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Register a new userThe Well-Tempered Cosmological Constant: Fugue in B$^flat$
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Zero point fluctuations of quantum fields should generate a large cosmological constant energy density in any spacetime. How then can we have anything other than de Sitter space without fine tuning? Well tempering -- dynamical cancellation of the cosmological constant using degeneracy within the field equations -- can replace a large cosmological constant with a much lower energy state. Here we give an explicit mechanism to obtain a Minkowski solution, replacing the cosmological constant with zero, and testing its attractor nature and persistence through a vacuum phase transition. We derive the general conditions that Horndeski scalar-tensor gravity must possess, and evolve in a fugue of functions, to deliver nothing and make the universe be flat.
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Well tempering is one of the few classical field theory methods for solving the original cosmological constant problem, dynamically canceling a large (possibly Planck scale) vacuum energy and leaving the matter component intact, while providing a viable cosmology with late time cosmic acceleration and an end de Sitter state. We present the general constraints that variations of Horndeski gravity models with different combinations of terms must satisfy to admit an exact de Sitter spacetime that does not respond to an arbitrarily large cosmological constant. We explicitly derive several specific scalar-tensor models that well temper and can deliver a standard cosmic history including current cosmic acceleration. Stability criteria, attractor behavior of the de Sitter state, and the response of the models to pressureless matter are considered. The well tempered conditions can be used to focus on particular models of modified gravity that have special interest -- not only removing the original cosmological constant problem but providing relations between the free Horndeski functions and reducing them to a couple of parameters, suitable for testing gravity and cosmological data analysis.
Self tuning is one of the few methods for dynamically cancelling a large cosmological constant and yet giving an accelerating universe. Its drawback is that it tends to screen all sources of energy density, including matter. We develop a model that tempers the self tuning so the dynamical scalar field still cancels an arbitrary cosmological constant, including the vacuum energy through any high energy phase transitions, without affecting the matter fields. The scalar-tensor gravitational action is simple, related to cubic Horndeski gravity, with a nonlinear derivative interaction plus a tadpole term. Applying shift symmetry and using the property of degeneracy of the field equations we find families of functions that admit de Sitter solutions with expansion rates that are independent of the magnitude of the cosmological constant and preserve radiation and matter dominated phases. That is, the method can deliver a standard cosmic history including current acceleration, despite the presence of a Planck scale cosmological constant.
It is well known that string theories naturally compactify on anti-de Sitter spaces, and yet cosmological observations show no evidence of a negative cosmological constant in the early Universes evolution. In this letter we present two simple nonlocal modifications of the standard Friedmann cosmology that can lead to observationally viable cosmologies with an initial (negative) cosmological constant. The nonlocal operators we include are toy models for the quantum cosmological backreaction. In Model I an initial quasiperiodic oscillatory epoch is followed by inflation and a late time matter era, representing a dark matter candidate. The backreaction in Model II quickly compensates the negative cosmological term such that the Ricci curvature scalar rapidly approaches zero, and the Universe ends up in a late time radiation era.
We present here how the gravothermal or Antonovs instability, which was originally formulated in the microcanonical ensemble, is modified in the presence of a cosmological constant and in the canonical ensemble. In contrast to the microcanonical ensemble, there is a minimum, and not maximum, radius for which metastable states exist. In addition this critical radius is decreasing, and not increasing, with increasing cosmological constant. The minimum temperature for which metastable states exist is decreasing with increasing cosmological constant, while above some positive value of the cosmological constant, there appears a second critical temperature. For lower temperatures than the second critical temperature value, metastable states reappear, indicating a typical reentrant phase transition. The two critical temperatures merge when the cosmological density equals one half the mean density of the system.
Bouncing models have been proposed by many authors as a completion, or even as an alternative to inflation for the description of the very early and dense Universe. However, most bouncing models contain a contracting phase from a very large and rarefied state, where dark energy might have had an important role as it has today in accelerating our large Universe. In that case, its presence can modify the initial conditions and evolution of cosmological perturbations, changing the known results already obtained in the literature concerning their amplitude and spectrum. In this paper, we assume the simplest and most appealing candidate for dark energy, the cosmological constant, and evaluate its influence on the evolution of cosmological perturbations during the contracting phase of a bouncing model, which also contains a scalar field with a potential allowing background solutions with pressure and energy density satisfying p = w*rho, w being a constant. An initial adiabatic vacuum state can be set at the end of domination by the cosmological constant, and an almost scale invariant spectrum of perturbations is obtained for w~0, which is the usual result for bouncing models. However, the presence of the cosmological constant induces oscillations and a running towards a tiny red-tilted spectrum for long wavelength perturbations.
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