Cosmological Non-Linearities as an Effective Fluid

Abstract: The universe is smooth on large scales but very inhomogeneous on small scales. Why is the spacetime on large scales modeled to a good approximation by the Friedmann equations? Are we sure that small-scale non-linearities do not induce a large backreaction? Related to this, what is the effective theory that describes the universe on large scales? In this paper we make progress in addressing these questions. We show that the effective theory for the long-wavelength universe behaves as a viscous fluid coupled to gravity: integrating out short-wavelength perturbations renormalizes the homogeneous background and introduces dissipative dynamics into the evolution of long-wavelength perturbations. The effective fluid has small perturbations and is characterized by a few parameters like an equation of state, a sound speed and a viscosity parameter. These parameters can be matched to numerical simulations or fitted from observations. We find that the backreaction of small-scale non-linearities is very small, being suppressed by the large hierarchy between the scale of non-linearities and the horizon scale. The effective pressure of the fluid is always positive and much too small to significantly affect the background evolution. Moreover, we prove that virialized scales decouple completely from the large-scale dynamics, at all orders in the post-Newtonian expansion. We propose that our effective theory be used to formulate a well-defined and controlled alternative to conventional perturbation theory, and we discuss possible observational applications. Finally, our way of reformulating results in second-order perturbation theory in terms of a long-wavelength effective fluid provides the opportunity to understand non-linear effects in a simple and physically intuitive way.

• The paper demonstrates that non-linear small-scale fluctuations behave as a viscous fluid, leading to minimal backreaction on large-scale cosmic evolution.
• It employs analytical integration of short-wavelength perturbations to renormalize the homogeneous background and introduces key parameters like sound speed and viscosity.
• The study implies that virialized scales decouple from cosmic dynamics, negating their influence on cosmic acceleration and dark energy alternatives.

Cosmological Non-Linearities as an Effective Fluid

The paper presented, "Cosmological Non-Linearities as an Effective Fluid" by Daniel Baumann et al., explores the challenge of modeling the universe's evolution by effectively capturing the impact of small-scale inhomogeneities on large-scale structures. This study delves deep into the implications of these non-linear perturbations and proposes an innovative approach by treating them as a viscous fluid to achieve a comprehensive cosmological understanding.

Key Concepts and Methodology

While the universe is notably smooth on grand scales, small-scale structures exhibit significant inhomogeneities. The predominant question addressed in this paper pertains to why large-scale spacetime can be reliably modeled by the Friedmann equations, despite the non-linearities at smaller scales. The authors propose that these small-scale fluctuations do not result in a large backreaction due to the scale separation between the non-linear fluctuations and the horizon scale. They present a theoretical framework where the long-wavelength behavior of the universe acts as a viscous fluid in gravitational interaction, thereby introducing dissipative elements into the dynamics.

The remarkable analytical development demonstrated by the authors incorporates the integration of short-wavelength perturbations, which not only renormalize the homogeneous background but also impart small dissipative dynamics to large-scale perturbations. This formulation leverages parameters such as the equation of state, sound speed, and viscosity coefficient, aligning the effective theory with numerical simulations and observational data.

Key Insights and Numerical Results

The research primarily finds that the backreaction from small-scale non-linearities is considerably suppressed due to the hierarchical scale difference between smaller fluctuations and the universe's horizon. Notably, the effective pressure emerging from treating the universe as a fluid remains positive but is inadequate to impact significantly the overall background evolution. Furthermore, the study establishes that virialized scales entirely decouple from the large-scale dynamics, contributing minimally to the backreaction, which nullifies any speculations around these non-linearities being responsible for cosmic acceleration obviating the need for dark energy considerations.

Implications and Future Research Directions

The theoretical insights laid out by this paper have substantial implications in the context of evolving cosmological models. By suggesting a viable alternative to traditional perturbation theory approaches, the effective fluid framework delivers a structured methodology to ascertain the impacts attributable to gravitational non-linearities on long-wavelength cosmic perturbations.

The potential to refine this approach further is immense. Future research can focus on empirical validations of the proposed effective theory, especially through high-resolution N-body simulations and astrophysical observations. Moreover, the foundational method devised here may inspire new models to address anomalies in dark energy and dark matter simulations by filling theoretical gaps with insights into complex fluid dynamics at cosmic scales.

In summary, Baumann and collaborators’ exploration into cosmological non-linearities as a viscous fluid provides a robust model to understand long-wavelength perturbations. They set an advanced platform for future studies to expand upon and refine current cosmological theories, emphasizing a reciprocal relationship between theoretical physics and observable phenomena in the universe.