The Higgs-Dilaton cosmological model is able to describe simultaneously an inflationary expansion in the early Universe and a dark energy dominated stage responsible for the present day acceleration. It also leads to a non-trivial relation between the spectral tilt of scalar perturbations ns and the dark energy equation of state ω. We study the self-consistency of this model from an effective field theory point of view. Taking into account the influence of the dynamical background fields, we determine the effective cut-off of the theory, which turns out to be parametrically larger than all the relevant energy scales from inflation to the present epoch. We finally formulate the set of assumptions needed to estimate the amplitude of the quantum corrections in a systematic way and show that the connection between ns and ω remains unaltered if these assumptions are satisfied.2 the introduction of a new scalar degree of freedom, the dilaton, which becomes the Goldstone boson of the broken symmetry and remains exactly massless. The coupling of the dilaton field to matter is weak and takes place only through derivative couplings, not contradicting therefore any 5th force experimental bounds [31]. Although the dilatation symmetry described above forbids the introduction of a cosmological constant term, the ever-present cosmological constant problem reappears associated to the fine-tuning of the dilaton self-interaction [29]. However, if the dilaton self-coupling β is chosen to be zero (or required to vanish due to some yet unknown reason), a slight modification of general relativity (GR), known as Unimodular Gravity (UG), provides a dynamical dark energy (DE) stage in good agreement with observations. The scale-invariant UG gives rise to a "run-away" potential for the dilaton [29], which plays the role of a quintessence field. The strength of such a potential is determined by an integration constant Λ 0 that appears in the Einstein equations of motion due to the unimodular constraintĝ = −1 on the metric determinant. The common origin of the inflationary and DE dominated stages in Higgs-Dilaton inflation allowed to derive extra bounds on the initial inflationary conditions 1 , as well as potentially testable relations between the early and late Universe observables [30].Some of the properties of the Higgs-Dilaton model described above were previously noted in the literature. The first attempt to formulate a viable SI theory non-minimally coupled to gravity was done by Fujii in Ref. [32], although without establishing any connection to the SM Higgs. The role of dilatation symmetry in cosmology was first considered by Wetterich in Refs. [33,34]. In these seminal papers, the dynamical dark energy, associated with the dilaton field, appears as a consequence of the dilatation anomaly and is related to the breaking of SI by quantum effects. The present paper has a number of formal analogies and similarities regarding the cosmological consequences for the late Universe with Refs. [33,34]. At the same time, our approach to the so...

We study the geometrical properties of scale-invariant two-field models of inflation. In particular, we show that when the field-derivative space in the Einstein frame is maximally symmetric during inflation, the inflationary predictions can be universal and independent of the details of the theory.Comment: 14 pages, no figure

In this paper we investigate the physical spectrum of the gravitational theory based on the Poincaré group with terms which are at most quadratic in tetrad and spin connection, allowing for the presence of parity-even as well as parity-odd invariants. We determine restrictions on the parameters of the action so that all degrees of freedom propagate and are neither ghosts nor tachyons. We show that the addition of parity non-conserving invariants extends the healthy parameter space of the theory. To accomplish our goal, we apply the weak field approximation around flat spacetime and in order to facilitate the analysis, we separate the bilinear action for the excitations into completely independent spin sectors. For this purpose, we employ the spin-projection operator formalism and extend the original basis built previously, to be able to handle the parity-odd pieces.

In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way.