Linear and Nonlinear Structure Formation in Horndeski-Inspired Dark Energy Models with Fast Transition

Core Concepts

This astrophysics research paper investigates the impact of fast-transitioning dark energy models, inspired by Horndeski theory, on the formation of cosmic structures, revealing that while recent transitions significantly influence structure growth, those occurring at redshifts zt ≥ 2 are indistinguishable from the ΛCDM model for freezing dark energy.

Abstract

• Bibliographic Information: Luongo, O., Pace, F., & Tomasi, S. (2024). Linear and nonlinear clusterings of Horndeski-inspired dark energy models with fast transition. arXiv preprint arXiv:2312.07318v2.
• Research Objective: This study aims to analyze the effects of fast-transitioning dark energy models on the formation of cosmic structures, both in the linear and nonlinear regimes.
• Methodology: The authors employ a generalized spherical collapse formalism that incorporates perturbations in fluids with pressure to model structure growth. They numerically solve the equations of motion for both the perturbations and the scalar field driving dark energy. Six different dark energy parameterizations, four of which belong to the fast transition class, are investigated.
• Key Findings: The research reveals that a true Heaviside step transition serves as a good approximation for most of the considered models. Transitions occurring at redshifts zt ≥ 2 become indistinguishable from the ΛCDM model if dark energy is freezing (approaching w = -1). For fast, recent transitions, the most significant impact on dark energy properties occurs at redshift z = 0.6 ± 0.2. Freezing models can lower σ8 values by approximately 8%, potentially alleviating the σ8 tension. These models also generally predict faster late-time merging rates but a lower number of massive galaxies at z = 0. The nonlinear matter power spectrum exhibits distinct features depending on the dark energy model.
• Main Conclusions: Fast-transitioning dark energy models can significantly impact structure formation, particularly for recent transitions. The study highlights the potential of these models to address the σ8 tension and makes predictions about galaxy merging rates and the matter power spectrum.
• Significance: This research contributes to the ongoing effort to understand the nature of dark energy and its role in the evolution of the Universe. The findings have implications for interpreting observational data related to large-scale structure and galaxy formation.
• Limitations and Future Research: The study focuses on a specific class of dark energy models inspired by Horndeski theory. Exploring other classes of models and comparing the predictions to observations from upcoming surveys like Euclid will be crucial for further validation and refinement of these models.

Stats

The redshift at which the properties of dark energy have the most significant effect is z = 0.6 ± 0.2.
In the freezing regime, the σ8 values can be lowered by about 8%.

Quotes

Key Insights Distilled From

Linear and nonlinear clusterings of Horndeski-inspired dark energy models with fast transition

by Orlando Luon... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2312.07318.pdf

Deeper Inquiries

How do the predictions of these fast-transitioning dark energy models compare to observational data from current and upcoming cosmological surveys?

Fast-transitioning dark energy models, as intriguing alternatives to the standard cosmological model, face the critical test of aligning with observational data from various cosmological probes. Here's a breakdown of how these models fare against current observations and the potential of upcoming surveys to offer more definitive answers:
Current Constraints:

Cosmic Microwave Background (CMB): CMB data, particularly from the Planck mission, provides stringent constraints on early-universe physics. While fast transitions primarily impact late-time cosmic evolution, they can leave subtle imprints on the CMB through the Integrated Sachs-Wolfe effect. Current CMB data generally favors simpler models like ΛCDM, but fast transitions with specific parameter choices (e.g., early transitions) remain compatible.
Baryon Acoustic Oscillations (BAO): BAO, as standard rulers in the cosmic web, offer a robust measure of the expansion history. Fast transitions can alter the BAO signal by modifying the late-time expansion rate. Current BAO measurements, while consistent with ΛCDM, do not definitively rule out fast transitions, especially if the transition redshift (zt) is relatively recent.
Supernovae Type Ia (SNe Ia): SNe Ia, as standardizable candles, provide direct measurements of the luminosity distance as a function of redshift. Fast transitions can influence the luminosity distance-redshift relation, potentially leaving a signature. However, the degeneracy among cosmological parameters and the limited redshift range of current SNe Ia data make it challenging to distinguish fast transitions from other dark energy models.
Upcoming Surveys and Their Potential:

