We delve into the first-order thermodynamics of Horndeski gravity, focusing
on spatially flat, homogeneous, and isotropic cosmologies. Our exploration
begins with a comprehensive review of the effective fluid representation within
viable Horndeski gravity. Notably, we uncover a surprising alignment between
the constitutive relations governing the “Horndeski fluid” and those of
Eckart’s thermodynamics. Narrowing our focus, we specialize our discussion to
spatially flat Friedmann-Lema{^i}tre-Robertson-Walker spacetimes. Within this
specific cosmological framework, we systematically analyze two classes of
theories: shift-symmetric and asymptotically shift-symmetric. These theories
are characterized by a non-vanishing braiding parameter, adding a nuanced
dimension to our investigation. On the one hand, unlike the case of the
“traditional” scalar-tensor gravity, these peculiar subclasses of viable
Horndeski gravity never relax to General Relativity (seen within this formalism
as an equilibrium state at zero temperature), but give rise to additional
equilibrium states with non-vanishing viscosity. On the other hand, this
analysis further confirms previous findings according to which curvature
singularities are “hot” and exhibit a diverging temperature, which suggests
that deviations of scalar-tensor theories from General Relativity become
extreme at spacetime singularities. Furthermore, we provide a novel exact
cosmological solution for an asymptotically shift-symmetric theory as a toy
model for our thermodynamic analysis.
Horndeski gravity is a topic of interest in the study of cosmology. In this article, we delve into the first-order thermodynamics of Horndeski gravity, specifically focusing on spatially flat, homogeneous, and isotropic cosmologies.
Before diving into the specifics, we provide a comprehensive review of the effective fluid representation within viable Horndeski gravity. Surprisingly, we uncover an alignment between the constitutive relations governing the “Horndeski fluid” and those of Eckart’s thermodynamics.
Next, we narrow our focus to spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes. Within this specific cosmological framework, we systematically analyze two classes of theories: shift-symmetric and asymptotically shift-symmetric. These theories are characterized by a non-vanishing braiding parameter, which adds depth to our investigation.
Our analysis reveals that unlike traditional scalar-tensor gravity, the peculiar subclasses of viable Horndeski gravity never relax to General Relativity as an equilibrium state at zero temperature. Instead, they give rise to additional equilibrium states with non-vanishing viscosity. This highlights the unique properties of Horndeski gravity.
Additionally, our findings confirm previous research showing that curvature singularities are “hot” and exhibit a diverging temperature. This implies that deviations of scalar-tensor theories from General Relativity become extreme at spacetime singularities.
To further support our analysis, we present a novel exact cosmological solution for an asymptotically shift-symmetric theory. This solution serves as a toy model for our thermodynamic analysis and adds another layer to our understanding.
Future Roadmap
The exploration of Horndeski gravity in the context of first-order thermodynamics opens up several potential avenues for future research. Here is a roadmap outlining potential challenges and opportunities on the horizon:
1. Investigating Other Cosmological Frameworks
While our analysis focuses on spatially flat FLRW spacetimes, it would be valuable to extend the study to other cosmological frameworks, such as non-flat or anisotropic spacetimes. Exploring the thermodynamics of Horndeski gravity in these contexts may reveal new insights and properties.
2. Experimental and Observational Confirmation
Validating the predictions and findings of our thermodynamic analysis through experiments or observations would further solidify the understanding of Horndeski gravity. This could involve testing the existence of additional equilibrium states with non-vanishing viscosity or investigating the temperature behavior near curvature singularities.
3. Quantum Effects and Thermodynamics
Examining the interplay between quantum effects and thermodynamics within the context of Horndeski gravity could lead to exciting discoveries. Investigating the behavior of Horndeski gravity at extreme energies or exploring the connection between thermodynamics and quantum field theory may unlock new perspectives.
4. Generalizing the Analysis
Expanding the analysis beyond the specific subclasses of shift-symmetric and asymptotically shift-symmetric theories could reveal a broader picture of Horndeski gravity. Generalizing the thermodynamic analysis to include a wider range of theories and scenarios would provide a more comprehensive understanding of the subject.
5. Applications in Cosmological Evolution
Exploring how the thermodynamics of Horndeski gravity affect cosmological evolution could have practical applications. This could involve studying the influence of additional equilibrium states with non-vanishing viscosity on the dynamics of the universe or investigating how the temperature behavior near curvature singularities impacts the evolution of cosmic structures.
Overall, the study of first-order thermodynamics in Horndeski gravity offers a rich field for future exploration. By addressing the outlined challenges and opportunities, researchers can gain a deeper understanding of the subject and potentially uncover new phenomena and insights.