Dark Energy and Modified Gravity

1. Dark Energy and Modified Gravity IGC Penn State May 2008 Roy Maartens ICG Portsmouth R Caldwell

2. LCDM fits the high-precision data galaxy distribution cosmic microwave background WMAP LCDM SDSS

3. 3 independent data sets intersect supernovae CMB galaxies

4. the improbable, mysterious universe there are particle physics candidates 0.2 or Modified Gravity? 0.75

5. LCDM fits the data well… but we cannot explain it • it’s the simplest model • compatible with all data up to now • no other model gives a better statistical fit • but …. theory cannot explain it • why so small? • and … why so fine-tuned?

6. ‘coincidence’ problem radiation (1/a4) log  matter ( 1/a3) cosmological constant log a Radiation dominated Matter dominated Dark energy dominated

7. String theory and vacuum energy string “landscape” and multiverse to explain fine-tuned small value? speculative & controversial

8. …. or from spacetime topology? • “self-tuning” braneworld • the higher-dimensional vacuum energy is large, as expected - but the 4D brane is protected from it • However: unstable 4D brane universe (4+n)D spacetime with a cut

9. Other quantum gravity approaches tothe vacuum energy • Loop Quantum Gravity: ask Abhay and Martin • Causal sets • Others

10. “minimalist” attitude LCDM is the best model • test this against data • wait for particle physics/QG to explain why • focus on * the best tests for w=-1 * the role of theoretical assumptions e.g. w=const, w(z) parametrizations, curvature=0

11. … but we can do more with the data We can test alternatives Dynamical Dark Energy in General Relativity • “quintessence”, coupled DE-dark matter,... • 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)] • higher-D: braneworld models [e.g. DGP] some alternatives to LCDM

12. NB – all these alternatives require that the vacuum energy does not gravitate: - they address the coincidence problem not the vacuum energy problem Dark Energy dynamics Modified Gravity dynamics

13. quintessence tracker scalar field, to solve the coincidence problem • but parameters in the potential must be highly fine-tuned • more complicated dynamical models are poorly motivated or suffer theoretical problems: eg phantom scalar field (ghost - vacuum unstable) k-essence (violates causality) Chaplygin gas (what phenomenology?)

14. coupled quintessence • alternative approach to the coincidence problem: * DM and DE only detected gravitationally * unavoidable degeneracy * there could be a coupling in the dark sector (coupling to SM fields strongly constrained) • intrinsic CDM bias – Euler equation violated • some models ruled out by instabilities • others lead to interesting features eg w<-1 without ghosts

15. effective ‘DE’ from structure formation? • more radical approach to the coincidence problem – “structure formation implies acceleration” • nonlinear averaging/ backreaction? • voids dominate over filaments – accelerating effect? • averaging effects are real and important – but probably too small to give acceleration • abandon Copernican principle?

16. Modified (dark) gravity is GR wrong on large scales ?* GR: acceleration via the anti-gravity of DE(or perhaps via nonlinear effects)* modified gravity: acceleration via the weakening of gravity on large scales Challenge the standard theory? Example from history: Mercury perihelion – Newton + ‘dark’ planet ? no – modified gravity! But – very hard to consistently modify GR in the IR and – must pass local as well as cosmological tests

17. Key assumptions on MG theories: • metric theory • energy-momentum conservation Key requirements • on small nonlinear scales – must recover GR • on superhorizon scales – perturbations must evolve compatibly with the background (‘separate universe’) On intermediate scales – Poisson equation is modified GR = spin-2 graviton + minimal coupled matter MG changes both features

18. Background modified Friedman: Examples: f(R)modified gravity (R = Ricci scalar) DGP modified gravity (braneworld model)

19. Geometric tests (eg supernovae, BAO) probe the background expansion history 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

20. 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 the observed H(z)? they predict different rates of growth of structure

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

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

23. L Guzzo et al

24. CMB photons carry the signature of the effect of DE or MG on structure formation R Caldwell integrated Sachs-Wolfe effect

25. Lensing also carries a signature of the effect of DE or MG complication: linear to nonlinear transition (need N-body simulations)

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

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

28. DGP – the simplest example Friedman on the brane • 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

29. … too good to be true • analysis of higher-D perturbations shows - there is a ghost in the scalar sector of the gravitational field This ghost is from higher-D 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?

30. The simplest models fail • f(R) and DGP – simplest in their class • – simplest modified gravity models • both fail because of their scalar degree of freedom: f(R) strongly violates solar system constraints DGP has a ghost in higher-D 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’ f(R) model – or find a new MG model? PHENOMENOLOGY: model-independent tests of the failure of GR ?

31. structure formation Poisson equation Euler equation stress constraint GR: MG: modified gravity strength + ‘dark’ anisotropic stress examples

32. Testing for MG In principle: • Total density perturbation gives • Galaxy velocities give • Lensing gives • Then determines We can also derive a consistency test for GR vs MG: Song & Koyama

33. MG versus Coupled DE? Coupled DE in GR introduces complications MG: all fields feel modified gravity equally, so equivalence principle is not violated Coupled DE: CDM breaks EP because of the coupling • Poisson equation is the same • But Euler equation is modified • This can be detected in principle via peculiar velocities

34. observations imply acceleration theory did not predict it – and cannot yet explain it GR with dynamical DE – no natural model modifications to GR – theory gives no natural model simplest models fail [f(R), DGP] Observations cannot ‘find’ a theory Too many models to test each one Need model-independent approaches key questions: 1. is Λ the dark energy? 2. if not, is it GR+dynamical DE – or Dark Gravity? In principle: expansion history + structure formation test can answer 1+2 As a by-product – we understand GR and gravity better some conclusions