Euclid: The Euclid mission, with its wide-field imaging and spectroscopy, will provide unprecedented measurements of weak lensing and galaxy clustering, probing the growth of structure and the expansion history with high precision. Euclid's sensitivity to the redshift evolution of these observables holds the potential to break parameter degeneracies and offer more conclusive tests of fast-transitioning dark energy.
Dark Energy Spectroscopic Instrument (DESI): DESI, focusing on mapping the large-scale structure through spectroscopic observations of millions of galaxies, will deliver precise BAO and redshift-space distortion measurements. These data will significantly improve constraints on the expansion history and the growth of structure, potentially revealing the signatures of fast transitions.
Vera C. Rubin Observatory (LSST): The LSST, with its wide-field survey capabilities, will observe billions of galaxies and provide a wealth of data on weak lensing, galaxy clustering, and SNe Ia. The combination of these probes, spanning a wide redshift range, will enable stringent tests of dark energy models, including those with fast transitions.
Challenges and Future Directions:

Parameter Degeneracies: A significant challenge lies in breaking the degeneracies among cosmological parameters, particularly when considering models with multiple free parameters like fast transitions. Combining data from different cosmological probes is crucial to alleviate this issue.
Systematics Control: As we aim for higher precision cosmology, controlling systematic uncertainties in observations and modeling becomes paramount. Careful calibration and analysis techniques are essential to extract robust constraints on dark energy models.
Theoretical Modeling: Refining theoretical predictions for fast-transitioning models, including their impact on structure formation and the nonlinear regime, is crucial for accurate comparisons with observational data.
In summary, while current cosmological data does not provide conclusive evidence for or against fast-transitioning dark energy models, upcoming surveys like Euclid, DESI, and LSST hold significant promise. Their enhanced sensitivity and wider redshift coverage have the potential to either uncover the signatures of fast transitions or place stringent constraints on their parameter space, ultimately advancing our understanding of the nature of dark energy.

Could alternative theories of gravity, such as modified gravity models, provide a different explanation for the observed cosmic acceleration and its impact on structure formation?

Yes, alternative theories of gravity, particularly modified gravity models, offer a compelling avenue to explain the observed cosmic acceleration and its influence on structure formation, providing a departure from the standard cosmological model's reliance on dark energy. Here's an exploration of how modified gravity tackles these cosmological puzzles:
Modifying Gravity's Grip:

Departing from General Relativity: Modified gravity theories propose alterations to Einstein's General Relativity, typically on cosmological scales, to account for the accelerated expansion without invoking dark energy.
Beyond the Inverse Square Law: Many modified gravity models introduce modifications to the gravitational force law, often weakening gravity's pull at large distances, which can drive the accelerated expansion.
Examples of Modified Gravity Models:

f(R) Gravity: This class of models generalizes the Einstein-Hilbert action by replacing the Ricci scalar (R) with a function f(R). Specific choices of f(R) can lead to late-time acceleration.
Scalar-Tensor Theories: These theories introduce a scalar field coupled to gravity, mediating a fifth force that can impact both the expansion history and the growth of structure.
Dvali-Gabadadze-Porrati (DGP) Model: This model proposes that our Universe is a 3-brane embedded in a higher-dimensional bulk, with gravity leaking into the extra dimensions at large distances, modifying its behavior.
Impact on Structure Formation:

Modified Growth Rate: Modified gravity models typically predict a different growth rate for cosmic structures compared to ΛCDM. The altered gravitational force can either enhance or suppress the clustering of matter.
Screening Mechanisms: To comply with stringent tests of gravity on Solar System scales, many modified gravity models incorporate screening mechanisms that effectively restore General Relativity in regions of high density, while allowing for deviations on cosmological scales.
Observational Tests and Challenges:

