Dark Energy Interactions, Nordita, October 3, 2014 Backreaction status report Syksy Räsänen University of Helsinki Department of Physics and Helsinki Institute

Dark Energy Interactions, Nordita, October 3, 2014

Backreaction status report

Syksy Räsänen

University of HelsinkiDepartment of Physics andHelsinki Institute of Physics

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Looking for a factor of 2

The early universe is well described by a model which is homogeneous and isotropic, contains only ordinary matter and evolves according to ordinary general relativity.

In the late universe, such a model underpredicts distance and expansion rate by a factor of 2.

Three possibilities:1) There is matter with negative pressure.2) General relativity does not hold on cosmological scales.3) The homogeneous and isotropic approximation is not valid.

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Our clumpy universe

At late times, the universe is only statistically homogeneous and isotropic, on scales >100 Mpc.

The average evolution of a clumpy spacetime is not the same as the evolution of a smooth spacetime, a feature known as backreaction.

Structures affect expansion rate, light propagation and their relationship.

Backreaction conjecture: the reason for the failure of the homogeneous and isotropic models is the known breakdown of local homogeneity and isotropy.

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The Buchert equations (T. Buchert: gr-qc/9906015)

Here

The backreaction variable is

The average expansion can accelerate, even though the local expansion decelerates.

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Understanding acceleration

The average expansion rate can increase, because the fraction of volume taken by faster regions grows.

Structure formation involves overdense regions slowing down more and underdense regions decelerating less.

Acceleration can be demonstrated with a toy model which has one overdense and one underdense region. (SR: astro-ph/0607626)

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Scales of acceleration

The magnitude of the change in the expansion rate and the 10 billion year timing emerge from the physics of structure formation. (SR: 0801.2692)

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Homogeneity is not enough We can build a Swiss Cheese model where the average

expansion rate is different from the background, even though the holes are small and their distribution is H&I. (M. Lavinto, SR, S. Szybka: 1308.6731)

The average expansion rate rises at late times relative to the background.

Holes are ‘larger on the inside than the outside’: Tardis.

The average expansion rate describes the redshift and (with caveats) DA well.

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Dark Energy Interactions, Nordita, October 3, 2014 8


Light and space

The result probably generalises: H&I imply that z and DA

are determined by the average expansion rate. (SR:

0812.2872, 0912.3370, P. Bull, T. Clifton: 1203.4479)

For the angular diameter distance, we have (with )

Due to conservation of mass,

The distance in terms of H(z) is the same as in ΛCDM. If H(z) deviates from ΛCDM, the relation between H and

DA is different than in FRW. 9


Newtonian gravity

When density contrast becomes non-linear, variance of θ and shear become large.

In Newtonian gravity, is a boundary term. (T. Buchert, J. Ehlers: astro-ph/9510056)

In general relativity, variance and shear do not in general cancel.

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Perturbation theory

In perturbation theory, variance and shear are of the order .

If the metric perturbations around FRW and their first derivatives are small, variance and shear cancel, so and z are close to FRW. (SR: 1107.1176; see also S. Green, R. Wald: 1011.4920)

This is not true for DA in general. (K. Enqvist, M. Mattsson, G.

Rigopoulos: 0907.4003)

If the universe remains close to the same FRW metric everywhere, backreaction is small. (See J. Adamek et al: 1308.6524, 1408.2741, 1408.3352)

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Observations

Backreaction is indirectly constrained by the fact that ΛCDM fits well.

This does not mean that well-fitting models have to be close to ΛCDM.

Backreaction has a unique signature: deviation from the FRW distance-expansion rate relation. (C. Clarkson, B.A. Bassett, T. H.-C. Lu: 0712.3457)

Can be tested with observations of H(z)1, cosmic parallax (SR:

1312.5738) and strong lensing.1A. Shafieloo, C. Clarkson: 0911.4858, E. Mörtsell, J. Jönsson:1102.4485, D. Sapone, E. Majerotto, S. Nesseris: 1402.2236, A. Heavens, R. Jimenez, L. Verde: 1409.6217 12

Dark Energy Interactions, Nordita, October 3, 2014 13

C. Boehm, SR: 1305.7139


Observations

Backreaction is indirectly constrained by the fact that ΛCDM fits well.

This does not mean that well-fitting models have to be close to ΛCDM.

Backreaction has a unique signature: deviation from the FRW distance-expansion rate relation. (C. Clarkson, B.A. Bassett, T. H.-C. Lu: 0712.3457)

Can be tested with observations of H(z)1, cosmic parallax (SR:

1312.5738) and strong lensing.1A. Shafieloo, C. Clarkson: 0911.4858, E. Mörtsell, J. Jönsson:1102.4485, D. Sapone, E. Majerotto, S. Nesseris: 1402.2236, A. Heavens, R. Jimenez, L. Verde: 1409.6217 14


Summary Statistically homogeneous and isotropic spaces do not in

general expand like FRW.

Structure formation has a timescale of 1010 years.

Light propagation can be described by the average expansion rate.

If the universe is close to the same FRW metric everywhere, backreaction is small.

Even if backreaction is small, it can be important for precision measurements. (C. Clarkson et al: 1405.7860)

Backreaction can be tested by comparing distance and expansion rate.

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Dark Energy Interactions, Nordita, October 3, 2014 Backreaction status report Syksy Räsänen University of Helsinki Department of Physics and Helsinki Institute