⚛️ phenomenology

Tight bounds on the Maxwell-Carroll-Field-Jackiw parameters using Fast Radio Bursts

This paper utilizes arrival time delays and Faraday rotation measurements from Fast Radio Bursts propagating through chiral cosmic media within the Maxwell-Carroll-Field-Jackiw framework to establish stringent upper bounds on chiral parameters, reaching as low as $10^{-43}$ GeV.

Original authors: Filipe S. Ribeiro, Pedro D. S. Silva, Rodolfo Casana, Manoel M. Ferreira

Published 2026-03-02

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CC BY 4.0

Original authors: Filipe S. Ribeiro, Pedro D. S. Silva, Rodolfo Casana, Manoel M. Ferreira

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, cosmic ocean. For decades, astronomers have been sending out "sonar pings" using radio waves to map this ocean. Recently, they've discovered some very loud, very short bursts of radio noise coming from deep space, called Fast Radio Bursts (FRBs). These are like cosmic firecrackers that flash for a millisecond and then vanish.

This paper is about using those cosmic firecrackers to test the fundamental rules of physics, specifically to see if the universe has a hidden "twist" in its fabric.

Here is the breakdown of what the scientists did, using some everyday analogies:

1. The Setup: The Cosmic Highway

Imagine radio waves traveling from a distant galaxy to Earth as cars driving on a highway.

The Highway: The space between galaxies isn't empty; it's filled with a thin, invisible fog of charged particles (plasma).
The Traffic: Usually, all cars (radio waves) travel at the same speed limit (the speed of light). However, because of the fog, different types of cars might get slowed down slightly differently.
The Twist (The Mystery): The scientists are testing a theory called MCFJ electrodynamics. Think of this theory as suggesting that the highway itself might have a secret "handedness" or a spiral twist. If this twist exists, it would affect "left-handed" cars differently than "right-handed" cars, even if they are driving at the same speed.

2. The Two Clues: The Stopwatch and the Compass

To detect this secret twist, the scientists looked at two things happening to the radio waves as they traveled through the cosmic fog:

Clue A: The Stopwatch (Time Delay)

The Concept: When a radio wave hits the cosmic fog, it gets delayed. It's like a runner hitting a patch of mud; they slow down.
The Twist: If the universe has that secret "twist," the delay would be slightly different than what standard physics predicts.
The Result: The scientists looked at the arrival times of several FRBs. They found that the "twist" in the universe must be incredibly small—so small that if the universe were the size of the Earth, the twist would be smaller than a single atom. They set a limit on this twist at roughly $10^{-25}$ (a number with 25 zeros after the decimal point).

Clue B: The Compass (Faraday Rotation)

The Concept: As radio waves travel through magnetic fields in space, their polarization (the direction they spin) rotates, like a compass needle turning. This is called Faraday Rotation.
The Twist: If the universe has that secret "twist," it would cause the compass needle to spin extra or wrongly compared to what we expect.
The Result: This was the big winner. By measuring how much the radio waves spun, they found the "twist" is even tinier than the stopwatch test suggested. They pinned it down to $10^{-43}$ .
- Analogy: If the "twist" were a speck of dust, the stopwatch test said it was the size of a grain of sand. The compass test said it's actually the size of a subatomic particle.

3. Why This Matters: The "Super-Microscope"

Before this study, scientists used pulsars (spinning dead stars in our own galaxy) to look for this twist. It was like trying to see a tiny detail through a blurry window.

This paper used Fast Radio Bursts from other galaxies. Because these signals travel billions of light-years, they pass through way more cosmic fog than signals from our own galaxy.

The Analogy: If you want to find a tiny crack in a wall, looking at a wall in your house is hard. But if you look at a wall that has been walked on by billions of people over millions of years, even the tiniest crack becomes obvious.
The Improvement: The new limits they set are 10 million times better (a factor of $10^7$ ) than the old limits from pulsars.

4. The Bottom Line

The scientists didn't find the "twist." In fact, they proved that if it exists, it is so incredibly weak that it's almost non-existent.

