View
217
Download
1
Category
Tags:
Preview:
Citation preview
Phenomenological Phenomenological Classification of Inflationary Classification of Inflationary
PotentialsPotentials
Katie Mack (Princeton University)
with George Efstathiou (Cambridge University)
Efstathiou & Mack, JCAP 05, 008 (2005)astro-ph/0503360
The Lyth Bound RevisitedThe Lyth Bound Revisited
Katie Mack (Princeton University)
with George Efstathiou (Cambridge University)
Efstathiou & Mack, JCAP 05, 008 (2005)astro-ph/0503360
Outline
• Current status of inflation
• What the observations can tell us
• Linking observations to fundamental theory (Lyth Bound)
• Phenomenological approach
• Implications for future theoretical work
The inflationary paradigm today
• Inflation is successful offers solution to
horizon problemflatness problem
general predictions have been upheldflat universegaussian and adiabatic metric fluctuationsnearly scale-independent spectrum
…but which inflation theory are we talking about?
The inflationary paradigm today
• Inflation is successful offers solution to
horizon problemflatness problem
general predictions have been upheldflat universegaussian and adiabatic metric fluctuationsnearly scale-independent spectrum
…but which inflation theory are we talking about?
S-dimensional assisted inflation assisted brane inflationanomoly-induced inflationassisted inflationassisted chaotic inflationboundary inflationbrane inflationbrane-assisted inflationbrane gas inflationbrane-antibrane inflationbraneworld inflationBrans-Dicke chaotic inflationBrans-Dicke inflationbulky brane inflationchaotic inflationchaotic hybrid inflationchaotic new inflationD-brane inflationD-term inflationdilaton-driven inflationdilaton-driven brane inflationdouble inflationdouble D-term inflation
dual inflation dynamical inflationdynamical SUSY inflationeternal inflationextended inflationextended open inflationextended warm inflationextra dimensional inflationF-term inflationF-term hybrid inflationfalse-vacuum inflationfalse-vacuum chaotic inflationfast-roll inflationfirst-order inflationgauged inflationHagedorn inflationhigher-curvature inflationhybrid inflationhyperextended inflationinduced gravity inflationintermediate inflationinverted hybrid inflationisocurvature inflation......................
@ Paul Shellard
• Tensor modesTensor modes– produced by gravitational waves– no contribution from density perturbations
• Detection would…– confirm prediction of primordial gravitational waves in
inflation– give the energy scale of inflation
the good news
“…we cannot yet distinguish between broad classes of inflationary theories that have different physical motivations.” –Peiris et al. (2003)
WMAP alone WMAP+2dF+Lyα
the bad news
Seljak et al., 2004 (astro-ph/0407372)
B-Mode Polarization
Current upper limits
r = 0.36
Beyond WMAP
• Currently proposed experiments (ground and balloon-borne) can reach r=0.01 at ~3σ level
• Space-based, with improved foreground knowledge, could get to r~10-3 at ~3σ
(Verde, Peiris & Jimenez, astro-ph/0506036)
You may ask…What about gravitational wave detectors?
Of the planned experiments, only Big Bang Observer (next generation after LISA) has any chance of detecting primordial
GWs
Linking observation to physics
• Future experiments may detect primordial gravitational waves, but what would this tell us about inflation itself?
• Goal: Find a way to link the observables to the fundamental physics without assuming a particular model
Phenomenological Approach
• Produce a set of inflationary models to be as general as possible
• Require only:– single field– inflation sustained long enough to solve
horizon problem (~ 55 e-foldings)
• Calculate r and Δφ, compare with Lyth Bound
The Lyth BoundDavid Lyth (1996) suggests rough relation:
for ΔN ~ 4 (CMB multipoles ~2 to ~100)
Considering the full course of inflation, with at least 50-60 e-folds, Δφ could exceed this by an order of magnitude
If slow-roll parameter
is monotonically increasing, a stronger condition is required:
The Lyth Bound
General expectation:
large r => large Δφ
High values of r require changes in the field value of order mPl
Monte Carlo Reconstruction Results (106 models)
But in the real world…
• Can improve the scatter by comparing with observables
• From Seljak et al. 2004, astro-ph/0407372
n run
0.92 < ns < 1.06-0.04 < nrun < 0.03
Remaining models
• Now have tighter empirical relationship between r and Δφ
Δφ/mPl ~ 6 r1/4
(for r > ~ 10-3)
What have we learned?
• To obtain a large value of r, you need a large variation in the scalar field
• For r ~ 10-3, need Δφ of order unity
If any conceivable CMB polarization experiment is to detect tensor modes,
Δφ must be large
Implications for inflationLarge field variations cannot be described by low-energy
effective field theory, where the potential is written as:
with . This is invalid for .
Does that mean we need new physics?Not necessarily… quantum gravity corrections may still be
small as long as V < mpl4
But we will need a new way to talk about such models.
The bottom line
Future CMB polarization experiments can only probe high field inflation models (e.g.,
chaotic inflation)
Understanding the physics of such models is important if such experiments are to tell us anything useful about the mechanism
behind inflation
NN=50 N=0
t=t_i t t=t_end
initialparameters
NN=50 N=0
t=t_i t t=t_end
initialparameters
NN=50 N=0
t=t_i t t=t_end
x
initialparameters
NN=50 N=0
t=t_i t t=t_end
x
observables
initialparameters
NN=50 N=0
t=t_i t t=t_end
observables
x
initialparameters
parameters at epsilon = 1
NN=50 N=0
t=t_i t t=t_end
observables
x
initialparameters
parameters at epsilon = 1
NN=50 N=0
t=t_i t t=t_end
x
observables
x
initialparameters
parameters at epsilon = 1
NN=50 N=0
t=t_i t t=t_end
x
observables
observables
x
initialparameters
parameters at epsilon = 1
parameters at N=50
V 50 e-foldings before end of
inflation
end of inflation
Single-field inflation
• Scalar field φ rolling down potential V(φ)
• Slow rolling of inflaton field causes inflation
• Some commonly considered models: V ~ φ2
V ~ φ4
Mechanics of inflation
Equations of Motion: • Change in Hubble Parameter depends on change in scalar field (“speed of roll”)
• In slow-roll inflation, take H ~ constant, slow roll of inflaton
• Expand Hubble Parameter in power series
• Use slow-roll parameters to represent this expansion
acceleration
Condition for inflation:
Satisfied when:
E mode and B mode polarization
E modes (no curl) B modes (no divergence)
WMAP vs. Planck
TE TE
E E
Planck projected B-mode measurement
B-mode: r = 0.1, = 0.17
Other experiments
Clover
QUIET
None of these experiments likely to probe below r ~10-2
Cooray, astro-ph/0503118
r = 0.13
r = 5 * 10-4
r = 10-5
Limits on future gravitational
wave experiments
Recommended