Modified Gravity and Dark Matter

Transcription

1 Modified Gravity and Dark Matter Jose A. R. Cembranos University Complutense of Madrid, Spain J. Cembranos, PRL102: (2009)

2 Modifications of Gravity We do not know any consistent renormalizable Quantum field theory of gravity with a finite number of parameters (terms). The present theory of gravity is renormalizable if understood in the framework of quantum effective field theories. J.F. Donoghue, gr-qc/ Gravity is not just Einstein equations. What is the scale of quantum gravity? Dark Energy/Dark Matter? IR vs UV modifications Jose A. R. Cembranos 1

3 Framework Standard Model Gravitational Sector SM scale: H? Gravity scale: J. Cembranos, PRL102: (2009) Jose A. R. Cembranos 2

4 CONTENTS Dark Matter solution from gravity. Quantum gravity. UV modifications: Effective Quantum Field Theory approach Fourth Order Gravity New metric modes: Abundance Phenomenology and detection Jose A. R. Cembranos 3

5 Quantum Gravity Einstein Gravity is not consistent at high energies: Non-Unitarity Non-renormalizable The present theory of gravity is renormalizable if treated in the framework of quantum effective field theories. J.F. Donoghue, gr-qc/ Jose A. R. Cembranos 4

6 Fourth Derivative Gravity The action is renormalizable: The gauge fixing condition can be introduced within the standard Faddev- Popov prescription: K.S. Stelle, PRD16:953,1976 K.S. Stelle, Gen.Rel.Grav.9:353,1978 Jose A. R. Cembranos 5

7 Graviton Spectrum The propagator in the transverse or physical gauge is given by: The same propagator can be written as: Jose A. R. Cembranos 6

8 The Model The gravitational action is reduced to: The rest of terms in the QEFTG are necessary in order to renormalize the divergences coming from radiative corrections. However, their effects will be negligible for the rest of the discussion. Validity of the model? Jose A. R. Cembranos 7

9 Graviton Spectrum The propagator in the transverse or physical gauge is given by: The same propagator can be written as: Jose A. R. Cembranos 8

10 Classical Dynamic The Einstein equations are modified: A. A. Starobinsky, PLB91:99,1980 Starobinsky and other authors studied this action and other extensions in the 80 s in order to generate inflation. Jose A. R. Cembranos 9

11 Einstein Limit In any case, we will work always at curvatures, when the EEs are a good approximation. In fact, we can work in the so called Einstein frame, where the new scalar degree of freedom is explicitly separated from the metric tensor, which has associated the standard Einstein-Hilbert action. Jose A. R. Cembranos 10

12 Einstein Frame Trough a conformal transformation: the standard action for gravity is recover in addition to a standard action for the scalaron with the potential given by: Jose A. R. Cembranos 11

13 Scalaron Couplings The scalaron is universally coupled to matter trough the trace of the energy momentum tensor: It means that at tree level, the coupling with SM particles are given by: Jose A. R. Cembranos 12

14 Radiative Scalaron Couplings On loop generates the coupling with photons and gluons: Contributions to the photon vertex: Jose A. R. Cembranos 13

15 Abundance Thermal abundance would require Beyond the validity of Einstein Equations. Misalignment mechanism For For oscillates around the minimum of its potential. These oscillations correspond to a zero-momentum condensate. Cold DM Abundance: J. Cembranos, PRL102: (2009) Jose A. R. Cembranos 14

16 R2-gravity as Dark Matter Parameter space of R2-gravity as DM: R2 abundance inside the WMAP limits. Constraints: Overproduction. Jose A. R. Cembranos 15

17 New Force Constraints The new scalar graviton generates a Yukawa new interaction among standard matter: The University of Washington Eöt-Wash group has tested the strength of gravity at distances down to 0.06 mm. D. J. Kapner et. al., hep-ph/ Consistent with Newton s inverse-square law. With. Jose A. R. Cembranos 16

18 R2-gravity as Dark Matter Parameter space of R2-gravity as DM: Scalaron abundance inside the WMAP limits. Constraints: Overproduction. Eöt-Wash experiments. Jose A. R. Cembranos 17

19 Electron-positron Decay Depending on its abundance, the mass is constrained from above. The e + e - decay is the most constraining if the R2- gravity constitutes the total non-baryonic DM. The decay rate in a generic pair fermionantifermion: In particular, for the e + e - decay: Jose A. R. Cembranos 18

