[Paper Review] Constraining Fundamental Constant Variations from Ultralight Dark Matter with Pulsar Timing Arrays

David E. Kaplan, Andrea Mitridate+1 more|arXiv (Cornell University)|May 13, 2022

Dark Matter and Cosmic Phenomena94 references38 citations

TL;DR

This paper proposes that pulsar timing arrays (PTAs) can constrain variations in fundamental constants induced by ultralight dark matter (ULDM) through two novel signals: pulsar spin fluctuations due to time-varying neutron star moment of inertia and reference clock shifts from ULDM-induced changes in particle masses. Using mock PTA data, the authors show PTAs outperform atomic clocks and torsion balance experiments for ULDM couplings to electrons, muons, or gluons, and match atomic clock sensitivity for couplings to quarks or photons.

ABSTRACT

Pulsar Timing Arrays (PTAs) are exceptionally sensitive detectors in the frequency band $ ext{nHz} \lesssim f \lesssim \mu ext{Hz}$. Ultralight dark matter (ULDM), with mass in the range $10^{-23}\, ext{eV} \lesssim m_\phi \lesssim 10^{-20}\, ext{eV}$, is one class of DM models known to generate signals in this frequency window. While purely gravitational signatures of ULDM have been studied previously, in this work we consider two signals in PTAs which arise in presence of direct couplings between ULDM and ordinary matter. These couplings induce variations in fundamental constants, i.e., particle masses and couplings. These variations can alter the moment of inertia of pulsars, inducing pulsar spin fluctuations via conservation of angular momentum, or induce apparent timing residuals due to reference clock shifts. By using mock data mimicking current PTA datasets, we show that PTA experiments outperform torsion balance and atomic clock constraints for ULDM coupled to electrons, muons, or gluons. In the case of coupling to quarks or photons, we find that PTAs and atomic clocks set similar constraints. Additionally, we discuss how future PTAs can further improve these constraints, and detail the unique properties of these signals relative to the previously studied effects of ULDM on PTAs.

Motivation & Objective

• . To investigate new PTA signals from ultralight dark matter (ULDM) that arise due to time-varying fundamental constants.
• . To assess the sensitivity of current and future PTA experiments to ULDM-induced variations in particle masses and couplings.
• . To compare PTA constraints with existing bounds from atomic clocks and torsion balance experiments.
• . To quantify the improvement in sensitivity achievable with future PTA datasets relative to current limits.
• . To establish the uniqueness and detectability of these signals compared to previously studied ULDM effects in PTAs.

Proposed method

• . Model ULDM as a classical scalar field oscillating at frequencies f ≈ mφ/2π, with mφ ∈ [10−23, 10−20] eV.
• . Introduce direct couplings between ULDM and SM sectors via effective operators, parameterized by dimensionless coefficients d, leading to time-varying fundamental constants.
• . Derive two PTA-observable signals: (1) pulsar spin fluctuations via angular momentum conservation when moment of inertia changes, and (2) timing residuals from reference clock shifts due to varying particle masses.
• . Use mock data mimicking the IPTA Data Release 2 and a futuristic PTA dataset to simulate realistic timing residuals.
• . Perform Bayesian inference using the PTMCMCSampler and ENTERPRISE software to set upper limits on coupling coefficients d.
• . Compare resulting constraints with existing bounds from atomic clocks and torsion balance experiments.

Experimental results

Research questions

• RQ1 . Can pulsar timing arrays detect ULDM-induced variations in fundamental constants through pulsar spin fluctuations?
• RQ2 . Can reference clock shifts due to ULDM-induced changes in particle masses produce measurable timing residuals in PTAs?
• RQ3 . How do PTA constraints on ULDM couplings compare to those from atomic clocks and torsion balance experiments?
• RQ4 . What is the sensitivity of current and future PTA datasets to ULDM couplings to electrons, muons, quarks, photons, and gluons?
• RQ5 . How do these new signals differ from previously studied ULDM effects in PTAs, such as those from metric fluctuations or fifth forces?

Key findings

• . For ULDM couplings to electrons, muons, or gluons, PTA constraints are competitive with or stronger than current atomic clock and torsion balance limits.
• . For couplings to quarks or photons, PTA constraints are comparable to those from atomic clocks, indicating similar sensitivity.
• . The pulsar spin fluctuation signal arises from conservation of angular momentum when ULDM-induced mass variations alter the pulsar's moment of inertia.
• . The reference clock shift signal manifests as apparent timing residuals due to time-dependent changes in the fundamental constants governing atomic clocks.
• . Future PTA datasets are expected to improve constraints significantly, especially for couplings to light fermions and gauge bosons.
• . These signals are distinct from previously studied ULDM effects in PTAs, such as those from gravitational wave background or metric fluctuations, offering a new probe of ULDM couplings to matter.