Konstantinos Dimopoulos Lancaster University. Hot Big Bang and Cosmic Inflation Expanding Universe:...
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Konstantinos Dimopoulos Lancaster University
Konstantinos Dimopoulos Lancaster University. Hot Big Bang and Cosmic Inflation Expanding Universe: Expanding Universe: Hot Early Universe: CMB Hot Early
Hot Big Bang and Cosmic Inflation Expanding Universe: Expanding
Universe: Hot Early Universe: CMB Hot Early Universe: CMB Finite
Age: On large scales: Universe = Uniform On large scales: Universe
= Uniform Structure: smooth over 100 Mpc: Universe Fractal
Structure: smooth over 100 Mpc: Universe Fractal CMB Anisotropy:
CMB Anisotropy:
Slide 3
Hot Big Bang and Cosmic Inflation Cosmological Principle: The
Universe is Homogeneous and Isotropic Cosmological Principle: The
Universe is Homogeneous and Isotropic Horizon Problem: Uniformity
over causally disconnected regions Horizon Problem: Uniformity over
causally disconnected regions Cosmic Inflation: Brief period of
superluminal expansion of space 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 The
CMB appears correlated The CMB appears correlated on superhorizon
scales on superhorizon scales (in thermal equilibrium at (in
thermal equilibrium at preferred reference frame) preferred
reference frame) Incompatible with Finite Age
Slide 4
Hot Big Bang and Cosmic Inflation Inflation imposes the
Cosmological Principle Inflation imposes the Cosmological Principle
Inflation + Quantum Vacuum Inflation + Quantum Vacuum C. Principle
= no galaxies! C. Principle = no galaxies! Where do they come from?
Where do they come from? Quantum fluctuations (virtual particles)
of light fields exit the Horizon Quantum fluctuations (virtual
particles) of light fields exit the Horizon After Horizon exit:
quantum fluctuations classical perturbations Sachs-Wolfe: CMB
redshifted when crossing overdensities Sachs-Wolfe: CMB redshifted
when crossing overdensities Horizon during inflation Event Horizon
of inverted Black Hole
Slide 5
The Inflationary Paradigm A flat direction is required The
Universe undergoes inflation when dominated by the potential
density of a scalar field (called the inflaton field) The Universe
undergoes inflation when dominated by the potential density of a
scalar field (called the inflaton field) Klein - Gordon Equation of
motion for homogeneous scalar : Potential density domination: Slow
Roll inflation: Friedman equation : exponential expansion (quasi)
de Sitter inflation
Slide 6
Solving the Flatness Problem Inflation enlarges the radius
Inflation enlarges the radius of curvature to scales much larger
than the Horizon of curvature to scales much larger than the
Horizon Flatness Problem: Flatness Problem: The Universe appears to
The Universe appears to be spatially flat despite the fact that
flatness is unstable be spatially flat despite the fact that
flatness is unstable
Slide 7
The end of Inflation Reheating must occur before BBN Inflation
terminates when: Inflation terminates when: Reheating: After the
end of Reheating: After the end of inflation the inflaton field
inflation the inflaton field oscillates around its VEV. oscillates
around its VEV. These coherent oscillations These coherent
oscillations correspond to massive correspond to massive particles
which decay into the thermal bath of the HBB particles which decay
into the thermal bath of the HBB
Slide 8
Particle Production during Inflation Semi-classical method for
scalar fieds Semi-classical method for scalar fieds Vacuum boundary
condition: Vacuum boundary condition: Promote to operator: Perturb:
Fourier transform: Canonical quantization: well before Horizon exit
Solution: Solution: Equation of motion:
Slide 9
Particle Production during Inflation Hawking temperature Light
field: Power spectrum: Power spectrum: Superhorizon limit:
Superhorizon limit: Scale invariance:
Slide 10
Particle Production during Inflation Curvature Perturbation:
Curvature Perturbation: Classical evolution: Classical evolution:
freezing: Spectral Index: Scale invariance WMAP satellite
observations: same scale dependence
Slide 11
The Inflaton Hypothesis Tight constraint Fine tuning The field
