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Register a new userCosmology of the de Sitter Horndeski models
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Horndeski models with a de Sitter critical point for any kind of material content may provide a mechanism to alleviate the cosmological constant problem. We study the cosmological evolution of two classes of families - the linear models and the non-linear models with shift symmetry. We conclude that the latter models can deliver a background dynamics compatible with the latest observational data.
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We review the most general scalar-tensor cosmological models with up to second-order derivatives in the field equations that have a fixed spatially flat de Sitter critical point independent of the material content or vacuum energy. This subclass of the Horndeski Lagrangian is capable of dynamically adjusting any value of the vacuum energy of the matter fields at the critical point. We present the cosmological evolution of the linear models and the non-linear models with shift symmetry. We come to the conclusion that the shift symmetric non-linear models can deliver a viable background compatible with current observations.
We perform a minisuperspace analysis of an information-theoretic nonlinear Wheeler-deWitt (WDW) equation for de Sitter universes. The nonlinear WDW equation, which is in the form of a difference-differential equation, is transformed into a pure difference equation for the probability density by using the current conservation constraint. In the present study we observe some new features not seen in our previous approximate investigation, such as a nonzero minimum and maximum allowable size to the quantum universe: An examination of the effective classical dynamics supports the interpretation of a bouncing universe. The studied model suggests implications for the early universe, and plausibly also for the future of an ongoing accelerating phase of the universe.
In this paper we focus on the gravitational thermodynamics of the far future. Cosmological observations suggest that most matter will be diluted away by the cosmological expansion, with the rest collapsing into supermassive black holes. The likely future state of our local universe is a supermassive black hole slowly evaporating in an empty universe dominated by a positive cosmological constant. We describe some overlooked features of how the cosmological horizon responds to the black hole evaporation. The presence of a black hole depresses the entropy of the cosmological horizon by an amount proportional to the geometric mean of the entropies of the black hole and cosmological horizons. As the black hole evaporates and loses its mass in the process, the total entropy increases obeying the second law of thermodynamics. The entropy is produced by the heat from the black hole flowing across the extremely cold cosmological horizon. Once the evaporation is complete, the universe becomes empty de Sitter space that (in the presence of a true cosmological constant) is the maximum entropy thermodynamic equilibrium state. We propose that flat Minkowski space is an improper limit of this process which obscures the thermodynamics. The cosmological constant should be regarded not only as an energy scale, but also as a scale for the maximum entropy of a universe. In this context, flat Minkowski space is indistinguishable from de Sitter with extremely small cosmological constant, yielding a divergent entropy. This introduces an unregulated infinity in black hole thermodynamics calculations, giving possibly misleading results.
We derive a noncovariant but simple representation for the self-energy of a conformally transformed graviton field on the cosmological patch of de Sitter. Our representation involves four structure functions, as opposed to the two that would be necessary for a manifestly de Sitter invariant representation. We work out what the four structure functions are for the one loop correction due to a massless, minimally coupled scalar. And we employ the result to work out what happens to dynamical gravitons.
We consider an O(N) symmetric scalar field model in the mean field (Hartree) approximation and show that the symmetry can be broken in de Sitter space. We find that the phase transition can be of first order, and that its strength depends non-analytically on the parameters of the model. We also show that the would-be Goldstone bosons acquire a mass, effectively becoming pseudo-Goldstone bosons, thus breaking the O(N) symmetry. Our results imply that topological defects can form during inflation.
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