Cosmic Microwave Background polarization as a test for fundamental physics

Size: px

Start display at page:

Download "Cosmic Microwave Background polarization as a test for fundamental physics"

Eleanore Bethanie Walker
5 years ago
Views:

1 Cosmic Microwave Background polarization as a test for fundamental physics Giulia Gubitosi Presentazione progetto di tesi - Relatore: Alessandro Melchiorri Roma 04/06/2009 Giulia Gubitosi, L. Pagano, G. Amelino-Camelia, A. Melchiorri, A. Cooray, arxiv: L. Pagano, P. de Bernardis, G. De Troia, Giulia Gubitosi, S. Masi, A. Melchiorri, P. Natoli, F. Piacentini, G. Polenta, arxiv: GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

Black-body spectrum peaked at 2.725 K (160 GHz or 6.

Anisotropies: T T 10 5 10% partially polarized : P P J.

2 Black-body spectrum peaked at K (160 GHz or ev ) What is the CMB? Anisotropies: T T % partially polarized : P P J. Kovac, et al., Nature 420 (2002) 772 T 10 1 T GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

3 CMB and standard cosmological model CMB recent data fit very well the predictions of the standard cosmological model M. Nolta, et al., 2009, ApJS, 180, Future experiments will be able to search for phenomenological clues of new physics (especially looking at polarization) GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

4 CMB and standard cosmological model CMB recent data fit very well the predictions of the standard cosmological model M. Nolta, et al., 2009, ApJS, 180, Future experiments will be able to search for phenomenological clues of new physics (especially looking at polarization) GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

5 Planck-scale phenomenology Quantum Gravity scale [QM and GR both non-negligible] E P c 5 G 1028 ev Need for experimental hints on features of the new theory Nowadays well established possibility to test effects originating at the Planck scale (mainly astrophysics) G. Amelino-Camelia, J. Ellis, N.E. Mavromatos, D.V. Nanopoulos and S. Sarkar, Nature 393 (1998) 763 S.D. Biller et al., Phys. Rev. Lett. 83 (1999) 2108 T. Jacobson, S. Liberati and D. Mattingly, Nature 424 (2003) 1019 Why CMB: high energies during inflation long travel time (accumulation of effects) GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

6 An intriguing circumstance Recent analysis of BOOMERANG+WMAP data found indications for rotation of the CMB polarization plane 6 ± 4 degrees [at 1σ] B. Feng, M. Li, J. Q. Xia, X. Chen and X. Zhang, Phys. Rev. Lett. 96 (2006) J. Q. Xia, H. Li, X. l. Wang and X. m. Zhang, Astron. Astrophys. 483 (2008) 715 Such a rotation (if confirmed) is still not explained by standard physics sign of some quantum-gravity effect originating at the Planck scale? GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

7 CMB formation Early universe: H + γ p + e Thomson scattering γ + e γ + e when the photon energy becomes sufficiently low H + γ p + e is disfavoured recombination (z rec 1370, T rec 3740K, t rec yr) no more free electrons to scatter photons free streaming of photons toward us (z dec 1100, T dec 3000K, t dec yr) GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

8 Thomson scattering cross section: dσ dω ˆɛ ˆɛ CMB polarization [ɛ, ɛ polarization resp. of outgoing and incoming radiation] scattered light polarization mainly orthogonal to the scattering plane incident radiation unpolarized but with quadrupolar anisotropies resulting radiation linearly polarized A. Kosowsky, astro-ph/ CMB does have quadrupolar anisotropies, mainly due to density perturbations GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

9 Formal description of polarization Stokes parameters I = Ex 2 + Ey 2 total intensity Q = Ex 2 Ey 2 polarization along ˆx or ŷ U = 2Re(E x Ey ) polarization along 45 between ˆx and ŷ Under rotation of an angle α (Q ± iu) (ˆn) = e 2iα (Q ± iu)(ˆn) decomposition in spin-weighted spherical harmonics ±2 Y lm [( ±s Y lm ) = e s i α ±sy lm ] E lm ± ib lm = d ˆn ±2 Ylm (ˆn)(Q ± iu)(ˆn) W. Hu, Annals Phys. 303 (2003) 203 GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

