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Register a new user$Lambda(t)$ cosmology induced by a slowly varying Elko field
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In this work the exact Friedmann-Robertson-Walker equations for an Elko spinor field coupled to gravity in an Einstein-Cartan framework are presented. The torsion functions coupling the Elko field spin-connection to gravity can be exactly solved and the FRW equations for the system assume a relatively simple form. In the limit of a slowly varying Elko spinor field there is a relevant contribution to the field equations acting exactly as a time varying cosmological model $Lambda(t)=Lambda_*+3beta H^2$, where $Lambda_*$ and $beta$ are constants. Observational data using distance luminosity from magnitudes of supernovae constraint the parameters $Omega_m$ and $beta$, which leads to a lower limit to the Elko mass. Such model mimics, then, the effects of a dark energy fluid, here sourced by the Elko spinor field. The density perturbations in the linear regime were also studied in the pseudo-Newtonian formalism.
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By allowing torsion into the gravitational dynamics one can promote the cosmological constant, $Lambda$, to a dynamical variable in a class of quasi-topological theories. In this paper we perform a mini-superspace quantization of these theories in the connection representation. If $Lambda$ is kept fixed, the solution is a delta-normalizable version of the Chern-Simons (CS) state, which is the dual of the Hartle and Hawking and Vilenkin wave-functions. We find that the CS state solves the Wheeler-DeWitt equation also if $Lambda$ is rendered dynamical by an Euler quasi-topological invariant, {it in the parity-even branch of the theory}. In the absence of an infra-red (IR) cut-off, the CS state suggests the marginal probability $P(Lambda)=delta(Lambda)$. Should there be an IR cutoff (for whatever reason) the probability is sharply peaked at the cut off. In the parity-odd branch, however, we can still find the CS state as a particular (but not most general) solution, but further work is needed to sharpen the predictions. For the theory based on the Pontryagin invariant (which only has a parity-odd branch) the CS wave function no longer is a solution to the constraints. We find the most general solution in this case, which again leaves room for a range of predictions for $Lambda$.
We study the dynamical properties of a large body of varying vacuum cosmologies for which dark matter interacts with vacuum. In particular, performing the critical point analysis we investigate the existence and the stability of cosmological solutions which describe de-Sitter, radiation and matter dominated eras. We find several cases of varying vacuum models that admit stable critical points, hence they can be used in describing the cosmic history.
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We show that a cosmology driven by gravitationally induced particle production of all non-relativistic species existing in the present Universe mimics exactly the observed flat accelerating $Lambda$CDM cosmology with just one dynamical free parameter. This kind of scenario includes the creation cold dark matter (CCDM) model [Lima, Jesus & Oliveira, JCAP 011(2010)027] as a particular case and also provides a natural reduction of the dark sector since the vacuum component is not needed to accelerate the Universe. The new cosmic scenario is equivalent to $Lambda$CDM both at the background and perturbative levels and the associated creation process is also in agreement with the universality of the gravitational interaction and equivalence principle. Implicitly, it also suggests that the present day astronomical observations cannot be considered the ultimate proof of cosmic vacuum effects in the evolved Universe because $Lambda$CDM may be only an effective cosmology.
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