Challenges for Dark Energy Models in Explaining a High Growth Index of Matter Perturbations

Core Concepts

Dark Energy models, even with complex parametrizations like the Chevallier-Polarski-Linder (CPL) model and considering both smooth and clustering Dark Energy scenarios, struggle to explain the high growth index of matter perturbations recently measured by some studies.

Abstract

This research paper investigates whether Dark Energy (DE) models can explain the high growth index (γ) of matter perturbations recently measured by Nguyen et al. (2023), which contradicts the standard ΛCDM cosmology prediction. The authors analyze both Smooth DE (SDE) and Clustering DE (CDE) scenarios, utilizing the CPL parametrization for the DE equation of state (EoS).

To assess the impact of DE on γ, the authors use data from 32 Cosmic Chronometers and minimally constrain the background evolution of the universe. They solve the perturbation equations for SDE and CDE models, considering the extreme case of negligible sound speed for CDE.

The results show that both SDE and CDE models, even with the flexibility of the CPL parametrization, fail to produce a significant number of γ samples compatible with the high value measured by Nguyen et al. (2023). This suggests that explaining the observed high γ poses a challenge for DE models.

The authors provide a detailed analysis of the correlations between γ and the EoS parameters, highlighting the influence of phantom and non-phantom DE on the growth of matter perturbations. They also present new and more accurate fitting functions for γ as a function of the EoS parameter w1, applicable to both SDE and CDE models.

The paper concludes by emphasizing the potential implications of this "γ tension" for our understanding of the universe. If the high γ value is confirmed by future observations, it might point towards the need for modified gravity theories or non-standard Dark Matter models.

Stats

The ΛCDM cosmology predicts a growth index γ = 0.55.
Observational data has measured a much higher γ = 0.633+0.025−0.024, excluding the ΛCDM value within 3.7σ.
A higher γ value reduces the S8 tension from 3.2σ to 0.9σ.
The study used data from 32 Cosmic Chronometers.
The authors analyzed both Smooth DE (SDE) and Clustering DE (CDE) scenarios.
The study considered the Chevallier-Polarski-Linder (CPL) parametrization for the DE equation of state (EoS).

Quotes

"Therefore, explaining the measured value of γ is a challenge for DE models."
"Therefore, our main result is that both SDE and CDE models described by the CPL EoS parametrization have very small probabilities of providing a growth index compatible with close to γ = 0.633+0.025−0.024, found in Ref. [1]."
"If this ‘γ tension’ persists, we might be seeing an early evidence of modified gravity or non-standard DM."

Key Insights Distilled From

Can dark energy explain a high growth index?

by Ícar... at arxiv.org 11-05-2024

https://arxiv.org/pdf/2411.00963.pdf

Deeper Inquiries

How might future advancements in observational cosmology, particularly in measuring the growth of structure, further illuminate the discrepancies between theoretical predictions and observed values of the growth index?

Answer: Future advancements in observational cosmology hold the potential to revolutionize our understanding of the growth index and its implications for dark energy and modified gravity. Here's how:

Increased Precision and Redshift Reach of Galaxy Surveys: Next-generation galaxy surveys like the Dark Energy Spectroscopic Instrument (DESI), Euclid, and the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will map the large-scale structure of the universe with unprecedented precision and reach deeper into the universe's history. This will allow cosmologists to measure the growth of structure over a wider range of redshifts, providing more data points to constrain the growth index and its evolution.
Improved Measurements of Weak Gravitational Lensing: Weak gravitational lensing, the subtle distortion of distant galaxy images due to the gravitational pull of intervening matter, offers a powerful probe of the growth of structure. Future surveys will benefit from wider survey areas, higher image resolution, and advanced analysis techniques, leading to more precise measurements of lensing signals and tighter constraints on the growth index.
Combining Multiple Probes: Combining data from different cosmological probes, such as galaxy clustering, weak lensing, cosmic microwave background (CMB) anisotropies, and redshift-space distortions, offers a powerful way to break degeneracies between cosmological parameters and obtain more robust constraints on the growth index. Future analyses will increasingly rely on multi-probe approaches to maximize the information extracted from cosmological observations.
Exploring the Non-Linear Regime: While the study focused on linear perturbations, future surveys will probe the growth of structure on smaller scales where non-linear effects become significant. Developing accurate theoretical models for non-linear structure formation is crucial for interpreting these observations and understanding the full impact of dark energy and modified gravity on the growth index.
By leveraging these advancements, future observations will provide stringent tests of cosmological models and shed light on the nature of dark energy and the viability of modified gravity theories.

