Transcript Curvature Perturbations from Non

Primordial density perturbations
from the vector fields
Mindaugas Karčiauskas
in collaboration with
Konstantinos Dimopoulos
Jacques M. Wagstaff
Plan
● Hot Big Bang and it’s problems;
● Primordial perturbations;
● Inflation and CMB parameters;
● New observable – statistical anisotropy;
● Vector curvaton model;
The Universe After 1s
● The Universe is expanding;
● Universe started being hot;
● Big bang nucleosynthesis;
● Large scale structure formation;
The Universe After 1s
● The Universe is expanding:
● Hubble’s discovery 1929;
● Current measurements:
Freedman et al. (2001)
The Universe After 1s
● The early universe was
hot
● Discovery of the CMB;
● A. Penzias & R. Wilson (1965);
● Radiation which cooled down
from ~3000K to 2.7K;
● Steady State Cosmology is
wrong;
The Universe After 1s
● Big Bang Nucleosynthesis
● H, He, Li and Be formed during
first 3 minutes;
● R. A. Alpher & G. Gamow (1948) ;
● Predictions span 9 orders of
magnitude:
● Confirmed by CMB observations
at
;
The Universe After 1s
● Large Scale Structure
formation
● Seed – perturbations of the
order
;
● Subsequent growth due to
gravitational instability;
Initial conditions for the
Hot Big Bang
● Horizon – the universe is so uniform;
● Flatness – the universe is so old;
● Primordial perturbations – what is their origin;
Inflation
● Horizon – the universe is
so uniform;
● Flatness – the universe is
so old;
● Primordial perturbations –
what is their origin;
==> Inflation:
ll
ll
<==/
Superhorizon Density
perturbations
● Perturbations are
superhorizon
TE cross correlation
● One can mimic acoustic
peaks…
Hu et al. (1997)
● … but not superhorizon
correlations;
● => Inflation
Barreiro (2009)
CMB – a Probe of Inflationary
Physics
● What are the properties of primordial
density perturbations and what can they
tell about inflation?
● Random fields;
● The curvature
perturbation:
●
is conserved on super-horizon scales if
.
Random Fields
● Curvature perturbations – random
fields
;
● Isotropic two point correlation
function:
isotropic =>
● Momentum space:
Correlation function
● Two point correlator in
momentum space:
● The shape of the
power spectrum:
● Inflation models =>
● WMAP 5yr measurements:
● Errorbars small enough to rule out
some inflationary models
Higher Order Correlators
● Three point correlator:
● Non-Gaussianity parameter:
● Single field inflation => Gaussian perturbations:
● WMAP 5yr measurements:
Statistical Anisotropy
● New observable;
● Anisotropic two point correlation
function
● Anisotropic if
for
● The anisotropic power spectrum:
● The anisotropic bispectrum:
Isotropic
Random Fields
with Statistical
Anisotropy
- preferred direction
Vector Field Model
● Until recently only scalar fields were
considered for production of primordial
curvature perturbations;
● We consider curvature perturbations
from vector fields;
Vector Fields
●
●
Vector fields not considered previously
because:
1.
Conformaly invariant => cannot undergo particle production;
2.
Induces anisotropic expansion of the universe;
3.
Brakes Lorentz invariance;
Solved by using massive vector field:
1.
Conformal invariance is broken;
2.
Oscillates and acts as pressureless isotropic matter;
3.
Decays before BBN;
Vector Curvaton Scenario
●
The energy momentum
tensor:
I.
Inflation
II.
Light Vector Field
III. Heavy Vector Field
IV.
Vector Field Decay.
Onset of Hot Big Bang
Particle Production
● Lagrangian
● De Sitter inflation with the Hubble
parameter
;
● Three degrees of freedom:
and
● If
and
=> scale invariant
perturbation spectra;
● At the end of inflation:
and
Power Spectra
Anisotropic Perturbations
● Curvature perturbations statistically anisotropic;
Groeneboom et al. (2009)
=> Vector contribution subdominant
● Non-Gaussianity:
● Correlated with statistical
anisotropy
● Itself anisotropic
● Smoking gun for the vector field contribution to
the curvature perturbations.
No Scalar Fields
● Curvature perturbations statistically isotropic;
=> No need for other sources of perturbations.
● Vector fields starts oscillating during inflation;
● Parameter space:
● Inflationary energy scale:
● Oscillations starts at least:
Summary
● Inflation – most successful paradigm for
solving HBB problems and explaining the
primordial density perturbations;
● New observable – statistical anisotropy;
● Massive vector curvaton model:
● Can produce the statistically anisotropic curvature
perturbations:
● Non-Gaussianity is correlated with statistical anisotropy;
● Non-Gaussianity is itself anisotropic;
● Possible inflationary model building without scalar fields;