Abstract
On the occasion of a century from the proposal of General relativity by Einstein, I attempt to tackle some open issues in modern cosmology, via a toy but non-trivial model. Specifically, I would like to link together: (i) the smallness of the cosmological constant today, (ii) the evolution of the universe from an inflationary era after the big-bang till now, and (iii) local supersymmetry in the gravitational sector (supergravity) with a broken spectrum at early eras, by making use of the concept of the "running vacuum" in the context of a simple toy model of four-dimensional N=1 supergravity. The model is characterised by dynamically broken local supersymmetry, induced by the formation of gravitino condensates in the early universe. As I will argue, there is a Starobinsky-type inflationary era characterising the broken supersymmetry phase in this model, which is compatible with the current cosmological data, provided a given constraint is satisfied among some tree-level parameters of the model and the renormalised cosmological constant of the de Sitter background used in the analysis. Applying the "running vacuum" concept, then, to the effective field theory at the exit of inflation, makes a smooth connection (in cosmic time) with the radiation dominance epoch and subsequently with the current era of the Universe, characterised by a small (but dominant) cosmological-constant contribution to the cosmic energy density. In this approach, the smallness of the cosmological constant today is attributed to the failure (due to quantum gravity non-perturbative effects) of the aforementioned constraint.
Highlights
Introduction and SummaryThe year 2015 celebrates a century since the proposal by Einstein for the theory of General Relativity (GR), an elegant and quite successful classical field theory of Gravitation, generalising Newtonian gravity
The structure of the talk is as follows: In Section 2 we review the formalism of the dynamical breaking of SUGRA in four dimensional N = 1 models, including superconformal extensions thereof that are necessitated for phenomenological reasons, as we shall see
This offers an interesting new insight into the cosmological constant problem, which, needless to say remains unsolved. In this talk we considered a minimal inflationary scenario, by means of which a gravitino condensate in supergravity models is held responsible for breaking local supersymmetry dynamically and inducing inflation in an indirect way by means of a Starobinsky-type inflation in the massive gravitino phase
Summary
This is realised via the higher (in particular quadratic-order) curvature corrections of the (quantum) effective action of the gravitino condensate field, obtained after path-integration of graviton and gravitino degrees of freedom in the massive gravitino phase These corrections induce a Starobinsky-type inflation [16], which occurs for quite natural values of the parameters of the N = 1 SUGRA model (its Jordan-frame variants [14]), with the inflation scale and gravitino mass in the ball park of the GUT scale. Upon appropriate breaking of conformal symmetry, induced by specific dilaton potentials (which we do not discuss here), one may assume that the dilaton field acquires a non-trivial vacuum expectation value φ 0 One consequence of this is that in the broken conformal symmetry phase, the resulting supergravity sector, upon passing (via appropriate field redefinitions) to the Einstein frame is described by an action of the form (2), but with the coupling of the gravitino four-fermion interaction terms being replaced by κ ≡ e− φ κ ,.
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