Chameleons Galore. IHES Bures- sur- Yve*e January Philippe Brax (IPhT CEA-Saclay)

Transcription

1 Chamelens Galre Philippe Brax (IPhT CEA-Saclay) Cllabratin with C. Burrage, C. vandebruck, A. C. Davis, J. Khury, D. Mta, J. Martin, D. Seery, D. Shaw, A. Weltman. IHES Bures- sur- Yve*e January 2010

2 Outline 1-Scalars and Csmic Acceleratin? 2-Chamelens and Thin Shell effect 3-The Casimir Effect 4- Chamelen Optics 5-Mdifying gravity at lw redshift.

3 Scalars and Dark Energy

4 Dark Energy V(! Planck scale nw Field rlling dwn a runaway ptential, reaching large values nw (Planck scale) Extremely flat ptential fr an almst decupled field

5 Hw Flat? Energy density and pressure: Runaway fields can be classified accrding t very fast rll slw rll (inflatin) gentle rll (dark energy ) strng gravitatinal cnstraints

6 Gravitatinal Tests Dark energy theries suffer frm the ptential presence f a fifth frce mediated by the scalar field. Alternatives: Nn-existent if the scalar field has a mass greater than : If nt, strng bund frm Cassini experiments n the gravitatinal cupling:

7 Scalar-Tensr Effective Thery Effective field theries with gravity and scalars: Scalars differ frm axins (pseud-scalars) inasmuch as they can cuple t matter with nn-derivative interactins. All the physics is captured by the functin A(ϕ). In the Einstein frame, masses becme cnfrmally related t the bare mass.

8 Gravitatinal Cnstraints Deviatins frm Newtn s law are tested n macrscpic bjects. The gravitatinal cupling is: The deviatin is essentially given by:

9 An Example: the radin The distance between branes in the Randall-Sundrum mdel: where Gravitatinal cupling: clse branes: cnstant cupling cnstant

10 Example: Mduli cupled t the standard mdel The Standard Mdel fermin masses becme mduli dependent Scalar-tensr thery Yukawa Kahler n=1 dilatn, n=3 vlume mdulus

11 Gravitatinal Prblems Deviatins frm Newtn s law are tested n macrscpic bjects. The gravitatinal cupling is: Fr mduli fields: T Large!

12 f(r) gravity The simplest mdificatin f General Relativity is f(r) gravity: The functin f(r) must be clse t R, s f(r)= R+ h(r), h<< R in the slar system. f(r) gravity addresses the dark energy issue fr certain chices f h(r).

13 f(r) vs Scalar-Tensr Theries f(r) ttally equivalent t an effective field thery with gravity and scalars The ptential V is directly related t f(r). Same prblems as dark energy: cincidence prblem, csmlgical cnstant value etc

14 A Few Examples A large class f mdels is such that h(r) C fr large curvatures. This mimics a csmlgical cnstant fr large value f Anther class f mdels leads t a quintessence like behaviur: V(! Ratra-Peebles! n=-(p+1)/p

15 Chamelens

16 Chamelens Chamelen field: field with a matter dependent mass A way t recncile gravity tests and csmlgy: Nearly massless field n csmlgical scales Massive field in the labratry

17 The effect f the envirnment When cupled t matter, scalar fields have a matter dependent effective ptential Envirnment dependent minimum V eff(! exp( " #""""""""! M Pl V(!

18 An Example: Ratra-Peebles ptential Cnstant cupling t matter V eff V eff fr f(r) theries Large Small

19 What is dense enugh? The envirnment dependent mass is enugh t hide the fifth frce in dense media such as the atmsphere, hence n effect n Galile s Pisa twer experiment! It is nt enugh t explain why we see n deviatins frm Newtnian gravity in the lunar ranging experiment It is nt enugh t explain n deviatin in labratry tests f gravity carried in vacuum

20 The Thin Shell Effect I The frce mediated by the chamelen is: The frce due t a cmpact bdy f radius R is generated by the gradient f the chamelen field utside the bdy. The field utside a cmpact bdy f radius R interplates between the minimum inside and utside the bdy Inside the slutin is nearly cnstant up t the bundary f the bject and jumps ver a thin shell Outside the field is given by:

21 ! [M] !!! [M] r[m -1 ] r [M -1 ] N shell Thin shell

22 The Thin Shell Effect II The frce n a test particle utside a spherical bdy is shielded: When the shell is thin, the deviatin frm Newtnian gravity is small. The size f the thin-shell is: Small fr large bdies (sun etc..) when Newtn s ptential at the surface f the bdy is large enugh.