responsible for the curvature perturbation is the same field which
drives the dynamics of inflation The field responsible for the
curvature perturbation is the same field which drives the dynamics
of inflation Inflaton = light Slow Roll Inflaton = light Slow Roll
Inflaton Perturbations Inflaton Perturbations Inflation is
terminated at different times at different points in space
Inflation is terminated at different times at different points in
space Slow Roll:
Slide 12
The Curvaton Hypothesis Curvaton = not ad hoc During inflation
the curvatons conribution to the density is negligible The curvaton
is a light field The curvaton is a light field Realistic candidates
include RH-sneutrino, orthogonal axion, MSSM flat direction
Realistic candidates include RH-sneutrino, orthogonal axion, MSSM
flat direction The field responsible for the curvature perturbation
is a field other than the inflaton (curvaton field ) The field
responsible for the curvature perturbation is a field other than
the inflaton (curvaton field ) The curvature perturbation depends
on the evolution after inflation Curvature Perturbation: where
Slide 13
The curvaton mechanism Inflation fine-tuning becomes alleviated
After unfreezing the curvaton oscillates around its VEV After
unfreezing the curvaton oscillates around its VEV Coherent curvaton
oscillations correspond to pressureless matter which dominates the
Universe imposing its own curvature perturbation Coherent curvaton
oscillations correspond to pressureless matter which dominates the
Universe imposing its own curvature perturbation Afterwards decays
into the thermal bath of the HBB Afterwards decays into the thermal
bath of the HBB Merits: The inflaton field may not be light and
bound only on the inflation scale: After inflation the curvaton
unfreezes when After inflation the curvaton unfreezes when During
inflation the curvaton is frozen with During inflation the curvaton
is frozen with
Slide 14
Scalar vs Vector Fields Scalar fields employed to address many
open issues: inflationary paradigm, dark energy (quintessence)
baryogenesis (Affleck-Dine) 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) 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 However, no scalar field has ever been observed
Designing models using unobserved scalar fields undermines their
predictability and falsifiability, despite the recent precision
data 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 The latest
theoretical developments (string landscape) offer too much freedom
for model-building Can we do Cosmology without scalar fields? Can
we do Cosmology without scalar fields? Some topics are OK: Some
topics are OK:Baryogenesis, Dark Matter, Dark Energy (CDM)
Inflationary expansion without scalar fields is also possible:
Inflationary expansion without scalar fields is also possible: e.g.
inflation due to geometry: gravity ( - inflation) However, to date,
no mechanism for the generation of the curvature/density
perturbation without a scalar field exists However, to date, no
mechanism for the generation of the curvature/density perturbation
without a scalar field exists
Slide 15
Why not Vector Fields? Basic Problem: the generatation of a
large-scale anisotropy is in conflict with CMB observations 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 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): Also, some weak large-scale anisotropy
might be present in the CMB (Axis of Evil): Inflation homogenizes
Vector Fields Inflation homogenizes Vector Fields To affect /
generate the curvature perturbation a Vector Field needs to
(nearly) dominate the Universe To affect / generate the curvature
perturbation a Vector Field needs to (nearly) dominate the Universe
Homogeneous Vector Field = in general anisotropic Homogeneous
Vector Field = in general anisotropic l=5 in galactic coordinates
l=5 in preferred frame
Slide 16
Massive Abelian Vector Field Massive vector field: Abelian
vector field: Equations of motion: Flat FRW metric: Inflation
homogenises the vector field: & Klein-Gordon To retain isotropy
the vector field must not drive inflation To retain isotropy the
vector field must not drive inflation Vector Inflation [Golovnev et
al. (2008)] uses 100s of vector fields