10 How can we detect a rotation of the original polarization? Polarization can be decomposed in Electric and Magnetic modes: E(ˆn) = lm E lm Y lm (ˆn) even under parity B(ˆn) = lm B lm Y lm (ˆn) odd under parity Density perturbations are scalars can produce only E-modes of polarization Rotation of original polarization generates B-modes tool of analysis: cross-correlation power spectra Cl XY = 1 < Xlm 2l + 1 Y lm >, m X, Y = T, E, B GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

11 How can we detect a rotation of the original polarization? Polarization can be decomposed in Electric and Magnetic modes: E(ˆn) = lm E lm Y lm (ˆn) even under parity B(ˆn) = lm B lm Y lm (ˆn) odd under parity Density perturbations are scalars can produce only E-modes of polarization Rotation of original polarization generates B-modes tool of analysis: cross-correlation power spectra Cl XY = 1 < Xlm 2l + 1 Y lm >, m X, Y = T, E, B GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

12 Effects of rotation on power spectra BLACK: standard spectra RED: spectra resulting from a rotation of 30 Figure: EE, TE, EB and TB spectra (from top to bottom and left to right) GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

13 (in-vacuo) Birefringence If the two helicity states of electromagnetic waves have different phase velocities E ± = Re ((ê 1 ± iê 2 ) e i(ω ±t k x) ) linearly polarized radiation rotates its polarization vector during propagation (e.g. light propagation through materials with chiral molecules, as sugar and quartz) Quantum-gravity-motivated effect: different polarization states could have different dispersion relations when propagating in vacuo R. Gambini and J. Pullin, Phys. Rev. D 59 (1999) G. Amelino-Camelia, New J. Phys. 6 (2004) 188 R.C. Myers, M.Pospelov, PRL 90 (2003) GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

14 Effective field theory for in-vacuo birefringence Several studies used CMB polarization data for testing birefringence, none tested if it was possible to constrain some Planck-scale effect Interested in effects governed by the Planck scale (1/M Pl effect), consider mass-dimension five corrections to the Lagrangian of electrodynamics Myers-Pospelov model: [R.C. Myers, M.Pospelov, PRL 90 (2003) ] The discrete nature of space at short distances is expected to induce violations of Lorentz invariance and CPT We define a preferred frame defined by a fixed four-vector n α GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

15 Myers-Pospelov model L = 1 4 F µνf µν + 1 2E p n α F αδ n σ σ (n β ε βδγλ F γλ ) MP assumed pure-time vector n α = (n 0, 0, 0, 0): L = 1 4 F µνf µν + ξ 2E p ε jkl F 0j 0 F kl [ ξ n 3 0 ] R.C. Myers, M.Pospelov, PRL 90 (2003) violated invariance under boost transformation preserved space isotropy Several astrophysical analyses on observable features of this model T. Jacobson, S. Liberati and D. Mattingly, Nature 424 (2003) 1019 [arxiv:astro-ph/ v2]. G. Amelino-Camelia, New J. Phys. 6 (2004) 188 [arxiv:gr-qc/ ]. R. J. Gleiser and C. N. Kozameh, Phys. Rev. D 64 (2001) [arxiv:gr-qc/ ]. D. Mattingly, Living Rev. Rel. 8 (2005) 5 [arxiv:gr-qc/ ]. L. Maccione and S. Liberati, JCAP 0808 (2008) 027 [arxiv: [astro-ph]]. GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

16 Birefringence emerging from MP Lagrangian Modified Maxwell equations E = 0 E = B t B = E t Modified equations of motion: + 2ξ E p 2 B t 2 B = 0 ( ω 2 + p 2 ± 2ξ ) ω 2 p E ± = 0 E p [E ± E 1 ± ie 2 right- and left- circularly polarized fields] GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

