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Register a new userMerging Gravitation with Thermodynamics to Understand Cosmology
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Added by
Ruxandra Bondarescu
Publication date
2013
fields
Physics
and research's language is
English
Authors
Andrew P. Lundgren
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We discuss the evolution of the universe in the context of the second law of thermodynamics from its early stages to the far future. Cosmological observations suggest that most matter and radiation will be absorbed by the cosmological horizon. On the local scale, the matter that is not ejected from our supercluster will collapse to a supermassive black hole and then slowly evaporate. The history of the universe is that of an approach to the equilibrium state of the gravitational field.
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We review current theoretical cosmology, including fundamental and mathematical cosmology and physical cosmology (as well as cosmology in the quantum realm), with an emphasis on open questions.
We present modified cosmological scenarios that arise from the application of the gravity-thermodynamics conjecture, using the Barrow entropy instead of the usual Bekenstein-Hawking one. The former is a modification of the black hole entropy due to quantum-gravitational effects that deform the black-hole horizon by giving it an intricate, fractal structure. We extract modified cosmological equations which contain new extra terms that constitute an effective dark-energy sector, and which coincide with the usual Friedmann equations in the case where the new Barrow exponent acquires its Bekenstein-Hawking value. We present analytical expressions for the evolution of the effective dark energy density parameter, and we show that the universe undergoes through the usual matter and dark-energy epochs. Additionally, the dark-energy equation-of-state parameter is affected by the value of the Barrow deformation exponent and it can lie in the quintessence or phantom regime, or experience the phantom-divide crossing. Finally, at asymptotically large times the universe always results in the de-Sitter solution.
We perform an analysis where Einsteins field equation is derived by means of very simple thermodynamical arguments. Our derivation is based on a consideration of the properties of a very small, spacelike two-plane in a uniformly accelerating motion.
We discuss dynamical systems approaches and methods applied to flat Robertson-Walker models in $f(R)$-gravity. We argue that a complete description of the solution space of a model requires a global state space analysis that motivates globally covering state space adapted variables. This is shown explicitly by an illustrative example, $f(R) = R + alpha R^2$, $alpha > 0$, for which we introduce new regular dynamical systems on global compactly extended state spaces for the Jordan and Einstein frames. This example also allows us to illustrate several local and global dynamical systems techniques involving, e.g., blow ups of nilpotent fixed points, center manifold analysis, averaging, and use of monotone functions. As a result of applying dynamical systems methods to globally state space adapted dynamical systems formulations, we obtain pictures of the entire solution spaces in both the Jordan and the Einstein frames. This shows, e.g., that due to the domain of the conformal transformation between the Jordan and Einstein frames, not all the solutions in the Jordan frame are completely contained in the Einstein frame. We also make comparisons with previous dynamical systems approaches to $f(R)$ cosmology and discuss their advantages and disadvantages.
With the theory of general relativity, Einstein abolished the interpretation of gravitation as a force and associated it to the curvature of spacetime. Tensorial calculus and differential geometry are the mathematical resources necessary to study the spacetime manifold in the context of Einsteins theory. In 1961, Tullio Regge published a work on which he uses the old idea of triangulation of surfaces aiming the description of curvature, and, therefore, gravitation, through the use of discrete calculus. In this paper, we approach Regge Calculus pedagogically, as well as the main results towards a discretized version of Einsteins theory of gravitation.
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