Slide 17
Vector Curvaton Pressureless and Isotropic Vector field can be
curvaton if safe domination of Universe is possible Vector field
can be curvaton if safe domination of Universe is possible Vector
field domination can occur without introducing significant
anisotropy. The curvature perturbation is imposed at domination
Vector field domination can occur without introducing significant
anisotropy. The curvature perturbation is imposed at domination
& Eq. of motion: Eq. of motion: harmonic oscillations
Slide 18
Particle Production of Vector Fields Conformal Invariance:
vector field does not couple to metric (virtual particles not
pulled outside Horizon during inflation) Breakdown of conformality
of massless vector field is necessary Breakdown of conformality of
massless vector field is necessary Mass termnot enoughno scale
invariance Find eq. of motion for vector field perturbations: Find
eq. of motion for vector field perturbations: Promote to operator:
Polarization vectors: Canonical quantization: Fourier transform:
(e.g.,, or ) Typically, introduce Xterm : Typically, introduce
Xterm :
Slide 19
Particle Production of Vector Fields Cases A&B: vector
curvaton = subdominant: statistical anisotropy only Cases A&B:
vector curvaton = subdominant: statistical anisotropy only Solve
with vacuum boundary conditions: Solve with vacuum boundary
conditions: & Obtain power spectra: Obtain power spectra:
expansion = isotropic Vector Curvaton = solely resonsible for only
in Case C Vector Curvaton = solely resonsible for only in Case C
Case C: Case C: isotropic particle production Case B: Case B:parity
conserving (most generic) Case A: Case A: parity violating
Observations: weak bound Statistical Anisotropy: anisotropic
patterns in CMB Statistical Anisotropy: anisotropic patterns in CMB
Lorentz boost factor: from frame with
Non-minimally coupled Vector Curvaton Longitudinal component:
Longitudinal component: The vector curvaton can be the cause of
statistical anisotropy The vector curvaton can be the cause of
statistical anisotropy Case B: The vector curvaton contribution to
must be subdominant Case B: The vector curvaton contribution to
must be subdominant saturates observational bound
Slide 22
Statistical Anisotropy and non-Gaussianity Observations:
Observations: The Planck sattelite will increse precision to: Non
Gaussianity in vector curvaton scenario: Non Gaussianity in vector
curvaton scenario: Non-Gaussianity = correlated with statistical
anisotropy: Non-Gaussianity = correlated with statistical
anisotropy: Smoking gun Ruduction to scalar curvaton case if:
Ruduction to scalar curvaton case if:& Non-minimally coupled
case: Non-minimally coupled case: measure of parity violation&
Non-Gaussianity in scalar curvaton scenario: Non-Gaussianity in
scalar curvaton scenario: : projection of unit vector onto the -
plane
Slide 23
Conclusions A vector field can contribute to the curvature
perturbation 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 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?) Hence, when the
oscillating vector field dominates, it introduces negligible
anisotropy (Axis of Evil?) The challenge is to obtain candidates in
theories beyond the standard model, which can play the role of the
vector curvaton The challenge is to obtain candidates in theories
beyond the standard model, which can play the role of the vector
curvaton The vector field can act as a curvaton if, after
inflation, its mass becomes: ( zero VEV: vacuum = Lorentz invariant
) The vector field can act as a curvaton if, after inflation, its
mass becomes: ( zero VEV: vacuum = Lorentz invariant ) Physical
Review D 74 (2006) 083502 : hep-ph/0607229 Physical Review D 76
(2007) 063506 : 0705.3334 [hep-ph] Journal of High Energy Physics
07 (2008) 119 : 0803.3041 [hep-th] If particle production is
isotropic then the vector curvaton can alone generate the curvature
perturbation in the Universe 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 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 Correlation of
statistical anisotropy and non-Gaussianity in the CMB is the
smoking gun for the vector curvaton scenario arXiv:0806.4680
[hep-ph] arXiv:0809.1055 [astro-ph]