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Equivalence Principles Pseudoscalar-Photon Interaction
and Cosmic Polarization Rotation
Wei-Tou Ni
National Tsing Hua U., Hsinchu, Taiwan, ROC
Ref.: [1] W.-T. Ni, PLA 378 (2014) 1217-1223; RoPP 73 (2010) 056901 [2] W.-T. Ni, Dilaton field and cosmic wave propagation, PLA 378 (2014) 3413

[3] S. di Serego Alighieri, W.-T. Ni and W.-P. Pan, Astrophys. J. 792, 35 (2014).
[4] W.-T. Ni, Spacetime structure ..., PLA 379(2015)12971303 [5] H.-H. Mei, W.-T. Ni, W.-P. Pan, L. Xu, S. di SA, ApJ (2015); arXiv:1412.8569
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Issues

Cosmology is becoming a precision science. When was precision metrology becoming possible? What are the basic principles as foundations to study cosmology? How to test or what are the empirical foundation of these basic principles? What are the constraints? What are the soft spots?
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Cosmology is becoming a precision science.

When was precision metrology becoming possible?

We need light and atoms. We need to know how to measure precisely the frequency of light. We need to use precise energy levels of atoms as metrological standards. Observers should be available: "Anthropological" principle
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Let there be light!

Light abundant at 100 ps (100 Gev): gamma rays

produced

CMB

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Atoms formed ......

First 3 minute: light nuclei formed 380,000 yr: atom formed, last scattering of CMB Stellar nuclear synthesis, more nuclei and atoms formed Living organisms and observers evolved Science and technology developed; precision metrology development; modern observations to discover and trace cosmological evolution through physical laws
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Study the laws of light, the laws of atoms to trace back the cosmology

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Light, WEP I, WEP II & EEP

Light is abundant since 100ps (Electroweak phase trans.) or earlier after Big Bang Galileo EP (WEP I) for photon: the light trajectory is dependent only on the initial direction no splitting & no retardation/no advancement, independent of polarization and frequency 1638 Galileo "... I say that, if the resistance of the medium were completely removed, all matter would fall with equal speed." WEP II, no polarization rotation EEP, no amplification/no attenuation, no spectral distortion
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Galileo's experiment on inclined planes (1592)

Galileo's Equivalence Principle T he t r a je c t o r ie s o f t e s t bo d i e s u n d e r g r a v i ty a r e t h e s am e , i nd e p e n de n t o f t h e i r c o m p os i t i o ns . The motion with constant force has constant acceleration.

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Experiment on inclined plane, moment of inertia and law of Motion (1997)

a = g sin

(in the absence of

friction and other f

orces)

2 laws: EP & f=ma with moment of inertia: asolid ball = (5/7)g sin ; ahollow ball = (3/5)g sin
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2014.12.09 Arcetri Observatory

Experiment on Inclined Plane

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EP: EM to Spacetime Structure

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Light and Electrodynamics

Light velocity measured (Roemer) Light polarization discovered, birefringence in materials discovered (200 yrs ago) Classical (Maxwell-Lorentz) electrodynamics (EM) Constant of light velocity discovered (1887) Special and General relativity completed (2005/15) Premetric formulation of EM in spacetime (vacuum) Derivation of spacetime metric from premetric local linear electrodynamics using phenomenological approach
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Premetric formulation of electromagnetism
In the historical development, special relativity arose from the invariance of Maxwell equations under Lorentz transformation. In 1908, Minkowski [1] further put it into 4-dimensional geometric form with a metric invariant under Lorentz transformation. The use of metric as dynamical gravitational potential [2] and the employment of Einstein Equivalence Principle for coupling gravity to matter [3] are two important cornerstones to build general relativity In putting Maxwell equations into a form compatible with general relativity, Einstein noticed that the equations can be formulated in a form independent of the metric gravitational potential in 1916 [5,6]. Weyl [7], Murnaghan [8], Kottler [9] and Cartan [10] & SchrЖdinger further developed and clarified this resourceful approach.

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Metric-Free and Connection-Free
Maxwell equations for macroscopic/spacetime electrodynamics in terms of independently measurable field strength Fkl (E, B) and excitation (density with weight +1) Hij (D, H) do not need metric as primitive concept (See, e. g., Hehl and Obukhov [11]): Hij,j = - 4 Ji, eijklFjk,l = 0, (1) with Jk the charge 4-current density and eijkl the completely antisymmetric tensor density of weight +1 with e0123 = 1. We use units with the light velocity c equal to 1. To complete this set of equations, a constitutive relation is needed between the excitation and the field: Hij = ijkl Fkl. (2)

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Since both Hij and Fkl are antisymmetric, ijkl must be antisymmetric in i and j, and k and l. Hence ijkl has 36 independent components.

Constitutive relation : Hij = ijkl Fkl.

