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Living with the Dark Energy in Horava Gravity

IEU-APCTP Workshop on Cosmology and Fundamental Physics (18 May 2010, IEU). Living with the Dark Energy in Horava Gravity. Mu-In Park Chonbuk Nat ’ al Univ. Based on arXiv:0905.4480 [JHEP] , arXiv:0906.4275 [JCAP],. 0. Outline.

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Living with the Dark Energy in Horava Gravity

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  1. IEU-APCTP Workshop on Cosmology and Fundamental Physics(18 May 2010, IEU) Living with the Dark Energy in Horava Gravity Mu-In Park ChonbukNat’al Univ. Based on arXiv:0905.4480 [JHEP], arXiv:0906.4275 [JCAP],

  2. 0. Outline 1. Horava gravity and its IR modification 2. FRW cosmology in IR modified Horava gravity 3. Comparison with observational data 4. Open problems

  3. 1. Motivation of IR modificationof Horava gravity Renormalizablegravity theory by abandoning Lorentz symmetry in UV : Foliation Preserving Diffeomorphism. Horava gravity ~ Einstein gravity (with a Lorentz deformation parameter ) + non-covariant deformations with higher spatial derivatives (up to 6 orders) + “detailed balance” in the coefficients ( 5 constant parameters: ) Cf.Einstein gravity:

  4. Detailed balance condition: • We need (foliation preserving Diff invariant) potential term having 6th order spatial derivatives at most (power-counting renormalizable with z=3) : • There are large numbers of possible terms, which are invariant by themselves, like …

  5. …, like • But there are too many couplings for explicit computations, though some of them may be constrained by the stability and unitarity. We need some pragmatic way of reducing in a reliable manner.

  6. Horavarequired the potential to be of by demanding for some D-dimensional action and the inverse of De Witt metric • There is a similar method in non-equilibrium critical phenomena.

  7. W is 3-dimensional Euclidean action. • First, we may consider Einstein-Hilbert action, then, this gives 4’th-derivative order potential • So, this is not enough to get 6’th order !!

  8. In 3-dim, we also have a peculiar, 3’rd- derivative order action, called(gravitational) Chern-Simons action. • This produces the potential with the Cotton tensor Christoffel connection

  9. Then, in total, he got the 6’th order from So, we have 5 constant parameters, which seems to be minimum, from the detailed balancing.

  10. Some improvedUV behaviors, without ghosts, are expected, i.e., renormalizability Predictable Quantum Gravity !!(?) • But, it seems that the detailed balance condition is too strong to get general spacetimes with an arbitrary cosmological constant. • For example, there is noMinkowski , i.e., vanishing c.c. vacuum solution ! (Lu, Mei, Pope): There is noNewtonian gravity limit !!

  11. A “soft” breaking of the detailed balance is given by the action : • It is found that there does exit the black hole which converges to the usual Schwarzschild solution in Minkowski limit, i.e., for (s.t. Einstein-Hilbert in IR) (Kehagias, Sfetsos) . IR modificationterm

  12. Black hole solution for limit ( ): ~ Schwarzshild Solution : Independently of !!

  13. General Remarks KS considered but it can be considered as an independent parameter:One more parameter than the Horava gravity with the detailed balance, i.e., we have 6 constant parameters • Cosmological constant ~ <0, i.e., AdS, for consistency ( >0 ) ! (Horava) IR modification parameter

  14. dS , i.e., positive c.c., can be obtained by the continuation (Lu,Mei,Pope): • Cf: KS:

  15. 2. FRW cosmology in IR modified Horava gravity • Homogeneous, isotropic cosmological solution of FRW form : • For a perfect fluid with energy density and pressure , the IR modified Horava action gives …

  16. Friedman equations is the current (a=1) radius of curvature of universe [ Upper(Lower) sign for AdS(dS) ]

  17. Remarks • The term, which is the contribution from the higher-derivative terms in Horava gravity, exists only for, i.e., non-flat universe and becomes dominant for small : The cosmological solutions for GR are recovered at large scales. (cf. Reyes, et al.) • There is no contribution from the soft IR modification to the second Friedman Eq.: Identical to that of Lu,Mei,Pope.

  18. What is the implication of the Horava gravity to our universe ? What will we see if we have been lived in Horava gravity, from the beginning ?

  19. If we have been lived in the Horava gravity (with some IR modifications), the additional contributions to the Friedman Eq. from the higher-(spatial) derivative terms may not be distinguishable from the darkenergy with (including C.C. term)

  20. We would see the Friedman Eq. as where

  21. The Eq. of state parameter is given by • And it depends on the constant parameters ...

  22. 3a. Comparison with observational data : Latest data, without knowing details of matters. • Previously, I neglected matters, which occupy about 30 % of our current universe, to get , so this would be good within about 70 % accuracy, only ! • Is there any more improved analysis to achieve better accuracy, without neglecting matters ? Yes ! …

  23. To this end, let me consider the series expansion of near the current epoch (a=1): • This agrees exactly with Chevallier, Polarski, and Linder (CPL)'s parametrization !

  24. By knowing and from observational data, one can determine as

  25. Remarks • I do not need to know about matter contents, separately. • Once are determined, the whole function is completely determined !

  26. Data analysis withoutassuming the flat universe

  27. Data analysis Ia, Ib: CMB+BAO+SN • K. Ichikawa, T. Takahashi [arXiv: 0710.3995v2 [astro-ph] 3 May 2008 Ia Ib

  28. +Gold06 (red,solid): Analysis Ia Best Fit: (-1.06,0.72) +David07 (blue,dotted) : Analysis Ib Best Fit: (-1.10,0.39)

  29. Data analysis II: CMB+BAO+SN • J.-Q.Xia, et. al., arXiv:0807.3878v2 [astro-ph] 22 Aug 2008

  30. Non-Flat (blue, dash-dotted) Best Fit: (-1.11,0.475) Flat (red, solid)

  31. The whole function of is determined as (a=1/(1+z)) Past Future Today

  32. Similar tendencies 1. Best Fit: Gold-HST=142 SNe U. Alam et. al., astro-ph/0403687 (Flat universe is asumed)

  33. Similar tendencies 2 Huterer and Cooray, PRD71, 023506 (2005): Uncorrealtedestimates (flat universe is assumed)

  34. Similar tendencies (?) 2’ R. Amanullah et al. astro-ph/ 1004.1711 (flat universe is assumed)

  35. Similar tendency 3 Shafieloo, astro-ph/0703034v3: SN Gold data set ( )

  36. Remark • For the consistency of our theory, we need • Otherwise, we would have imaginary valued and , though would not !! :

  37. Consistency Conditions : Forbidden !! Forbidden !!

  38. In our data sets Ia II Ib Cosmological Constant

  39. Within confidence levels Ia 68.3 % Confidence

  40. II

  41. Consistency condition may be tested near future, like in Planck (2012), by sharpening the data sets !

  42. 4. Open problems • We need some more systematic fitting for the range of allowed constant parameters to see whether our theory is really consistent with our universe. • “Can we reproduce other complicated stories with (dark) matters, i.e. density perturbations? “ (cf. A. Wang, et. al) • Inflation without inflation ??

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