What they did: They used cosmic firecrackers (FRBs) as a super-precise ruler.
What they found: The universe is extremely "straight" and follows the standard rules of physics very closely.
Why it's cool: Even though they didn't find the new physics they were looking for, they managed to rule out a huge range of possibilities. It's like saying, "We looked for a ghost in the mansion, and while we didn't find one, we proved that if a ghost is there, it must be invisible to the naked eye and smaller than a speck of dust."

This study pushes the boundaries of our knowledge, showing that our current understanding of how light and magnetism work is incredibly robust, even when tested across the vast distances of the cosmos.

1. Problem Statement

The paper addresses the search for Lorentz symmetry violation (LV) and CPT (Charge, Parity, Time) violation within the framework of the Standard Model Extension (SME). Specifically, it investigates the Maxwell-Carroll-Field-Jackiw (MCFJ) electrodynamics, a CPT-odd extension of Maxwell's equations characterized by a constant background 4-vector $(K_{AF})_\mu$ .

While previous studies (e.g., Ref. [16]) used pulsar timing data to constrain these parameters, the authors argue that Fast Radio Bursts (FRBs) offer a superior probe due to:

Their extragalactic origin, allowing for the accumulation of effects over cosmological distances.
The availability of precise Dispersion Measure (DM) and Rotation Measure (RM) data.
The necessity to incorporate cosmological redshift corrections, which were not fully accounted for in previous pulsar-based analyses of extragalactic signals.

The core problem is to derive modified expressions for signal propagation (time delay and Faraday rotation) in a chiral cosmic plasma described by MCFJ electrodynamics and to use FRB observational data to establish tighter bounds on the magnitude of the LV parameters ( $K^0_{AF}$ and $|\mathbf{K}_{AF}|$ ).

2. Methodology

Theoretical Framework

The authors model the interstellar and intergalactic media as a cold, ionized chiral plasma. They utilize the MCFJ Lagrangian density:
$\mathcal{L} = -\frac{1}{4}G_{\mu\nu}F^{\mu\nu} + \frac{1}{4}\epsilon^{\mu\nu\alpha\beta}(K_{AF})_\mu A_\nu F_{\alpha\beta}$
where $(K_{AF})_\mu$ is the Lorentz-violating vector.

They derive the refractive indices and group velocities for Right-Handed (RCP) and Left-Handed (LCP) circularly polarized waves, considering two configurations of the chiral vector relative to the magnetic field:

Timelike component ( $K^0_{AF}$ ).
Spacelike component ( $|\mathbf{K}_{AF}|$ ), split into parallel ( $K_{AF} \parallel B_0$ ) and orthogonal ( $K_{AF} \perp B_0$ ) configurations.

Derivation of Observables

The authors derive modified expressions for two key observables in the observer frame, incorporating redshift ( $z$ ) corrections:

Time Delay (Dispersion Measure):
The standard dispersion delay $\tau \propto \text{DM}/\omega^2$ is modified by an additional chiral term $\text{DM}_{CFJ}$ .
$\tau = \frac{e^2}{2m\omega^2} \left[ \text{DM}_{obs} + \text{DM}_{CFJ} \right]$
Crucially, the chiral contribution depends on the comoving distance ( $d_C$ ) and redshift:
$\text{DM}_{CFJ} \propto \frac{(K_{AF})^2}{1+z} d_C$
Faraday Rotation (Rotation Measure):
The rotation angle $\Delta\phi = \lambda^2 \text{RM}$ is modified to include a chiral term $\text{RM}_{CFJ}$ .
$\Delta\phi = \lambda^2 \left[ \text{RM}_{obs} - \text{RM}_{CFJ} \right]$
The chiral RM terms depend on $\lambda$ , $d_C$ , and redshift, differing significantly between timelike and spacelike configurations.

Data Analysis Strategy

The authors treat the chiral contributions ( $\text{DM}_{CFJ}$ and $\text{RM}_{CFJ}$ ) as small corrections bounded by the observational uncertainties ( $\epsilon_{DM}$ and $\epsilon_{RM}$ ) of the measured values.

