Abstract
In this Letter, we study thermodynamical properties of the apparent horizon in a universe governed by quasi-topological gravity. Our aim is twofold. First, by using the variational method we derive the general form of Friedmann equation in quasi-topological gravity. Then, by applying the first law of thermodynamics on the apparent horizon, after using the entropy expression associated with the black hole horizon in quasi-topological gravity, and replacing the horizon radius, r+, with the apparent horizon radius, r˜A, we derive the corresponding Friedmann equation in quasi-topological gravity. We find that these two different approaches yield the same result which shows the profound connection between the first law of thermodynamics and the gravitational field equations of quasi-topological gravity. We also study the validity of the generalized second law of thermodynamics in quasi-topological cosmology. We find that, with the assumption of the local equilibrium hypothesis, the generalized second law of thermodynamics is fulfilled for the universe enveloped by the apparent horizon for the late time cosmology.
Highlights
The most general Lagrangian which keeps the field equations of motion for the metric of second order, as the pure Einstein-Hilbert action, is Lovelock Lagrangian [1]
In the late time, the generalized second law (GSL) of thermodynamics is fulfilled for the universe governed by quasi-topological gravity
This implies that for the late time cosmology, the GSL of thermodynamics is fulfilled in the universe governed by quasi-topological gravity, regardless of the nature of the energy content of the universe
Summary
The most general Lagrangian which keeps the field equations of motion for the metric of second order, as the pure Einstein-Hilbert action, is Lovelock Lagrangian [1]. In the cosmological setup, it was shown that the corresponding Friedmann equations of Einstein, Gauss-Bonnet and Lovelock gravity can be derived by applying the energy balance relation −dE = T dS to the apparent horizon of a Friedmann- Robertson-Walker universe (FRW) with any spatial curvature [19]. In the framework of Horava-Lifshitz gravity, it was shown that the corresponding Friedmann equation cannot be derived by applying the first law of thermodynamics on the apparent horizon and using the entropy expression for static spherically symmetric black holes in this gravity theory [20]. The action of Horava-Lifshiz gravity is invariant only under a restricted class of diffeomorphism [22] This implies that the connection between first law of thermodynamics and gravitational field equations is not a generic feature of any theory of gravity.
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