Gaining confidence on General Relativitywith Cosmic Polarization Rotation

Sperello di Serego AlighieriOsservatorio Astrofisico di Arcetri

Internat. J. Mod. Phys. D 24, 1530016 (2015)

LeCosPA Symposium, Taipei, 15 December 2015

Why are searches for CPR important?

Photons carry almost all the information which we have about the Universe outside the Solar System (a few cosmic rays and several elusive neutrinos are the only exceptions).

The information carried by a photon consists of:1.The direction (RA and Dec)2.The energy or wavelength3.The position angle (PA) of the polarization ellipse.

To make a proper use of this information, it is important to know whether it is changed while the photon travels in vacuum across the Universe towards us. The direction can be changed by a strong gravitational field. The wavelength is changed by the expansion of the Universe. CPR deals with eventual changes in PA, and none has been measured yet. So the polarization PA appears to be the most constant characteristic of photons. They are able to carry across the Universe the information about the orientation of a plane.Clearly changes in PA would violate symmetry, since they should be either positive (counter clockwise, IAU convention) or negative (clockwise). This suggests that CPR is connected with the violation of fundamental physical principles.Indeed CPR is connected with Lorentz invariance violation, CPT violation, neutrino number asymmetry, and violation of the Einstein Equivalence Principle (EEP).For a review about the physical principles connected with CPR see Ni (2010) and his talk. We advise to use the term CPR, not birefringence (rotation, no splitting).

CPR and EEPThe equivalence principle equates a gravitational field and a uniformly accelerated frame (inertial mass = gravitational mass). It has been stated in various forms:1. The weak equivalence principle (WEP, or Galilean EP) states the equivalence as far as the motion of free falling bodies is concerned.

The WEP is tested to an accuracy of ~10-13 by Eötvös type (torsion balance) experiments, and future space missions (STEP) would test it to 10-17.

However Ni (1977) has found a unique counterexample to Schiff’s conjecture: a pseudoscalar field φ that couples to electromagnetism in a Lagrangian of the form: L=-1/(16π) φ eμνρσ Fμν Fρσ

leading to a violation of the EEP, while obeying the WEP.Ni (1973) and Carroll & Field (1991) have shown that, if such coupling were significant in a cosmological context, then the plane of polarization of light coming from very distant objects would be rotated during its journey across the Universe, i.e. CPR angle α ≠ 0. If we could show that such a rotation is not observed (α = 0), we would conclude that the EEP is not violated in this unique fashion.

2. The EEP extends the equivalence to all experiments involving non-gravitational forces; all metric theories of gravity, including General Relativity, are based on the EEP.The EEP is tested to an accuracy of only ~10-4 by gravitational redshift experiments.In 1960 Schiff has conjectured that any complete, self-consistent theory of gravity, which obeys the WEP, would necessarily obey also the EEP. If this were true, then the EEP would also be tested to 10-13.

How to test for CPRTesting for CPR is simple in principle: it requires a distant source of linearly polarized radiation, for which the orientation PAem of the polarization at the emission can be established. Then CPR is tested by comparing the observed orientation PAobs with PAem:α = PAobs − PAem.In practice, it is not easy to know a priori the orientation of the polarization for a distant source: in this respect the fact that scattered radiation is polarized perpendicularly to the plane containing the incident and scattered rays has been of great help, applied both to radio galaxies (RGs) and to the cosmic microwave background (CMB) radiation. For those cases in which CPR depends on wavelength, one can also test for CPR by simply searching for variation of PA with wavelength, even without knowing PAem.

I will summarize the results on CPR obtained with the astrophysical methods which have been used to test it, discuss some of the problems of the various methods and suggest future prospects for these tests.

CPR test with the radio polarization of distant RGCarroll, Field & Jackiw (1990) have looked at the difference between the PA (χ) of the radio polarization, corrected for Faraday rotation (θ(λ) = αλ2 + χ), and the PA (ψ) of the radio axis of RG with 0.4<z<2 and P>5% and find a peak in the distribution at 90° (and a smaller one at 0°). From the width of the distribution they conclude that any rotation of the polarization must be smaller than 6.0° at the 95% confidence level.

Claimed discovery of CPRNodland & Ralston (1997), re-examining the data on the radio polarization of RG used by Carroll, Field & Jackiw (1990), claimed to have found a systematic rotation of the plane of polarization as large as 3 rad., independent of the Faraday one, and correlated with the angular position and with the distance of the RG.However several authors (Wardle et al. 1997, Eisenstein & Bunn 1997, Carroll & Field 1997, Laredo et al. 1997) have independently and convincingly argued against this claim. In particular Wardle et al. (1997) have shown that the misalignment for a sample of 29 quasars is consistent with zero and incompatible with the rotation claimed by Nodland and Ralston (1997).