23 Labratry tests In a typical experiment, ne measures the frce between tw test bjects and cmpare t Newtn s law (this is very crude, mre abut the Et-wash experiment later ). The test bjects are taken t be small and spherical. They are placed in a vacuum chamber f size L. In a vacuum chamber, the chamelen resnates and the field value adjusts itself accrding t: The vacuum is nt dense enugh t lead t a large chamelen mass, hence the need fr a thin shell. Typically fr masses f rder 40 g and radius 1 cm, the thin shell requires fr the Ratra-Peebles case: We will be mre precise later.

24 The Casimir Effect

25 Casimir Frce Experiments Measure frce between Tw parallel plates A plate and a sphere

26 The Casimir Frce The inter-plate frce is in fact the cntributin frm a chamelen t the Casimir effect. The acceleratin due t a chamelen is: The attractive frce per unit surface area is then: where is the change f the bundary value f the scalar field due t the presence f the secnd plate.

27 The Casimir Frce We fcus n the plate-plate interactin in the range: Mass in the plates Mass in the cavity The frce is algebraic: The dark energy scale sets a typical scale:

28 Behaviur f Chamelenic Pressure fr V = 4 0 (1+ n / n ); n = Chamelenic Pressure: (V( c ) 4 0 ) 1 F /A Cnstant frce behaviur d = m c 1 Pwer law behaviur d = m b 1 Expnential behaviur Separatin f plates: m d c

29 Detectability The Casimir frces is als an algebraic law implying: This can be a few percent when d=10µm and wuld be 100% fr d=30 µm

30

31

32 Et Wash Experiment Measurement f the trque between tw plaques with hles (n effect fr Newtnian frces) The ptential energy f the system due t a chamelen frce between the plates is The frce per unit surface area can be apprximated by the frce between tw plates, the trque becmes:

33 Pwer Law Example Pwer law: Cnstraints n Pwer Law f(r) theries: f(r) = R+h(R) Integrating the field equatins between the plates: We find cnstraints n the scale: Energy scale in h(r): 0 (GeV) Allwed Regin Et Wash bund (thin shells assumed) Csmlgical thin shell bund m c D p >> 1 Excluded Regin Slpe f h(r): p

34 Chamelen Optics

35 Induced Cupling When the cupling t matter is universal, and heavy fermins are integrated ut, a phtn cupling is induced.

36

37 Experimental Setup

38

39 Chamelens Cupled t Phtns Chamelens may cuple t electrmagnetism: Cavity experiments in the presence f a cnstant magnetic field may reveal the existence f chamelens. The chamelen mixes with the plarisatin rthgnal t the magnetic field and scillatins ccur (like neutrin scillatins) The cherence length depends n the mass in the ptical cavity and therefre becmes pressure and magnetic field dependent: The mixing angle between chamelens and phtns is:

40 Ellipticity and Rtatin Phtns remain N passes in the cavity. The perpendicular phtn plarisatin after N passes and taking int accunt the chamelen mixing becmes: The phase shifts and attenuatins are given by: identified with the phase shift and attenuatin after ne pass f length nl. At the end f the cavity z=l, this can be easily identified fr cmmensurate cavities whse lengths crrespnds t P cherence lengths Rtatin ellipticity

41 Realistic Chamelen Optics Must take ther effects int accunt. m c Very fast (step like) change in the Chamelen Mass Chamelens never leave the cavity (utside mass t large, n tunnelling) m Chamelens d nt reflect simultaneusly with phtns. m b 0 distance frm surface f mirrr Mre realistic m ~ O(1)/d change in Chamelen Mass m c Chamelens prpagate slwer in the n-field zne within the cavity m m b 0 distance frm surface f mirrr

42 10 10 Rtatin predictins: n = 1 & = 2.3! 10 3 ev PVLAS 2.3T upper bund Rtatin (rad / pass) T 2.3T 11.5T Chamelen t matter cupling: M (GeV)

43 Ellipticity predictins: n = 1 & = 2.3! 10 3 ev 5.5T 2.3T 11.5T Ellipticity (rad / pass) PVLAS 2.3T upper bund Expected BMV sensitivity Chamelen t matter cupling: M (GeV)

44 Light Shining thrugh a Wall Axin-like particles, nce generated can g thrugh the wall and then regenerate phtns n the ther side. Chamelens cannt g thrugh but can stay in a jar nce the laser has been turned ff and then regenerate phtns.

