A note on a mimetic scalar-tensor cosmological model

A specific Horndeski scalar-gravity mimetic model is investigated within a FLWR space-time. The mimetic scalar field is implemented via a Lagrangian multiplier, and it is shown that the model has equations of motion formally similar to the original simpler mimetic matter model of Chamseddine-Mukhanov-Vikman. Several exact solutions describing inflation, bounces, future time singularities are presented and discussed.Comment: 9 page

One-loop F(R,P,Q) gravity in de Sitter universe

Motivated by the dark energy issue, the one-loop quantization approach for a class of relativistic higher order theories is discussed in some detail. A specific F(R,P,Q) gravity model at the one-loop level in a de Sitter universe is investigated, extending the similar program developed for the case of $F(R)$ gravity. The stability conditions under arbitrary perturbations are derived.Comment: Latex, 10 pages, to appear in J. Phys. A: Math. Theor. (special issue in honor of Prof. S. Dowker

Dirac Functional Determinants in Terms of the Eta Invariant and the Noncommutative Residue

The zeta and eta-functions associated with massless and massive Dirac operators, in a D-dimensional (D odd or even) manifold without boundary, are rigorously constructed. Several mathematical subtleties involved in this process are stressed, as the intrisic ambiguity present in the definition of the associated fermion functional determinant in the massless case and, also, the unavoidable presence (in some situations) of a multiplicative anomaly, that can be conveniently expressed in terms of the noncommutative residue. The ambiguity is here seen to disappear in the massive case, giving rise to a phase of the Dirac determinant - that agrees with very recent calculations appeared in the mathematical literature - and to a multiplicative anomaly - also in agreement with other calculations, in the coinciding situations. After explicit, nontrivial resummation of the mass series expansions involving zeta and eta functions, the results are expressed in terms of quite simple formulas.Comment: Minor changes. Two references added. 24 pages, no figures, LaTeX fil

A non-polynomial gravity formulation for Loop Quantum Cosmology bounce

Recently the so-called mimetic gravity approach has been used to obtain corrections to Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists in adding geometric non-polynomial higher derivative terms to Hilbert-Einstein action, which are nonetheless polynomials and lead to second order differential equation in Friedmann-Lema\^itre-Robertson-Walker spacetimes. Our explicit action turns out to be a realization of the Helling proposal of effective action with infinite number of terms. The model is investigated also in presence of non vanishing cosmological constant and a new exact bounce solution is found and studied.Comment: 7 pages, minor modifications, references added, accepted versio