Principal part: 20 degrees of freedom Axion part: 1 degree of freedom (Ni 1973,1974,1977; Hehl et al. 2008 Cr2O3) Skewon part: 15 degrees of freedom (Hehl-Ohbukhov-Rubilar skewon 2002)

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Galileo EP Electromagnetism Charged particles and photons
Ni (1973-1977)
Special Relativity
1 ikjl jl dsI k 1/ 2 LI ( ) Fij Fkl Ak j ( g ) I mI ( x xI ) 16 dt g framework 1 dsI ijkl k 1/ 2 LI ( ) Fij Fkl Ak j ( g ) I mI ( x xI ) 16 dt
i jkl

Galileo EP constrains to 1974 Ni i jkl 1 / 2 1 ik jl 1 il kj ( g ) [ g g g g 2 2
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]
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(Pseudo)scalar-Photon Interaction

Related formulations in the photon sector: SME (Mews & Kostelecky 1998, 2004, ...) & SMS (Bo-Qiang Ma 2012-2015)

The photon sector of the SME Lagrangian is given by Lphotontotal = - (1/4) F F - (1/4) (kF)F F + (1/2) (kAF)AF (equation (31) of [7]). The CPT-even part (-(1/4) (kF)F F) has constant components (kF) which correspond one-to-one to our 's when specialized to constant values minus the special relativistic with the constant axion piece dropped, i.e. (kF) = (1/2) ( - ). The CPT-odd part (kAF) also has constant components which correspond to the derivatives of axion , when specilized to constant values. 2004..., extensions with higher order terms in momentum. SMS in the photon sector due to Bo-Qiang Ma is different (but intersects with) from both SME and -framework.
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Comments

In cosmology with spacetime as arena, it is much easier to work with a spacetime phenomenological framework. In local physics, a momentum formulation might be good for highenergy phenomena.
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(Why Minkowski Metric? from gravity/spacetime point of view)

The ISSUE

How to derive spacetime structrure/the lightcone from classical, local and linear electrodynamics (i) the closure condition (ii) The Galileo weak equivalence principle (iii) The non-birefringence (vanishing double refraction) and "no amplification/dissipation" condition of astrophysical/cosmological electromagnetic wave propagation from observations
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Skewonless case: EM wave propagation

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Dispersion relation and Nonbirefringence condition

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Three approaches to Axions/Pseudoscalar-photon interactions

Top down approach string theory Bottom up approach QCD axion Phenomenological approach -- gravitation

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: Pseudoscalar field or

pseudoscalar function of gravitational or relevant fields

, AF~ (1/2) FF
(Mod Divergence)

~

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Galileo EP Electromagnetism Charged particles and photons
Special Relativity
1 ikjl jl dsI k 1/ 2 LI ( ) Fij Fkl Ak j ( g ) I mI ( x xI ) 16 dt g framework 1 dsI ijkl k 1/ 2 LI ( ) Fij Fkl Ak j ( g ) I mI ( x xI ) 16 dt

Galileo EP constrains

to

i jkl

( g )

1/ 2

1 ik jl 1 il kj [ g g g g 2 2
Ni

i jkl

]
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(Pseudo)scalar-Photon Interaction

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The birefringence condition in Table I historical background

ijkl Ѕ (-h)1/2[hik hjl - hil hkj] + e

ijkl

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Empirical Nonbirefringence Constraint

to 10-38, i.e., less than 10-34 = O(Mw/Mplanck)2 a significant constraint on quantum gravity
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Empirical foundations of the closure relation for the skewonless case

Less than 100 operations

The (generalized) closure relation is satisfied

From table I, this is verified to 10в 10-38
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The Cosmic MW Background Spectrum: 2.7255 ± 0.0006 K
D. J. Fixsen, Astrophys. J. 707 (2009) 916
No amplification/ No attenuation (No dilaton)

No distortion (No Type I Skewon
Redshifted(Acceleration Equivalent)
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Present & Past

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A&A 2014

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Results

Constraint from CMB spectrum

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Dilaton and variation of constants

Fritzsch et al, variation of the fine structure constant (some astophysical observations) Shu Zhang & Bo-Qiang Ma, (Possible) Lorentz violation from gamma-ray bursts (10 Gev)
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The current combined evidence so far is consistent with a null CPR and upper limits are of the order of 1 degree with fluctuations and mean is constrained to about 1 degree.

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BB power spectrum from SPTpol, ACTpol, BICEP2/Keck, and POLARBEAR. The solid gray line shows the expected lensed BB spectrum from the Planck+lensing+WP+highL best-fit model. The dotted line shows the nominal 150 GHz BB power spectrum of Galactic dust emission derived from an analysis of polarized dust emission in the BICEP2/Keck field using Planck data. The dash-dotted line shows the sum of the lensed BB power and dust BB power.

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Emode:1502.01589(fig.3)(PLANCK) Data Lensing-B:1502.01591v1(fig.4)(PLANCK) Gravity-Bmode:1403.3985v2(fig.14)(BICEP2) SPT:1503.02315v1; POLARBEAR:1403.2369v1 ACTPol:1405.5524v2; dust:1409.5738(fig.9)(PLANCK)

Collaborators:

Baccigalupi, Pan, Xia, Xu, Ni Di Serego Alighieri,

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r - 0.050.1 100500 mrad2 Fluctuation amplitude bound: 17 mrad (1 degree)
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for EP experiments with polarized bodies & Spin-Spin Experiments, see following

References

W.-T. Ni, Equivalence principles, spacetime structure and the cosmic connection, to be published as Chapter 5 in the book:
One Hundred Years of General Relativity: from Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, edited by Wei-Tou Ni (World Scientific, Singapore, 2015).

W-T Ni, Rep. Prog. Phys. 73 (2010) 056901. W.-T. Ni, Spacetime structure and asymmetric metric from the premetric formulation of electromagnetism, PLA 379(2015)12971303 and references therein together with references in the 5 articles of the title page

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Summary

Pseudoscalar-photon (axion) interactions arisen from the study of EP, QCD, string theory and pre-metric EM CPR is a way to probe pseudoscalar-photon interaction and a possible way to probe inflation dynamics, New CPR constraints from B-mode are summarized Good calibration is a must for measuring CPR CPR is a means to test EEP or to find new physics From the empirical route to construct spacetime structure, axion, dilaton and type II skewon are possibilities which could be explored further
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Thank you

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