45 GammeV (Fermilab) and ADMX (Seattle) will cver a large part f the parameter space.

46 Mdifying gravity at lw z

47 Chamelen Csmlgy 2 Slutin including ki Slutin neglecting k!! / M Pl Electrn kick during BBN 0.5 Late time acceleratin Pssibility f variatin f cnstants e+08 1e+12 1e+16 Lurking csmlgical cnstant 1+z

48 Mdified Gravity at lw z? Gravity is well tested in the slar system. Fr larger scales, gravity may be mdified. A test f mdified gravity can be btained by studying the grwth f structures at lw redshift (in the linear regime): This is mst sensitive t the behaviur f the grwth factr n subhrizn scales and the rati f the Newtn ptentials In general relativity, the slip functin and the grwth index are knw t be: Recently, Rachel Bean fund sme «evidence» in favur f a mdificatin f gravity at lw redshift. When scalars cuple t matter, nt a unique definitin f «a» slip functin.

49

50 Linear Grwth factr At the perturbatin level, the grwth factr evlves like: The new factr in the brackets is due t a mdificatin f gravity depending n the cmving scale k. Here the cupling is cnstant.

51 Everything depends n the cmving Cmptn length: Gravity acts in an usual way fr scales larger than the Cmptn length Gravity is mdified inside the Cmptn length with a grwth:

52 Everything depends n the time dependence f m(a). If m is a cnstant then the Cmptn length diminishes with time. S a scale inside the Cmptn length will eventually leave the Cmptn length Mdified gravity z=z* General Relativity On the ther hand, fr chamelens the Cmptn length increases implying that scales enter the Cmptn length. General Relativity Mdified gravity z=z*

53 General Framewrk We will generalise the previus mdels and wrk with a different cupling fr each species. The Einstein equatin and the Bianchi identity are satisfied with: The Klein-Grdn equatin becmes: The metric is specified by tw ptentials: At late times, in the absence f anistrpic stress, the Pissn equatin is satisfied:

54 Grwth f structures The density cntrast f each species satisfies: Gravity is mdified because the cupling cnstants depend n time: In the fllwing: A=baryns, B=CDM. As lng as a scale des nt crss the Cmptn length: After crssing the Cmptn length, the relatin changes:

55 Grwth index Mdified gravity implies that the grwth is altered: The defrmatin is a slwly varying functin: B=CDM A=baryns

56 Slip functin I Weak lensing which is sensitive t the ttal Newtn ptential Recnstructing the effective Newtn ptential frm the Pissn law assuming that baryns track CDM as in General Relativity leads t: Our first slip functin cmpares this ptential t weak lensing:

57 Slip functin II Anther slip functin can be btained by crrelating the ISW effect and galaxies: This ne is sensitive t the grwth index and differs frm ne even if the cuplings are equal:

58 ISW slip functin Despite the large uncertainty, this slip functin gives the tightest cnstraints n the cuplings when n cupling t baryns is present. When the cupling is universal, this is equivalent t the barynic grwth index.

59 Cmbining the slip functins If the crssing f the Cmptn length is arund z*=4, ne culd expect at mst and at the 1-sigma level a discrepancy with General Relativity t be f rder If the crssing is at z*=2, this reduces t

60 The Dilatn String thery in the strng cupling regime suggests that the dilatn has a ptential: Damur and Plyakv suggested that the cupling shuld have a minimum: The cupling t matter becmes:

61 In the presence f matter, the minimum plays the rle f an attractr: The cupling becmes: Three regimes: i) early in the universe, large density: small cupling. ii) recent csmlgical past: large scale mdificatin f gravity. iii) cllapsed bjects: small cupling.

62 The Dilatnic case

63 Cnclusins Chamelens culd be arund if scalar fields are the reasn behind csmic acceleratin Light scalars are under experimental scrutiny (Casimir, ptics) Weak lensing surveys culd give a hint abut late time deviatins frm General Relativity