Novel geometrical test of cosmological expansion from photometric data

The gist: This research proposes a novel geometrical test for cosmological expansion using tomographic cosmic-shear observations, specifically leveraging the Bernardeau-Nishimichi-Taruya (BNT) transform to build weak lensing maps independent of low redshift lenses to constrain dark energy parameters.

Tomographic Analysis and the BNT Transform

Tomographic analyses allow researchers to differentiate redshifts and epochs of expansion of the Universe, typically strengthening constraints on cosmological parameters. In this construction, for a given bin of source redshifts, the cosmic-shear map results from the superposition of matter density fluctuations along the line of sight. The BNT transform is a technique to build linear combinations of cosmic shear maps that are only sensitive to lenses from a restricted redshift range. This property allows us to sort out the physical scales that contribute to the lensing signals at a given angular scale on the sky and are otherwise mixed by projection effects along the line of sight.

Implementation in Euclid-like Experiments

The study illustrates a possible implementation of nulling and its performances in the context of an Euclid-like experiment using the setting described in [18] and [19]. The BNT transform is given as a matrix pai that transforms lensing kernels as ˆwa = paiwi and convergence maps as ˆκa = paiκi (we used implicit summation on repeated indices). The transformation is built from the two following quantities or moments n(0)i=Z dχ ni(χ) and n(1)i=Z dχ FK(χ), (5). It is clear that this transformation is independent from both scale and the regime of gravitational instabilities, as it only depends on the redshift distribution of the sources and the angular distance-redshift relation.

Constraining Cosmological Parameters

The constraints one can obtain on cosmological parameters from such a nulling probe rely therefore entirely on how the coefficients pai vary when the angular distance-redshift relation is changed. In particular they are independent of both σ8, the amplitude of the matter fluctuation, and H0, two cosmological parameters that are affected by tensions between different measurements. The analysis shows that nulling alone has a weak constraining power. However, it allows us to derive cosmological constraints on the background evolution at scales that are beyond reach of standard 3x2pt analysis, that is to say deeply into the nonlinear regime.

Performance and Future Prospects

The performance of the nulling probe relies ultimately on the significance with which one can assert that nulled convergence maps on one side and low redshift LSS probes on the other, are statistically independent. The study shows that adding Planck’s constraints on omegam improves the FoM by more than a factor 10. The constraining power of this approach is not yet limited by cosmic variance. Improving the number of source galaxies, i.e., reducing the shape noise, leads to a significant boost in the FoM. This opens up possibilities for future dedicated surveys to constrain dark energy equation of state with a pure geometrical test. The constraints on key cosmological parameters are likely to be intricately linked with those describing nonlinear structure growth.

Statistical Framework

The null test is built by studying the cross spectra C˜κˆgai(l) between nulled observed convergence maps ˜κˆa(n) and binned low redshift galaxy density fields δ˜g i(n)<ref:2502.

1. Bold header: Precision constraint on dark energy equation of state

This approach allows for robust null tests that achieves a complete separation between background evolution and structure growth modeling, enabling weak lensing surveys to constrain the dark energy equation of state with a pure geometrical test.

2. Bold header: Enhanced sensitivity at small physical scales

The BNT transform is useful because it only depends on the redshift distribution of the sources and the angular distance-redshift relation, providing a way to probe expansion rate even at small scales where simulations and modelling usually depend on unknown or unresolved small-scale effects.

3. Bold header: Quantification of nulling bias correction

The system can incorporate a nuisance parameter, such as Q3, by accounting for the nulling bias correction, which is proportional to the Bispectrum, allowing for a more accurate likelihood calculation: Taking this bias into account, we now have ⟨C˜κˆgai (l)⟩ = Q3 × δBC˜κˆgai (l).

Aim. In tomographic cosmic-shear observations, the Bernardeau, Nishimichi, Taruya (BNT) transform allows us to build weak lensing transformed maps for which the contribution from low-redshift lenses is nulled. As this transformation depends specifically on the expansion rate of the Universe and is independent of the matter distribution properties, it can be leveraged to extract information from large-scale structure probes at arbitrary non-linear scales. Thus, it provides constraints on cosmological background evolution. Methods. We demonstrate the applicability of the BNT transform as a probe by designing a null test and evaluating its performance for Stage IV weak lensing projects. Results. Using a Fisher matrix analysis combined with parameter sampling, we show that this approach can significantly enhance constraints on the dark energy equation of state. In such surveys, apart from photometric redshifts uncertainties, performance is expected to be limited primarily by shape noise, rather than cosmic variance, making substantial improvements possible thanks to better designed surveys in the future.