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Constraining Inverse Curvature Gravity with Supernovae. O. Mena, J. Santiago and JW PRL, 96, 041103, 2006. Supernovae Measurements. SNe allow measurement of distance - redshift relation at large redshifts: The expansion of the Universe is accelerating ! - PowerPoint PPT Presentation
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Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Constraining Inverse Constraining Inverse Curvature Gravity with Curvature Gravity with
SupernovaeSupernovae
O. Mena, J. Santiago and JW
PRL, 96, 041103, 2006
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Supernovae Supernovae MeasurementsMeasurements
SNe allow measurement of distance - redshift relation at large redshifts: The The expansion of the expansion of the Universe is Universe is accelerating !accelerating !
Perlmutter et al.; Riess et al.; Knop et al.; Astier et al.
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Dark EnergyDark Energy
Simplest explanation; consistent with SNe, CMB, LSS, clusters of galaxies, ...
Cosmological Constant problem: Why << (TeV)4 ?
Why now: m ?Maybe something else ...
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Maybe gravity is standard at short distances...
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
but gets modified on large distances ...
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
New Gravitational New Gravitational ActionAction
Simple approach: F(R) = R+mRn
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Well known for n>1 early de Sittere.g. Starobinsky (1980)
Interest here: Late time modification n<0 n<0 (inverse curvature)
modification becomes important at low curvatureand can lead to accelerated expansion[Capozziello, Carloni, Troisy (’03), Carroll, Duvvuri, Trodden, Turner (’03), Carroll, De Felice, Duvvuri, Easson, Trodden, Turner (’04)]
Simplest model (1/R) ruled out by solar system data[Chiva (‘03), Soussa, Woodard (‘03),...]
but: accelerated attractor:[CDDETT]
H
dH/dt
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
The new modelThe new model
Flat metric Corrections negligible in the past (large curvature),
but dominant for R 2; acceleration today for H0 (Again why now problem ?)
Late time accelerated attractor [CDDTT’04] Passes solar system tests and no ghosts under
certain circumstances (see Karel van Acoleyen talk on Friday)
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Modified Friedman Modified Friedman EquationEquation
Stiff, 2nd order non-linear differential equation, solution is hard numerical problem - initial conditions in radiation dominated era are close to singular point.
Source term is matter and radiation: NO DARK ENERGY
Effectively dependent on 3 extra parameters:
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Solving the Friedman Solving the Friedman Equation for n=1Equation for n=1
Numerical codes can not solve this from initial conditions in radiation dominated era or matter domination
Approximate analytic solution in distant past
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Approximation and Approximation and Numerical SolutionNumerical Solution
Very accurate for z ≥ few (7), better than 0.1% with HE
2=8G/the standard Einstein gravity solution at early times.
Use approximate solution as initial condition at z=few (7) for numerical solution (approximation very accurate and numerical codes can cope)
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Dynamical AnalysisDynamical Analysis
is fixed by the dynamical behavior of the system Four special values of
For 1: both values of are acceptable For 1 2: =+1 hits singularity in past For 2 4 : =-1 hits singularity in past For 2 3 : stable attractor that is decelerated
for <32/21 and accelerated for larger . For 3 4 : no longer stable attractor and
singularity is reached in the future through an accelerated phase. For small this appears in the past.
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Include intrinsic magnitude of Supernovae as free parameter:Degenerate with value of H0 or better absolute scale of H(z).Measure all dimensionful quantities in units of
Remaining parameters: and
1 leads to very bad fits of the SNe data; remaining regions
Fit to Supernovae DataFit to Supernovae Data
low
high
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Fit to Riess et al (2004) gold sample; a compilation of 157 high confidence Type Ia SNe data.
very good fits, similar to CDM (2 = 183.3)
Universe hitssingularity in thepast
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
low high
Combining DatasetsCombining Datasets
In order to set scale use prior from Hubble Key Project: H0 = 728 km/sec/Mpc [Freedman et al. ‘01]
Prior on age of the Universe: t0 > 11.2 Gyrs[Krauss, Chaboyer ‘03]
marginalized 0.07 < marginalized 0.07 < mm < < 0.21 (95% c.l.); require dark matter0.21 (95% c.l.); require dark matter
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
CMB for the BraveCMB for the Brave
Small scale CMB anisotropies are mainly affected bythe physical cold dark matter and baryon densities andthe angular diameter distance to last scattering
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Angular Diameter Angular Diameter Distance to Last Distance to Last
ScatteringScattering
For the brave:Angular diameter distance to lastlast scattering with WMAP data - might as well be bogus !
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Inverse curvature gravity models can lead to accelerated expansion of the Universe and explain SNe data without violation of solar system tests and being ghost free. No need for dark energy !No need for dark energy !
Use of other data sets like CMB, LSS, Baryon Oscillations and clusters require careful analysis of perturbation regime and post - Newtonian limit on cluster scales (in progress)
No alternative for dark matter !No alternative for dark matter ! But only studied one functional form (n=1) ! But see Karel van Acoleyen talk on Friday.
ConclusionsConclusions
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
The Model vs Dark The Model vs Dark EnergyEnergy
Require also small parameter:
Ghost free version has only scalar degree of freedom: is there a simple scalar-tensor theory ?
Is there any deeper motivation for this model ?
“If at first an idea is not absurd, there is no hope for it”
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Baryon Oscillations as Baryon Oscillations as Cosmological ProbeCosmological Probe
Measuring acoustic oscillations of baryons with SDSS large scale correlations
angular diameter distance scale to position of oscillation peak at z = 0.35
Eisenstein et al.2005
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Using Baryon Using Baryon Oscillations for the Oscillations for the
InvincibleInvincibleangular diameter scale to acoustic peak at z=0.35
Growth of Perturbations ???Growth of Perturbations ???
Jochen Weller
XLI Recontres de MoriondMarch, 18-25, 2006
Putting it all Putting it all togethertogether
Combined constraints form SNe, H0 , Age, WMAP and BAO