Dark Energy Constraints on Modified Gravities

1. Ishwaree Neupane University of Canterbury New Zealand Dark Energy Constraints on Modified Gravities Spring Symposium 2008 A Decade of Dark Energy May 5, 2008, STScI, Baltimore

2. There has been a renewal of interest in scenarios that propose alternatives to the standard model of dark energy – i.e. the cosmological constant The proposals are of differing origin as well as motivations: some are based on higher dimensional braneworld models, others on scalar-tensor theories.

3. A simple theory of cosmic acceleration (or quintessence), with a canonically normalized scalar field, is described by the Lagrangian Observations require so unlike a naïve expectation the leading corrections to cosmological parameters arise from terms that are quadratic in the curvature.

4. James T. Wheeler: A Strong Advocate of Modified Gravity The most general gravitational Lagrangian which can be constructed from the curvature two-form, the vielbein one-form, and tensors invariant in the tangent space involves dimensionally extended Euler characteristics densities Cosmology requires FRW and non-constant scalar couplings, i.e. So, the Gauss-Bonnet density would affect the field equations (even in four dimensions) because its coefficient is not constant The coupling can be eliminated by a redefinition of the metric

5. Gauss-Bonnet Dark Energy An exact non-singular inflationary solution The coupling may grow with time but not the term

6. An Inflationary Solution Choose the gauge We can think of as well as as both being of order at horizon exit Further IPN: hep-th/0605266

7. The Simplest Potentials hold some validity as a post-inflation approximation Koivisto & Mota hep-th/0609155 Solid lines (SNe IA plus CMBR shift parameter) Shaded regions (including Baryon Acoustic Oscillation scale)

8. Ghost and Superluminal modes Tensor modes Scalar modes

9. Observing the effects of a scalar-GB coupling? The growth of matter fluctuations is the matter density contrast In conventional models where if dark energy is the cosmological constant For an extra dimensional modification of gravity: DGP claim L. Guzzo et al. arXiv:0802.1944 

10. Growth of matter perturbations With the input the observational limit on growth factor implies that on cosmological scales

11. Lambda-CDM Scalar-CDM The choice yields To get we simply require IPN & C. Scherer: arXiv:0712.2468 [JCAP:0805]

12. Coupled Dark Energy (Quintessence) Local GR constraints on and its derivatives (Damour et al. 1993, Esposito-Farese 2003)

13. SNLS SNLS+WMAP+SDSS SNIa-Gold SNIa-Gold+WMAP+SDSS

14. A time-varying matter-quintessence coupling affects both the dark energy EoS and the Hubble parameter in an interesting way: For the exponential coupling The Hubble parameter in the physical Jordan frame is A positive may increase the chi-squared minimized value of

15. Gold-SNIa Gold-SNIa Top to bottom is minimized for Where is the usual post-Newtonian parameter we get For the best fit value

16. Summary • 1) Scalar-Gauss-Bonnet gravity is a healthy modification of Einstein’s GR, irrespective of a type of background chosen. The theory is promising as it • naturally connects the classical GR with superstring theory through its low energy description. • admits non-singular cosmological solutions, both inflationary and non-inflationary types. • 2) But it is not by default that any such effective theory becomes free from ghosts or short distance instabilities. This well depends on the type of the scalar-curvature couplings that one would allow. • 3) The case of decreasing due to the parameter of the non-minimal coupling corresponds to a time-varying Newton’s constant that usually boosts acceleration and decreases the dark EoS