Constraining Inverse Curvature Gravity with Supernovae

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


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.

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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 ...

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Maybe gravity is standard at short distances...

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but gets modified on large distances ...

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New Gravitational New Gravitational ActionAction

Simple approach: F(R) = R+mRn

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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

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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)

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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:

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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

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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)

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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.

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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

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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

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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

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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

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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 !

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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

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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”

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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

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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 ???

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Putting it all Putting it all togethertogether

Combined constraints form SNe, H0 , Age, WMAP and BAO

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Constraining Inverse Curvature Gravity with Supernovae