17 Effects on CMB photons Dispersion law: ( ω ± = p 1 ± ξ ) p E p Polarization rotation angle (if radiation initially linearly polarized): α(t ) = (ω ω + )T = 2 ξ E p p 2 T α depends on energy must consider energy redshift ω(z) = (1 + z)ω(0) α(z) = 2 ξ E p p 2 0 H 0 z 0 (1+z ) Ωm(1+z ) 3 +Ω Λ dz [assuming Λ-CDM cosmological model] (after this it is also necessary to infer how power spectra are modified) GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

18 Analysis on recent experiments data Data from WMAP5 (94GHz) and Boomerang (145GHz) E. Komatsu et al. [WMAP Collaboration], arxiv:astro-ph/ C. J. MacTavish et al., arxiv:astro-ph/ previous estimates of rotation coming from combined datasets or from just one dataset J. Q. Xia, H. Li, G. B. Zhao and X. Zhang, Astrophys. J. 679 (2008) L61 α is energy-dependent, we cannot give a WMAP+BOOMERANG joint estimation on it, but a joint estimation is useful for ξ, wich does not depend on energy. Experiment α ± σ(α) ξ ± σ(ξ) WMAP (94 GHz) -1.6 ± ± 0.12 BOOMERanG (145 GHz) -5.2 ± ± WMAP+BOOMERanG ± Table: Mean values and 1σ error on α (in degrees) and ξ First limit on ξ in CMB reference frame GG, L. Pagano, G. Amelino-Camelia, A. Melchiorri, A. Cooray, arxiv: GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

19 Forecasts on future experiments Future experiments will be able to significantly improve limits on ξ, thanks also to multi-frequency data availability Experiment Channel σ(α) σ(ξ) PLANCK Spider EPIC CVL Table: Expected 1σ error for PLANCK 70, 100, 143, 217 GHz, Spider 145 GHz, EPIC 70, 100, 150, 220 GHz and two ideal CVL experiment at 150 GHz and 217 GHz on α (in degrees) and ξ. GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

20 Further developments - Anisotropic LIV CMB observations cover entire sky good laboratory to look for space anisotropies Test model: anisotropic generalization of Myers-Pospelov model L = 1 4 F µνf µν + 1 2E p n α F αδ n σ σ (n β ε βδγλ F γλ ) (never constrained before) GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

21 Further developments - How to proceed investigate phenomenological implications of the anisotropic model [First results: still a birefringence effect, but modulated in space, depending on the relative orientation of n α and propagation direction of photons] CMB power spectra exploit spatial isotropy need for new tools to analyze data [some very recent papers on how to extract informations on anisotropic effects]... GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

22 Extra Slides GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

23 Consequences on CMB Stokes parameters Modified Boltzmann equations [A. Kosowsky, A. Loeb, Astrophys. J. 469 (1996) 1] Q + ikµ Q = τ [ Q + 12 ] (1 P 2(µ))S P + 2 α U Integral solution U + ikµ U = τ U 2 α Q ( Q ± i U )(η 0 ) = η0 [τ(η) = R η 0 η dη τ(η ) and η 0 is the conformal time today] if α and η η 0 dη α(η ) are small 0 [ dη τ(η)e ikµ(η η0) τ(η) S p (η)e ±2i R ] η η dη α(η ) 0 Q (η 0 ) = Q (η 0 ) cos (2α) + U (η 0 ) sin (2α) U (η 0 ) = Q (η 0 ) sin (2α) + U (η 0 ) cos (2α) [we verified that the error is less than 1%] GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

24 Modification of cross-correlation power spectra Cl EE = C BB l = C EB l = 1 2 Cl TE = C TB l = EE C l EE C l C TE l C TE l cos 2 (2α) + sin 2 (2α) + ( CEE l C BB l cos (2α) sin (2α) C BB l C BB l ) sin (4α) sin 2 (2α) cos 2 (2α) GIULIA GUBITOSI CMBP AS TEST FOR FUNDAMENTAL PHYSICS ROMA 04/06/ / 22

Testing parity violation with the CMB

Testing parity violation with the CMB Paolo Natoli Università di Ferrara (thanks to Alessandro Gruppuso)! ISSS L Aquila 24 April 2014 Introduction The aim is to use observed properties of CMB pattern to