20 511 kev g from the GC We have had observations of 511 photons coming form the center of the galaxy for the last 30 years with different instruments. Pierre Jean et al, astro-ph/ ~8.5 Kpc ~9º = ~1.3 Kpc 511 kev signal by SPectromètre Integral Jose A. R. Cembranos 19

21 511 kev g line signal The signal comes from e + e -, but it is difficult to find a source of 10^43 positrons per second inside the bulge with kinetic energies smaller than ~ 4 MeV as it is required. J.F. Beacom and H. Yuksel, astro-ph/ Proposed sources of positrons 1. Supernovas Type II, Ia and Ic 2. Wolf-Rayet Stars 3. Neutron stars, pulsars 4. Cosmic rays 5. Black holes 6. Dark Matter: 6.1. Annihilating DM 6.2. Decaying DM Jose A. R. Cembranos 20

22 511 kev g from Decaying DM Several authors have studied this signal within different decaying Dark Matter models: 1. Sterile neutrinos 2. Axinos 3. Moduli 4. WIMPs 5. Branons C. Picciotto and M. Pospelov, hep-ph/ D. Hooper and L.T. Wang, hep-ph/ S. Kasuya and M. Kawasaki, astro-ph/ M. Pospelov and A. Ritz, hep-ph/ J. Cembranos and L. Strigari, [astro-ph] To account for the signal, all of them find the conditions (supposing a total DM abundance): M ( or DM) ~ 1 MeV t ~ 10^26 sec / M (MeV) Jose A. R. Cembranos 21

23 Decaying DM, source of 511 kev g Decaying DM could account for the 511 kev line with cuspy dark halos ( ). J. Cembranos and L. Strigari, PRD77: (2008) The preferred life-time is dominated by high uncertainties in the halo profile and substructure: J. Cembranos, PRL102: (2009) Jose A. R. Cembranos 22

24 Decaying DM, source of 511 kev g Decaying DM could account for the 511 kev line with cuspy dark halos ( ). J. Cembranos and L. Strigari, PRD77: (2008) The preferred life-time is dominated by high uncertainties in the halo profile and substructure: J. Cembranos, PRL102: (2009) Jose A. R. Cembranos 23

25 R2-gravity as Dark Matter Parameter space for R2-gravity as DM: Abundance inside the WMAP limits. Constraints: Overproduction. Eöt-Wash experiments. Gamma rays. 511 kev line from the GC (INTEGRAL data). J. Cembranos, PRL102: (2009) Jose A. R. Cembranos 24

26 Conclusions New degrees of freedom in the gravitational sector are viable candidates for DM. We have studied R2-gravity, as a particular example. Other signatures: 1.- Observations of lines from the GC: Potentially able to test the heavy part of the allowed spectrum. J. Cembranos, PRL102: (2009) Jose A. R. Cembranos 25

27 Back-up Slides Jose A. R. Cembranos 26

28 The Model The self-couplings of the gravitational degrees of freedom are given by a series in: The number of fields suppressed by M p The number of derivatives suppressed by m 0 The interesting case is. The leading order at high energies would be given by the interaction with highest number of derivatives (4) and lower number of fields (3). Jose A. R. Cembranos 27

29 Four Scalar Amplitude The leading order at high energies: Jose A. R. Cembranos 28

30 Four Scalar Amplitude The leading order at high energies: Jose A. R. Cembranos 29

31 Four Scalar Amplitude The leading order at high energies: Jose A. R. Cembranos 30

32 Oscillating Expansion For long times, : Scalar mode evolution Relation between scale factors: Relation between Hubble rates: A. Vilenkin, PRD32:2511,1985 S. Kalara, N. Kaloper, K. Olive, Nuc.Phys.B341:252,1990 Jose A. R. Cembranos 31

33 Other Signatures If, the only observable decay channel is in two photons. It is loop suppressed: 1.- Observations of lines from the GC: Potentially able to test heavy part of the spectrum. 2.- Modifications in the CMB through injection of energy in baryons WMAP is able to test life-times around 10^25 s. PLANCK wont improve enough to be sensitive to R2-gravity. Jose A. R. Cembranos 32