On Optimization Modulo Theories, MaxSMT and Sorting Networks

Optimization Modulo Theories (OMT) is an extension of SMT which allows for finding models that optimize given objectives. (Partial weighted) MaxSMT --or equivalently OMT with Pseudo-Boolean objective functions, OMT+PB-- is a very-relevant strict subcase of OMT. We classify existing approaches for MaxSMT or OMT+PB in two groups: MaxSAT-based approaches exploit the efficiency of state-of-the-art MAXSAT solvers, but they are specific-purpose and not always applicable; OMT-based approaches are general-purpose, but they suffer from intrinsic inefficiencies on MaxSMT/OMT+PB problems. We identify a major source of such inefficiencies, and we address it by enhancing OMT by means of bidirectional sorting networks. We implemented this idea on top of the OptiMathSAT OMT solver. We run an extensive empirical evaluation on a variety of problems, comparing MaxSAT-based and OMT-based techniques, with and without sorting networks, implemented on top of OptiMathSAT and {\nu}Z. The results support the effectiveness of this idea, and provide interesting insights about the different approaches.Comment: 17 pages, submitted at Tacas 1

Beyond-one-loop quantum gravity action yielding both inflation and late-time acceleration

A unified description of early-time inflation with the current cosmic acceleration is achieved by means of a new theory that uses a quadratic model of gravity, with the inclusion of an exponential $F(R)$-gravity contribution for dark energy. High-curvature corrections of the theory come from higher-derivative quantum gravity and yield an effective action that goes beyond the one-loop approximation. It is shown that, in this theory, viable inflation emerges in a natural way, leading to a spectral index and tensor-to-scalar ratio that are in perfect agreement with the most reliable Planck results. At low energy, late-time accelerated expansion takes place. As exponential gravity, for dark energy, must be stabilized during the matter and radiation eras, we introduce a curing term in order to avoid nonphysical singularities in the effective equation of state parameter. The results of our analysis are confirmed by accurate numerical simulations, which show that our model does fit the most recent cosmological data for dark energy very precisely.Comment: 20 pages, to appear in NP

Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion

A theory of exponential modified gravity which explains both early-time inflation and late-time acceleration, in a unified way, is proposed. The theory successfully passes the local tests and fulfills the cosmological bounds and, remarkably, the corresponding inflationary era is proven to be unstable. Numerical investigation of its late-time evolution leads to the conclusion that the corresponding dark energy epoch is not distinguishable from the one for the $\Lambda$CDM model. Several versions of this exponential gravity, sharing similar properties, are formulated. It is also shown that this theory is non-singular, being protected against the formation of finite-time future singularities. As a result, the corresponding future universe evolution asymptotically tends, in a smooth way, to de Sitter space, which turns out to be the final attractor of the system.Comment: 22 pages, 10 figures, version to appear in PR

Cosmic history of viable exponential gravity: Equation of state oscillations and growth index from inflation to dark energy era

A generic feature of viable $F(R)$ gravity is investigated: It is demonstrated that during the matter dominated era the large frequency oscillations of the effective dark energy may influence the behavior of higher derivatives of the Hubble parameter with the risk to produce some singular unphysical solutions at high redshift. This behavior is explicitly analyzed for realistic $F(R)$ models, in particular, exponential gravity and a power form model. To stabilize such oscillations, we consider the additional modification of the models via a correction term which does not destroy the viability properties. A detailed analysis on the future evolution of the universe and the evolution history of the growth index of the matter density perturbations are performed. Furthermore, we explore two applications of exponential gravity to the inflationary scenario. We show how it is possible to obtain different numbers of $e$-folds during the early-time acceleration by making different choices of the model parameters in the presence of ultrarelativistic matter, which destabilizes inflation and eventually leads to the exit from the inflationary stage. We execute the numerical analysis of inflation in two viable exponential gravity models. It is proved that at the end of the inflation, the effective energy density and curvature of the universe decrease and thus a unified description between inflation and the $\Lambda$CDM-like dark energy dominated era can be realized.Comment: 35 pages, 23 figures, version accepted for publication in Classical and Quantum Gravit

Unification of Constant-roll Inflation and Dark Energy with Logarithmic R2R^2-corrected and Exponential F(R)F(R) Gravity

In this paper we investigate how to describe in a unified way a constant-roll inflationary era with a dark energy era, by using the theoretical framework of $F(R)$ gravity. To this end, we introduce some classes of appropriately chosen $F(R)$ gravity models, and we examine in detail how the unification of early and late-time acceleration eras can be achieved. We study in detail the inflationary era, and as we demonstrate it is possible to achieve a viable inflationary era, for which the spectral index of primordial curvature perturbations and the scalar-to-tensor ratio can be compatible with the latest observational data. In addition, the graceful exit issue is briefly discussed for a class of models. Finally, we discuss the dark energy oscillations issue, and we investigate which model from one of the classes we introduced, can produce oscillations with the smallest amplitude.Comment: Nuclear Physics B accepte

The instabilities and (anti)-evaporation of Schwarzschild-de Sitter black holes in modified gravity

We investigate the future evolution of Nariai black hole which is extremal limit of Schwarzschild-de Sitter one in modified gravity. The perturbations equations around Nariai black hole are derived in static and cosmological patches for general $F(R)$-gravity. The analytical and numerical study of several realistic $F(R)$-models shows the occurence of rich variety of scenarios: instabilities, celebrated Hawking evaporation and anti-evaporation of black hole. The realization of specific scenario depends on the model under consideration. It is remarkable that the presence of such primordial black holes at current universe may indicate towards the modified gravity which supports the anti-evaporation as preferrable model. As some generalization we extend the study of Nariai black hole evolution to modified Gauss-Bonnet gravity. The corresponding perturbations equations turn out to be much more complicated than in the case of $F(R)$ gravity. For specific example of modified Gauss-Bonnet gravity we demonstrate that Nariai solution maybe stable.Comment: 23 pages, 10 figures, last version, accepted for publication in PR