Could alternative Dark Energy models beyond the scope of this study, such as those involving interactions between Dark Energy and Dark Matter, potentially reconcile the observed high growth index with current cosmological constraints?

Answer: Yes, alternative Dark Energy models that go beyond the standard minimally coupled scalar fields with a constant sound speed, as explored in the study, could potentially reconcile the observed high growth index with current cosmological constraints. Here are some possibilities:

Interacting Dark Energy: Models where dark energy interacts with dark matter, either gravitationally or through a new force, can significantly alter the growth of structure. Depending on the nature and strength of the interaction, these models can either suppress or enhance the growth rate compared to the standard ΛCDM model. Finding an interaction that leads to a higher growth index without conflicting with other cosmological observations would be key.
Modified Gravity with Screening Mechanisms: Some modified gravity theories, such as certain scalar-tensor theories and f(R) gravity, exhibit screening mechanisms that can suppress deviations from General Relativity on small scales while still allowing for significant modifications on large scales. These screening mechanisms could potentially lead to a higher growth index on large scales while remaining consistent with local tests of gravity.
Early Dark Energy: Models with early dark energy, where a non-negligible fraction of dark energy exists even at early times, can impact the growth of structure during matter domination. The precise impact on the growth index depends on the specific model and evolution of the early dark energy component.
Clustering Dark Energy with Non-Constant Sound Speed: While the study considered the limiting case of clustering dark energy with zero sound speed, models with a time-varying or scale-dependent sound speed could lead to different effects on the growth index. Exploring these more complex scenarios might reveal viable models that can accommodate a higher growth index.
It's important to note that any successful alternative model must not only explain the observed high growth index but also remain consistent with the wealth of existing cosmological data from CMB, supernovae, and baryon acoustic oscillations.

If the "γ tension" indeed points towards modified gravity, what are the broader implications for our understanding of fundamental physics and the evolution of the universe on the largest scales?

Answer: If the "γ tension" persists and is definitively confirmed as a robust discrepancy from the predictions of standard cosmology with dark energy, it would have profound implications for our understanding of fundamental physics and the evolution of the universe:

Breakdown of General Relativity on Cosmological Scales: The most direct implication is that General Relativity, our current best theory of gravity, might not hold true on cosmological scales. This would be a revolutionary discovery, forcing us to rethink the fundamental laws governing the universe's evolution.
New Gravitational Physics: A discrepancy in the growth index could point towards the existence of new gravitational physics beyond General Relativity. This could involve new fundamental forces, extra spatial dimensions, or modifications to the geometry of spacetime.
Impact on the Cosmic Expansion History: Modified gravity theories can alter the expansion history of the universe, potentially affecting the interpretation of observations related to dark energy and the Hubble constant tension. Resolving the γ tension could provide crucial insights into the nature of the accelerated expansion and the properties of dark energy.
Implications for the Early Universe: Some modified gravity theories predict deviations from General Relativity in the strong gravity regime of the early universe. If confirmed, the γ tension could have implications for our understanding of inflation, the formation of large-scale structure, and the evolution of the very early universe.
Search for New Fundamental Particles: Some modified gravity theories are closely linked to particle physics, predicting the existence of new fundamental particles that mediate the modified gravitational force. Confirmation of modified gravity would motivate searches for these new particles in high-energy experiments and astrophysical observations.
In essence, confirming the "γ tension" as a signature of modified gravity would usher in a new era in cosmology and fundamental physics, requiring us to re-examine our understanding of gravity, the universe's evolution, and the fundamental constituents of the cosmos.