 (2006) ]
&
harmonic oscillations
Pressureless
and Isotropic
Vector field domination occurs without introducing significant anisotropy
is imposed at (near) domination

18. Statistical Anisotropy and non-Gaussianity
Vector curvaton:
Karciauskas, KD and Lyth (2009)
: projection of on - plane
Non-Gaussianity = correlated with statistical anisotropy:
Smoking gun
model:
Predominantly anisotropic
model:
identical to scalar curvaton

19. Conclusions
Cosmic structure originates from growth of quantum fluctuations during a period of cosmic inflation in the Early Universe
The particle production process generates an almost scale invariant spectrum of superhorizon perturbations of suitable fields
These pertubrations give rise to the primordial density/curvature perturbation via a multitude of mechanisms (inflaton, curvaton etc.)
Observables such as the spectral index or the non-linearity parameter will soon exclude whole classes of inflation models
The Planck satellite will increase precision to:
Recently the possibility that vector fields contribute or even generate (vector curvaton) is being explored
Vector fields can produce distinct signatures such as statistical anisotropy in the CMB (bi)spectrum
Planck precision:
Cosmological observations allow for detailed modelling and open a window to fundamental physics complementary to LHC