1. Modified (dark) gravity Roy Maartens, Portsmouth or Dark Gravity? 0.75 0.2

2. it’s the simplest model it’s the simplest model compatible with all data so far compatible with all data so far no other model is a better fit no other model is a better fit but …. theory cannot explain it but …. theory cannot explain it why so small? why so small? and … why and … why so fine-tuned? LCDM fits the data well… LCDM fits the data well… but we cannot explain it

3. LCDM is the best model test this against data test this against data wait for particle physics/QG to explain wait for particle physics/QG to explain focus on focus on * the best tests for w=-1 * the role of theoretical assumptions e.g. w=const, curvature=0 curvature=0 “minimalist” approach

4. Dynamical Dark Energy in General Relativity “quintessence”,… “quintessence”,… effective ‘Dark Energy’ via nonlinear effects of structure formation? effective ‘Dark Energy’ via nonlinear effects of structure formation? Dark Gravity –Modify GR on large scales 4D: scalar-(vector)-tensor theories [e.g. f(R)] 4D: scalar-(vector)-tensor theories [e.g. f(R)] higher-D: braneworld models [e.g. DGP] higher-D: braneworld models [e.g. DGP] alternatives to LCDM … but we can do more with the data with the data We can test gravity The problem is so big that we need to test alternatives

5. NB – these alternatives require that the vacuum energy does not gravitate: Dark Energy dynamics Dark Gravity dynamics

6. is GR wrong on large scales ? i.e. acceleration via the weakening of gravity Example from history: Example from history: Mercury perihelion – Newton + ‘dark’ planet ? no – modified gravity! Today: Today: Modified Friedman equations (schematic) Modified Friedman equations (schematic) Modified (dark) gravity

7. modifiedFriedman:Examples: f(R) modified gravity DGP modified gravity (5D braneworld model)

8. modifiedFriedman: general feature geometric tests on their own cannot distinguish modified gravity from GR why? geometric tests are based on the comoving distance - the same H(z) gives the same expansion history

9. we can find a GR model of DE to mimic the H(z) of a modified gravity theory: how to distinguish DG and DE models that both fit observed H(z)? they predict different rates of growth of structure

10. structure formation is suppressed by acceleration in different ways in GR and modified gravity: * in GR – because DE dominates over matter * in DG – because gravity weakens (G determined by local physics) by local physics) δ/a

11. Distinguish DE from DG via growth of structure DE and DG with DE and DG with the same H(z) the same H(z) rates of growth of structure differ rates of growth of structure differ bias evolution? bias evolution? (Y Wang, 0710.3885) DE + DG models LCDM DG model (modification to GR) DE model (GR) LCDM f

12. simplest scalar-tensor gravity: a new light scalar degree of freedom eg. at low energy, 1/R dominates 1/R dominates This produces late-time self-acceleration but the light scalar strongly violates solar system constraints but the light scalar strongly violates solar system constraints all f(R) models have this problem all f(R) models have this problem way out: ‘chameleon’ mechanism, i.e. the scalar becomes massive in the solar system way out: ‘chameleon’ mechanism, i.e. the scalar becomes massive in the solar system - very contrived f(R) gravity

13. Scalar-tensor gravity (‘extended quintessence’): also a new light scalar degree of freedom But now there are 2 free functions: late-time self-acceleration is possible without violating solar system constraints late-time self-acceleration is possible without violating solar system constraints (no chameleon is needed) (no chameleon is needed) Interesting - but the models do not improve on standard GR quintessence models Scalar-vector-tensor gravity – even more complicated; no advantage unless it solves the DM and DE problems gravitationally Generalising f(R) gravity

14. String theory - our 4D universe may be moving in 10D spacetime ST unifies the 4 interactions Dark gravity from braneworlds? Dark gravity from braneworlds?

