Probing alternative cosmologies through the inverse distance ladder (2002.01487v2)

Abstract: We study the implications of a combined analysis of cosmic standard candles and standard rulers on the viability of cosmological models beyond the cosmological concordance model. To this end, we employ well-established data in the form of the joint light-curve analysis supernova compilation, baryon acoustic oscillations, and cosmic microwave background data on the one hand, and a recently proposed set of quasars as objects of known brightness on the other hand. The advantage of including the latter is that they extend the local distance measures to redshifts which have previously been out of reach and we investigate how this allows one to test cosmologies beyond $\Lambda$CDM. While there exist various studies on parametric extensions of $\Lambda$CDM, we present here a comparative study of both parametric and fundamental extensions of the standard cosmology. In order to keep the scope of this manuscript contained, we focus on two particular modifications: One is the consistent theory of two interacting spin-2 objects, so-called bigravity, and the other conformal gravity, a theory of gravity that has no knowledge of fundamental length scales. The former of the two constitutes a veritable extension of General Relativity, given that it adds to the metric tensor of gravity a second dynamical tensor field. The resulting dynamics have been proposed as a self-accelerating cosmology. Conformal gravity on the other hand is a much more drastic change of the underlying gravitational theory. Its ignorance towards fundamental length scales offers a completely different approach to the origin of late time acceleration. In this sense, both models offer - in one way or another - an explanation for the dark energy problem. We perform a combined cosmological fit which provides strong constraints on these extensions. We also briefly comment on the implications of the long-standing $H_0$-tension.

• The paper evaluates alternative cosmological models like bigravity and conformal gravity using an inverse distance ladder approach combining SNe, quasars, BAO, and CMB data.
• The analysis found that neither bigravity nor conformal gravity models consistently outperformed or significantly improved fits compared to the standard ext{\ensuremath{\Lambda}}CDM model with current data.
• The study emphasizes the statistical penalty (BIC) alternative models face unless they provide substantially better data fits than the simpler ext{\ensuremath{\Lambda}}CDM model.

Evaluating Alternative Cosmologies via the Inverse Distance Ladder Approach

The paper by Lindner et al. offers a comprehensive examination of alternative cosmological models through the application of the inverse distance ladder methodology. This approach leverages the combination of cosmic standard candles—specifically supernovae and a recent set of quasars—and standard rulers like baryon acoustic oscillations (BAO) and cosmic microwave background (CMB) data. The primary goal is to evaluate the viability of cosmological models that extend beyond the standard cosmological concordance model, commonly referred to as $\Lambda$CDM (a flat universe model with cold dark matter and a static cosmological constant, $\Lambda$).

Comparative Analysis of Cosmological Models

The authors perform an in-depth comparative analysis of both parametric and fundamental extensions of the standard cosmological model. The discussion centers around two specific alternatives to $\Lambda$CDM: bigravity and conformal gravity. Bigravity introduces dynamics to its cosmological model via a second tensor field interacting with the metric tensor of gravity. This model attempts self-acceleration without a cosmological constant. In contrast, conformal gravity, which does not recognize any inherent length scale, provides a different mechanism for the late-time acceleration observed in the universe.

Methodological Approach

To evaluate these models, the paper utilizes a highly data-driven approach. It incorporates:

• Type Ia Supernovae (SNe) and Quasars: The supernovae data is well-established and provides constraints at relatively low redshifts. Meanwhile, quasars extend the distance ladder to higher redshifts, offering tests for cosmological models in a regime less accessible to supernovae alone.
• Baryon Acoustic Oscillations (BAO): Providing standard rulers, BAO measurements offer constraints on the universe's expansion history and can infer critical cosmological parameters.
• Cosmic Microwave Background (CMB): CMB data, especially through its acoustic peaks, provides a foundational benchmark for any cosmological model due to its precision regarding early universe conditions.

Combining these datasets allows the authors to constrain cosmological parameters effectively and to test the robustness of these models.

Results and Implications

The results of this paper indicate that neither bigravity nor conformal gravity can consistently outperform the $\Lambda$CDM model when subjected to cosmological fits using the data available. Specifically:

• Bigravity models showed compatibility with observational data; however, they did not significantly improve the fit compared to $\Lambda$CDM. The need for multiple parameters perhaps dilutes its predictive power relative to the simplest $\Lambda$CDM model.
• Conformal Gravity, while having a unique position by omitting a fundamental length scale, struggles with tensions when confronted with both local (galactic rotation curves without dark matter) and cosmological data. The incompatibility between galaxy rotation curve data and cosmological fits presents a significant challenge for conformal gravity.

The analysis further reveals that alternative cosmological models that introduce more parameters are penalized statistically (per the Bayes Information Criterion, BIC) unless they provide significantly improved fits to the data. As such, the simplicity and established performance of $\Lambda$CDM mean that it remains the preferred model given current observational constraints.

Future Directions

While this paper does not find evidence to support a clear superiority of bigravity or conformal gravity over $\Lambda$CDM, it highlights the ongoing importance of exploring alternative cosmologies. Future advancements, particularly with more precise datasets like those anticipated from upcoming missions (e.g., Euclid and LSST), may provide further insights. Additionally, resolving the $H_0$ tension—currently a significant discrepancy between local and global measurements of the Hubble constant—remains a critical frontier where alternative cosmologies could provide broader understanding or resolution.

In conclusion, the work by Lindner et al. exemplifies the intricate balancing act in modern cosmology between model complexity and empirical adequacy, urging continued exploration of theoretical models alongside precise observational efforts to enhance our understanding of the universe's foundational principles.