[Paper Review] The Power of Cosmic Flexion in Testing Modified Matter and Gravity

S. Camera, Antonaldo Diaferio|arXiv (Cornell University)|Apr 20, 2011

Astronomy and Astrophysical Research3 citations

TL;DR

This paper demonstrates that cosmic flexion—measuring second-order distortions in lensed galaxy images—provides a powerful, noise-resistant probe to distinguish between ΛCDM and alternative cosmological models, including unified dark matter, brane-world, and f(R) gravity theories. With Euclid-like survey parameters, flexion's signal-to-noise ratio exceeds that of cosmic shear, enabling clear discrimination at several standard deviations.

ABSTRACT

Flexion is the weak lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. The flexion signal-to-noise ratio can be an order of magnitude larger than that of shear. For the first time, we show how this makes flexion an invaluable tool for discriminating among alternative cosmological models. We analyse a scalar field model of unified dark matter and dark energy, a brane-world cosmology and two f(R) modified-action theories. We show that these models can be distinguished from LCDM at several standard deviations by measuring the power spectrum of cosmic flexion.

Motivation & Objective

• To investigate whether cosmic flexion can break degeneracies between ΛCDM and alternative cosmological models that are indistinguishable using cosmic shear.
• To assess the sensitivity of flexion power spectra to modified gravity and modified matter theories, including unified dark matter and f(R) gravity.
• To evaluate the feasibility of distinguishing these models with realistic noise levels expected from the Euclid space mission.
• To quantify the improvement in model discrimination offered by flexion over traditional weak lensing observables like shear.
• To establish that flexion's higher signal-to-noise ratio makes it uniquely suited for probing the nature of dark energy and gravity.

Proposed method

• The study computes the cosmic flexion power spectrum $ C^\mathcal{F}(\ell) $ using the spin-1 flexion field $ \mathcal{F} = \frac{1}{2} \partial \partial \partial^* \psi $, derived from the projected gravitational potential $ \psi $.
• The analysis uses linear and non-linear matter power spectra for ΛCDM, unified dark matter (UDM), eDGP brane-world, and two $ f(R) $ models (St, HS), all with matching background expansion to ΛCDM.
• Non-linear corrections are applied via the PPF (Peak-Pressure) and KW (Kaiser-Wilkinson) mappings for the eDGP and UDM models, respectively.
• The flexion power spectrum is computed with a noise power spectrum $ N^\mathcal{F}_\ell \propto \ell^{-2} \bar{n}^{-1} $, incorporating an intrinsic flexion rms of $ \langle \mathcal{F}_{\text{int}}^2 \rangle^{0.5} \approx 0.03 \, \text{arcsec}^{-1} $.
• Error bars are estimated using $ \Delta C^\mathcal{F}(\ell) = \sqrt{ \frac{2}{(2\ell+1)f_{\text{sky}}} \left[ C^\mathcal{F}(\ell) + N^\mathcal{F}_\ell \right] } $, adapted from shear formalism.
• The analysis assumes a Euclid-like survey with $ f_{\text{sky}} \approx 0.48 $, $ \bar{n} = 35 \, \text{arcmin}^{-2} $, and a redshift distribution $ n(z) \propto z^2 e^{-(z/z_0)^{1.5}} $ with $ z_0 = 0.9/1.4 $.

Experimental results

Research questions

• RQ1 Can cosmic flexion distinguish between ΛCDM and alternative cosmological models with similar background expansion?
• RQ2 How does the signal-to-noise ratio of flexion compare to that of cosmic shear in detecting deviations from ΛCDM?
• RQ3 To what extent do modified gravity models (e.g., f(R), eDGP) and modified matter models (e.g., UDM) produce distinct flexion power spectra?
• RQ4 How do non-linear mapping schemes (PPF, KW) affect the flexion power spectrum in non-ΛCDM models?
• RQ5 What level of statistical significance can be achieved in discriminating models using flexion in a Euclid-like survey?

Key findings

• The cosmic flexion power spectrum $ C^\mathcal{F}(\ell) $ shows clear, distinct features in the $ f(R) $ models (St and HS), with scale-dependent Newtonian gravitational constant $ G $ reaching $ \sim 4G/3 $ in the scalar-tensor regime.
• The unified dark matter (UDM) model exhibits a significant suppression of flexion power at small angular scales due to the scalar field's sound speed, which suppresses power on scales below the Jeans scale.
• The eDGP model remains very close to ΛCDM in the flexion power spectrum, especially with the PPF non-linear mapping, as it is designed to recover general relativity on small scales.
• Despite similar shear signals, the flexion power spectra of the alternative models are separated by several standard deviations from ΛCDM and from each other, indicating strong discriminative power.
• The signal-to-noise ratio of flexion is an order of magnitude higher than that of shear, enabling model discrimination at higher significance levels even with realistic intrinsic flexion noise.
• With Euclid-like survey parameters, the flexion power spectrum achieves a 1σ separation between models that are nearly degenerate in cosmic shear, demonstrating its unique potential for testing gravity and matter modifications.