15. new massive graviton modes new massive graviton modes new effects from higher-D fields and other branes new effects from higher-D fields and other branes perhaps these could dominate at low energies perhaps these could dominate at low energies matter gravity + dilaton, form fields… extra dimension our brane different possibilities * ‘bulk’ fields as effective DE on the brane (eg ekpyrotic/ cyclic) * matter on a ‘shadow’ brane as effective DE on the ‘visible’ brane * effective 4D gravity on the brane modified on large scales (eg DGP) shadow brane

16. DGP – the simplest example 4D brane universe in 5D bulk early universe – recover GR dynamics late universe – acceleration without DE gravity “leaks” off the brane therefore gravity on the brane weakens passes the solar system test: DGP GR The background is very simple – like LCDM Friedman on the brane

17. Expansion history Density perturbations (sub-horizon) (cannot neglect 5D effects!) More suppression of structure than LCDM δ/a

18. … too good to be true 5D analysis of perturbations shows - there is a ghost in the scalar sector of the gravitational field - there is a ghost in the scalar sector of the gravitational field This ghost is from 5D gravity * It is not apparent in the background * It is the source of suppressed growth The ghost makes the quantum vacuum unstable Can DGP survive as a classical toy model?

19. The simplest models fail f(R) and DGP – simplest in their class f(R) and DGP – simplest in their class – simplest modified gravity models – simplest modified gravity models both fail because of their scalar degree of freedom: both fail because of their scalar degree of freedom: f(R) strongly violates solar system constraints DGP has a ghost in 5D gravity Either GR is the correct theory on large scales Or Modified gravity is more complicated THEORY: find a ghost-free generalized DGP or find a ‘non-ugly’ ST model ? find a ‘non-ugly’ ST model ? PHENOMENOLOGY: model-independent tests of the failure of GR ? of the failure of GR ?

20. Model-independent tests of GR There is no natural DE model in GR There is no natural DE model in GR (but LCDM is preferred by simplicity) (but LCDM is preferred by simplicity) There is no natural or preferred modified MG There is no natural or preferred modified MG (theory gives no guidance) Aim = without choosing a DE model in GR, and without specifying a modified DG model, try to find constraints on deviations from GR Aim = without choosing a DE model in GR, and without specifying a modified DG model, try to find constraints on deviations from GR Problem = find tests that do not depend on the DE or the DG model Problem = find tests that do not depend on the DE or the DG model In parallel: In parallel: 1. Test for Lambda vs dynamical DE in GR 2. Test for GR vs modified DG

21. Some complications: Some complications: * modified gravity has ‘dark’ anisotropic stress examples DE (smooth) – only need growth rate for CMB,LSS DG – also need anisotropic stress + G eff DG – also need anisotropic stress + G eff * linear-nonlinear transition (nonlinear regime should recover GR) can severely complicate WL tests

22. Degeneracies Degeneracies * DE with clustering and anisotropic stress can look like MG – (physical?) * DE with clustering and anisotropic stress can look like MG – (physical?) * astrophysical (eg bias evolution vs growth rate) Approaches: Approaches: (1) Growth rate: compare the observed growth rate with the theoretical rate – is it DE or DG? compare the observed growth rate with the theoretical rate – is it DE or DG? we need to know the DE and the DG models f

23. (2) Parameter-splitting: (2) Parameter-splitting: check for a breaking of GR consistency between ‘geometry’ and ‘growth’ check for a breaking of GR consistency between ‘geometry’ and ‘growth’ eg eg inconsistency could mean a more complicated DE model or data problems CMB CMB+Gal CMB+SN CMB+WL All (S Wang et al, 0705.0165)

24. (3) Parametrised post-Friedman approach (3) Parametrised post-Friedman approach Parametrised post-Newtonian formalism has been very successful for testing deviations from GR in the solar system Parametrised post-Newtonian formalism has been very successful for testing deviations from GR in the solar system Develop a PPF for modified DG? Develop a PPF for modified DG? Need basic assumptions: Need basic assumptions: * DE is smooth * modified gravity is a metric theory with energy conservation To close the system – 3 functions To close the system – 3 functions (Hu, Sawicki 0708.1190; Jain, Zhang 0709.2375)

25. some conclusions observations imply acceleration observations imply acceleration theory did not predict it – and cannot explain it theory did not predict it – and cannot explain it simplest model LCDM is the best we have simplest model LCDM is the best we have GR with dynamical DE – no natural model GR with dynamical DE – no natural model modifications to GR – dark gravity: modifications to GR – dark gravity: * theory gives no natural model * simple f(R) model fails solar system test * simplest braneworld model DGP has a ghost theorists need to keep exploring theorists need to keep exploring * better models * better observational tests (model-independent?) (model-independent?)