χ: radio polarization angle, corrected for Faraday rotationΨ: radio axis orientationr: distance to the QSOγ: angle between the direction of the quasar and the direction of the pole claimed by Nodland & Ralston (1997)

Improvement on the radio CPR test on RGIn addition Leahy (1997) suggested an important improvement to the radio CPR test: since the radio emission is due to synchrotron, its Faraday-corrected polarization is perpendicular to the projected magnetic field, which in turn is perpendicular to strong gradients in the radio intensity direction, as can be checked on high angular resolution radio data.

The southern lobe of 3C 47 and the close alignment of the polarization with intensity gradients

CPR test with the optical/UV polarization of distant RGCimatti, di Serego Alighieri, Field & Fosbury (1994) have used the perpendicularity between the optical/UV axis and the direction of the plane of optical/UV polarization to show that this plane is not rotated by more than 10° for every distant RG with z>0.5 and with a polarization measurement, up to z=2.63. This perpendicularity is strictly expected, since the elongation and the polarization are due to scattering of anisotropic nuclear radiation. The advantages of the optical/UV test over the radio one are:1. It does not require correction for Faraday rotation.2. It is based on a strict physical predition of the polarization orientation due to scattering.3. It holds for every single distant RG, not just statistically.

Image Polarimetry of 3C 265 by Cohen et al. 1996V band, at z=0.811 λ~3000Å (α ≤ 4° at 3σ)

Scattering of anisotropic optical/UV nuclear radiation in powerful radio galaxies

An update on the CPR test with the UV polarization of distant RGSince our first test based on the optical/UV polarization of distant RG in 1994, several new polarization data have become available. Therefore we have made an update of the test (di Serego Alighieri, Finelli & Galaverni 2010, ApJ 715, 33).We have taken all the RG with z>2, P>5% in the UV (λ~1300Å), and elongated UV morphology, and measured the difference between the PA of the linear UV polarization and the PA of the UV axis.

An update on the CPR test with the UV polarization of distant RGAssuming that the rotation of the polarization plane should be the same in every direction, we can set the average constraint on the rotation at <z>=2.8:

α = -0°.8 ± 2°.2

Further developments of the CPR test with the UV pol. of RG

Kamionkowski (2010) has used the data of di Serego Alighieri et al. (2010) to set limits on CPR in the case that the rotation of the plane of polarization depends on the direction in the sky α(RA, Dec). In this case the constraint on the variance of the CPR is

<α2>½ ≤ 3.7°

This non-uniform rotation is foreseen by some quintessence models (e.g. Li & Zhang 2010) and by some dark-matter models (Gardner 2008).

Also, Kostelecky & Mewes (2001, 2002) have developed a formalism in which CPT is conserved, but Lorentz invariance is violated, and CPR effects grow with photon energy. In this case our test based on UV photon is more suitable than those at longer wavelengths.

CPR test based on the CMB

WMAP7 data (Komatsu et al. 2010) on CMB temperature and polarization.Top panel: model for a temperature hot spot.Bottom panel: coadded WMAP7 data for temperature hot spots.There is a correlation between temperature gradients and polarization.

Temperature and polarization of the CMB

TemperaturePolarization

E-mode pol.E-mode pol.

B-mode pol.B-mode pol.

A summary of CPR tests with different methods

di Serego Alighieri: Internat. J. Mod. Phys. D 24, 1530016 (2015)

All results are consistent with a null CPR. All CPR test methods have reached so far an accuracy of the order of 1° and 3σ upper limits to any rotation of a few degrees.

A summary of CPR tests with different methodsdi Serego Alighieri 2015 (IJMPD 24, 1530016)

RG radio, Carroll et al. 1990

RG UV, Cimatti et al. 1994

RG UV, Wardle et al. 1997

RG radio, Carroll 1998

CMB BOOMERanG, Pagano et al. 2009

CMB QUAD, Brown et al. 2009

RG UV, di Serego Alighieri et al. 2010

CMB WMAP9, Hinshaw et al. 2013

CMB BICEP1, Kaufman et al. 2014

CMB ACTPol, Mei et al. 2015

Problems in testing the CPR with the CMB1. CMB Polarization PA calibration problem

One problem is the calibration of the polarization PA for the lack of sources with precisely known PA at CMB frequencies. This introduces a systematic error, which is similar (if not bigger) than the statistical measurement error, of the order of 1°. Recently the polarization PA of the Crab Nebula (α Tau) has been measured with an accuracy of 0.2° at 89.2 GHz (Aumont et al. 2010). However most CMB polarization measurements are made at higher frequencies (100 – 150 GHz) and the Crab is not visible from the South Pole. In order to overcome this problem, some CMB polarization experiments have used a TB and EB nulling procedure (Keating et al. 2013). However this procedure would also eliminate any CPR angle α, so it cannot be used for CPR tests.

