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In this note by use of the holographic principle together with the equipartition law of energy and the Unruh temperature, we derive the Friedmann equations of a Friedmann-Robertson-Walker universe.
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Applying Clausius relation, $delta Q=TdS$, to apparent horizon of a FRW universe with any spatial curvature, and assuming that the apparent horizon has temperature $T=1/(2pi tilde {r}_A)$, and a quantum corrected entropy-area relation, $S=A/4G +alpha ln A/4G$, where $tilde {r}_A$ and $A$ are the apparent horizon radius and area, respectively, and $alpha$ is a dimensionless constant, we derive modified Friedmann equations, which does not contain a bounce solution. On the other hand, loop quantum cosmology leads to a modified Friedmann equation $H^2 =frac{8pi G}{3}rho (1-rho/rho_{rm crit})$. We obtain an entropy expression of apparent horizon of FRW universe described by the modified Friedmann equation. In the limit of large horizon area, resulting entropy expression gives the above corrected entropy-area relation, however, the prefactor $alpha$ in the logarithmic term is positive, which seems not consistent with most of results in the literature that quantum geometry leads to a negative contribution to the area formula of black hole entropy.
In this paper, we propose a model in which an additional pressure due to the effects of the entropic force is added to the ideal fluid. Furthermore, we obtain the dynamic equation in the FRW universe which contains the quantum gravitational effects based on the description of entropic force and emergence of space. Our model can well explain the age of the universe and the effect of the current accelerating expansion. We give the relation between the luminosity distance and the redshift factor, and compare this relation with that of lambda cold dark matter model($Lambda CDM$ model).
In this paper we study the effects of quantum scalar field vacuum fluctuations on scalar test particles in an analog model for the Friedmann-Robertson-Walker spatially flat geometry. In this scenario, the cases with one and two perfectly reflecting plane boundaries are considered as well the case without boundary. We find that the particles can undergo Brownian motion with a nonzero mean squared velocity induced by the quantum vacuum fluctuations due to the time dependent background and the presence of the boundaries. Typical singularities which appears due to the presence of the boundaries in flat spacetime can be naturally regularized for an asymptotically bounded expanding scale function. Thus, shifts in the velocity could be, at least in principle, detectable experimentally. The possibility to implement this observation in an analog cosmological model by the use of a Bose-Einstein condensate is also discussed.
With the help of a masslike function which has dimension of energy and equals to the Misner-Sharp mass at the apparent horizon, we show that the first law of thermodynamics of the apparent horizon $dE=T_AdS_A$ can be derived from the Friedmann equation in various theories of gravity, including the Einstein, Lovelock, nonlinear, and scalar-tensor theories. This result strongly suggests that the relationship between the first law of thermodynamics of the apparent horizon and the Friedmann equation is not just a simple coincidence, but rather a more profound physical connection.
First order rotational perturbations of the Friedmann-Robertson-Walker metric are considered in the framework of the brane-world cosmological models. A rotation equation, relating the perturbations of the metric tensor to the angular velocity of the matter on the brane is derived under the assumption of slow rotation. The mathematical structure of the rotation equation imposes strong restrictions on the temporal and spatial dependence of the brane matter angular velocity. The study of the integrable cases of the rotation equation leads to three distinct models, which are considered in detail. As a general result we find that, similarly to the general relativistic case, the rotational perturbations decay due to the expansion of the matter on the brane. One of the obtained consistency conditions leads to a particular, purely inflationary brane-world cosmological model, with the cosmological fluid obeying a non-linear barotropic equation of state.
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