Distinguishing from Dark Energy: Disentangling the effects of modified gravity from those of dark energy poses a significant observational challenge. Precise measurements of the expansion history, the growth of structure, and lensing potentials are crucial for this task.
Testing Screening Mechanisms: Verifying the effectiveness of screening mechanisms in high-density environments is essential to validate modified gravity models. Observations of galaxies and clusters provide valuable testing grounds.
Theoretical Consistency: Ensuring the theoretical consistency and stability of modified gravity models is crucial. Some models suffer from instabilities or ghost-like degrees of freedom, requiring careful theoretical scrutiny.
In Conclusion:
Modified gravity models offer a compelling alternative explanation for cosmic acceleration and its impact on structure formation, challenging the standard cosmological paradigm. While current observations have not definitively favored modified gravity over dark energy, ongoing and future surveys, with their enhanced precision and sensitivity, hold the potential to provide more conclusive tests. The quest to unravel the true nature of cosmic acceleration continues to drive theoretical and observational advancements in cosmology.

If dark energy transitions from a matter-like behavior to a cosmological constant-like behavior, what are the implications for the ultimate fate of the Universe?

The transition of dark energy from a matter-like behavior to a cosmological constant-like behavior has profound implications for the ultimate fate of the Universe. Let's explore the cosmological consequences of such a transition:
Early Matter-like Phase:

Slower Expansion: During this phase, dark energy mimics the behavior of matter, implying a negative pressure but with a magnitude smaller than that of a cosmological constant. This leads to a slower expansion rate compared to a Universe dominated by a cosmological constant from the outset.
Enhanced Structure Formation: The reduced Hubble drag due to the slower expansion allows for more time for gravity to pull matter together, potentially leading to enhanced structure formation. More galaxy clusters and superclusters might form in this scenario.
Transition to Cosmological Constant-like Behavior:

Accelerated Expansion: As dark energy transitions to a cosmological constant-like behavior, its negative pressure becomes more pronounced, eventually dominating the energy density of the Universe. This triggers a phase of accelerated expansion, similar to what we observe today.
Hindered Structure Formation: The accelerated expansion acts as an anti-gravitational force, working against the pull of gravity. Structure formation becomes suppressed as the expansion pulls apart matter faster than it can clump together.
Ultimate Fate: The Big Freeze Scenario:

Eternal Expansion: With dark energy behaving like a cosmological constant, the accelerated expansion continues indefinitely. The Universe expands forever, becoming increasingly cold and dilute.
Galactic Isolation: The expansion eventually isolates galaxies within their own expanding cosmic horizons. As distant galaxies recede beyond the observable Universe, the night sky would grow darker over cosmic timescales.
Heat Death: As the Universe expands and cools, stars eventually exhaust their nuclear fuel and die out. Black holes might dominate the distant future, slowly evaporating through Hawking radiation. The Universe approaches a state of maximum entropy, often referred to as "heat death," where no further significant cosmic events occur.
Important Considerations:

Transition Redshift: The redshift at which the transition occurs significantly impacts the details of this scenario. An earlier transition leads to a Universe more closely resembling ΛCDM, while a later transition allows for more structure formation before the accelerated expansion takes over.
Nature of Dark Energy: The exact nature of dark energy and the mechanism driving its transition remain open questions. Understanding these aspects is crucial for making more precise predictions about the Universe's fate.
In Summary:
A transition of dark energy from a matter-like behavior to a cosmological constant-like behavior leads to a Universe that experiences a period of enhanced structure formation in its early stages, followed by an eternal phase of accelerated expansion. The ultimate fate, under this scenario, is the Big Freeze, characterized by an ever-expanding, cooling, and increasingly empty Universe. However, the precise details of this cosmic evolution heavily depend on the transition redshift and the underlying physics of dark energy, areas of active research in cosmology.