A rotation of linear polarization produces a couplingbetween T, E-mode and B-mode polarization of CMB

Problems in testing the CPR with the CMB2. CMB Polarization PA convention problem

A second problem is that unfortunately the CMB polarimetrists have adopted the convention that the polarization PA increases clockwise (looking at the source), which is opposite to the standard convention adopted by all other polarimetrists for centuries and enforced by the IAU (PA increses counter-clockwise). This is obvioulsy producing problems when comparing measurements with different methods, like for CPR tests, also because the “CMB convention” has not been well documented in the CMB polarization papers.

Two opposite conventions for the polarization PA1. IAU convention: looking at the source, the polarization PA increases counter-clockwise.

2. “CMB” convention: looking at the source, the polarization PA increases clockwise.

IAU coordinates “CMB” coordinates

North

East East

South

A summary of CPR tests with different methodsarXiv:1409.xxxxv1)

A summary of CPR tests with different methodsarXiv:1409.xxxxv2

The IAU convention for the polarization PAdefined by Commission 40 at the IAU General Assembly in Sidney in 1973

and coded in the IAU Transactions, Vol. XVB, p. 166

The origin of the “CMB” convention for the polarization PA

But a map making software in the IAU convention exists…

A new test of CPR using B-mode polarization of CMB

⟨δα2 ≤ (1.56⟩ °)2 Mei et al. (2015) ApJ 805, 107

Other methods for testing for CPR 1. Tests in X-rays could be useful, even on nearby sources, if CPR effects increase

with frequency and if made with high accuracy. Hard X-ray polarization observations of the Crab Nebula have been used to set a limit to CPR angle α = −1° ± 11° (Maccione et al. 2008).

2. GRB can be used to test for birefringence, i.e. an energy-dependent rotation of the polarization angle, such as that produced by Lorentz invariance violation, since the detection of linear polarization in a gamma-ray band excludes a significant rotation of the polarization within that energy band. In this way Gubitosi et al. (2009) were able to put an upper limit to the dimensionless parameter of this birefringence effect of ξ < 1 × 10−16 from the gamma-ray polarization of a GRB at z = 2.74.

3. The rotation of the plane of linear polarization can be seen as different propaga- tion speeds for right and left circularly polarized photons (∆c/c). The sharpness of the pulses of pulsars in all Stokes parameters can be used to set limits correspond- ing to ∆c/c ≤ 10−17. Similarly the very short duration of GRB gives limits of the order of ∆c/c ≤ 10−21. However the lack of linear polarization rotation discussed in the previous slides can be used to set much tighter limits (∆c/c ≤ 10−32)(Goldhaber & Trimble 1997).

Summary and outlook1.All results are consistent with a null CPR. All CPR test methods have reached so far an accuracy of the order of 1° and 3σ upper limits to any rotation of a few degrees. This excludes violations of the EEP and improves our confidence on GR.

2. They are complementary in many ways. They cover different wavelength ranges and the methods at shorter wavelength have an advantage, if CPR effects grow with photon energy. They also reach different distances, and the CMB method reaches furthest.

3. Improvements can be expected by better targeted high resolution radio polarization measurements of RGs and quasars, by more accurate UV polarization measurements of RGs with the coming generation of giant optical telescopes, and by future CMB polarimeters such as Planck and BICEP3. Indeed the Planck satellite is expected to have a very low statistical error ( 0.03°, Gruppuso et al. 2015) for CPR ∼measurements. Unfortunately, although Planck has completed its observations more than a year ago, its final results on CPR have not yet been released. Planck will have to reduce accordingly also the systematic error in the calibration of the polarization angle, which at the moment is of the order of 1◦ for CMB polarization experiments. The best prospects to achieve this improvement are likely to be more precise measurements of the polarization angle of celestial sources at CMB frequencies with the ATCA and ALMA and a calibration source on a satellite (CalSat, Kaufman et al. 2014).

Talks slides on www.arcetri.astro.it/cprSelected presentations will soon be published in IJMPD