Constraint Condition: $\text{DM}_{CFJ} \lesssim \epsilon_{DM}$ and $\text{RM}_{CFJ} \lesssim \epsilon_{RM}$ .
Datasets:
- Non-repeating FRBs: FRB 20190102, FRB 20190608, FRB 191108, FRB 20220610A.
- Repeating FRBs: FRB 121102, FRB 20180916B, FRB 20190303A.
Cosmology: Comoving distances ( $d_C$ ) were calculated using Planck 2018 cosmological parameters via the astropy.cosmology package.

3. Key Contributions

Redshift-Corrected MCFJ Formalism: The paper provides the first rigorous derivation of time delay and Faraday rotation formulas for MCFJ electrodynamics in an extragalactic context, explicitly replacing physical distance $d$ with redshift-dependent comoving distance $d_C/(1+z)$ .
Superior Constraints via RM: The study demonstrates that Faraday Rotation (RM) measurements provide constraints on LV parameters that are orders of magnitude tighter than those derived from Dispersion Measure (DM) alone.
Comprehensive Dataset Analysis: By analyzing both repeating and non-repeating FRBs, the authors maximize the statistical power and distance range (up to $z \approx 1.016$ ) of the constraints.

4. Results

The authors obtained the following upper bounds on the magnitude of the MCFJ parameters (in GeV):

A. Constraints from Dispersion Measure (DM)

Using the time delay data from non-repeating FRBs (e.g., FRB 20190102, FRB 20190608):

Timelike ( $K^0_{AF}$ ) and Parallel Spacelike ( $K^0_{AF} \parallel B$ ): Bounds in the range of $10^{-25}$ to $10^{-24}$ GeV.
Orthogonal Spacelike ( $K_{AF} \perp B$ ): Bounds in the range of $10^{-26}$ to $10^{-25}$ GeV.
Improvement: These results represent a two-order-of-magnitude improvement over previous constraints derived from pulsar DM data ( $10^{-23}$ GeV).

B. Constraints from Rotation Measure (RM)

Using Faraday rotation data from repeating and non-repeating FRBs:

Repeating FRBs (e.g., FRB 121102): Constraints reached $10^{-43}$ to $10^{-42}$ GeV.
Non-repeating FRBs (e.g., FRB 20190102, FRB 20220610A): Constraints reached $10^{-43}$ GeV.
Improvement: These results improve upon previous pulsar-based RM bounds ( $10^{-36}$ GeV) by a factor of $10^7$ .

C. Comparison with Other Limits

The derived bounds ( $10^{-43}$ GeV) are competitive with the tightest existing astrophysical limits:

CMB Polarization: $10^{-45}$ GeV (the current tightest limit).
Astrophysical Birefringence: $10^{-42}$ GeV.
Solar Wind / Resonant Cavities: $10^{-24}$ to $10^{-21}$ GeV (significantly weaker).

5. Significance

Validation of MCFJ Limits: The study confirms that FRBs are among the most powerful tools for testing Lorentz invariance in the photon sector, rivaling Cosmic Microwave Background (CMB) polarization studies.
Chiral Plasma Physics: It reinforces the hypothesis that the intergalactic medium can be effectively modeled as a chiral plasma, where even minute Lorentz-violating effects accumulate over gigaparsec distances to become observable.
Methodological Advancement: The explicit inclusion of redshift corrections in the MCFJ framework sets a new standard for analyzing extragalactic transient signals in the context of fundamental physics.
Future Prospects: As the sample size of FRBs with precise DM, RM, and redshift data grows (e.g., with the Square Kilometre Array), these bounds are expected to tighten further, potentially probing the Planck scale or ruling out specific CPT-odd extensions of the Standard Model.

In conclusion, the paper establishes that Faraday rotation measurements of Fast Radio Bursts provide the most stringent astrophysical constraints on CPT-odd Lorentz-violating parameters to date (excluding CMB), pushing the sensitivity to the $10^{-43}$ GeV scale.