Large distance modification of gravity and dark energy

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Presentation transcript:

Large distance modification of gravity and dark energy Kazuya Koyama ICG, University of Portsmouth

Cosmic acceleration Cosmic acceleration Big surprise in cosmology Simplest best fit model LCDM 4D general relativity + cosmological const.

3 independent data sets intersect

Problem of LCDM Huge difference in scales (theory vs observation) vacuum energy =0 from fundamental theory (1) tiny vacuum energy is left somehow (2) Potential energy of quintessence field

Alternative models Tiny energy scale unstable under quantum corrections Alternative - modified gravity dark energy is important only at late times large scales / low energy modifications cf. from Newton to GR

Is cosmology probing breakdown of GR on large (IR) scales ?

Options Modify the Friedmann equation empirically or how to perturb? Modify the Einstein-Hilbert action cf. (Freese, …) (Dvali and Turner, …) (Carol et.al., …)

Problems of IR modification Modified gravity graviton has a scalar mode Solar system constraints - theory must be GR cf. difficult to explain dark energy purely from modified gravity (Chiba)

DGP model Crossover scale 4D Newtonian gravity 5D Newtonian gravity (Dvali, Gabadadze,Porrati) Crossover scale 4D Newtonian gravity 5D Newtonian gravity gravity leakage Infinite extra-dimension

Consistent with local experiments? DGP also has a scalar mode of graviton :4D Newtonian but not 4D GR! (Scalar-Tensor theory) Non-linear shielding theory becomes GR at solar-system constraints can be evaded if 5D ST GR 4D (Deffayet et.al.)

Cosmology of DGP Friedmann equation early times 4D Friedmann late times As simple as LCDM model and as fine-tuned as LCDM (stability against quantum corrections can be different) (Deffayet)

LCDM vs DGP Can we distinguish between DGP and LCDM ? Friedmann equation cf. LCDM

SNe + baryon oscillation SNLS + SDSS ‘Gold’ set + SDSS (Maartens and Majerotto in preperation) (Fairbairn and Goobar astro-ph/0511029) (cf. Alam and Sahni, astro-ph/0511473)

Why baryon oscillation? angular diameter at z=0.3 + shape parameter of power spectrum K=0 equivalent to dark energy model with (Lue.et.al) VS (LCDM)

DGP Cosmology As simple as LCDM a falsifiable model now the model is under pressure from the data measurements of is crucial Fit to SNe assuming flat universe A parameter is fixed!

Dark energy vs DGP Can we distinguish between dark energy in GR and DGP ? DGP model is fitted by DGP (Linder) Dvali and Turner

Cosmology as a probe of DGP gravity Non-linear linear Einstein Scalar tensor 4D 5D CMB ISW LSS CMB SNe Weak lensing Non-linear mapping Growth rate Expansion history

Growth rate of structure formation Evolution of CDM over-density GR If there is no dark energy dark energy suppresses the gravitational collapse DGP an additional modification from the scalar mode

Expansion history vs growth rate Growth rate resolves the degeneracy (Lue.et.al, Linder) LCDM dark energy DGP

Experiments ASSUME our universe is DGP braneworld (Ishak et.al, astro-ph/0507184) ASSUME our universe is DGP braneworld but you do not want to believe this, so fit the data using dark energy model m(z): apparent magnitude R: CMB shift parameter G(a): Growth rate OR SNe+CMB SNe+weak lensing Inconsistent!

Consistent 5D analysis of growth factor KK and R.Maartens astro-ph/0511634 Use correct 5D physics growth rate is sensitive to truncation of 5D physics Consistency in 5D physics (1) Analysis based on (2) must be revisited (1) Lue.et.al astro-ph/0401515 (2) Song astro-ph/0407489 LCDM Dark energy

Solutions for metric perturbations (Lue et.al, KK and R,Maartens) Solutions for metric perturbations Scalar tensor theory with Brans-Dick parameter

ISW effects and weak lensing Growth rate is determined by ISW effects and weak lensing effects depends on the same as GR! Difference comes from growth rate of

Einstein Scalar tensor 4D 5D Non-linear P(k) Large scale ISW Need 5D solutions Need non-linear mapping Non-linear linear Einstein Scalar tensor 4D 5D CMB ISW LSS CMB SNe Weak lensing

Summary Alternative to LCDM from large scale modification DGP model as an example The model is already in tension with the data Structure formation is different from GR 5D study of perturbations is crucial cf. Theoretical difficulties of DGP model strong coupling / a ghost in de Sitter spacetime (Luty, Porrati, Rattazi) (Nicolis, Rattati; KK hep-th/0503191 Gorbunov, KK, Sibiryakov; to appear)

Lessons from DGP Gravity is subtle modification at present day horizon scale does not mean no modification under horizon structure formation is different from GR great opportunity to exploit future observations Build consistent models Structure formation is sensitive to underlying theory Build consistent theory (ghost free etc.) Address fundamental questions (fine-tuning, coincidence)