Some major developments of physics in the last three decades are addressed by highly qualified specialists in different specific fields. They include renormalization problems in QFT, vacuum energy fluctuations and the Casimir effect in different configurations, and a wealth of applications. A number of closely related issues are also considered. The cosmological applications of these theories play a crucial role and are at the very heart of the book; in particular, the possibility to explain in a unified way the whole history of the evolution of the Universe: from primordial inflation to the present day accelerated expansion. Further, a description of the mathematical background underlying many of the physical theories considered above is provided. This includes the uses of zeta functions in physics, as in the regularization problems in QFT already mentioned, specifically in curved space-time, and in Casimir problems as.

Part I QFT and the Casimir Effect.-1. I. Ya. AREFEVA.Colliding Hadrons as Cosmic Membranes and Possible Signatures of Lost Momentum.- 2. M. ASOREY, I. CaveroPeláez and J. M. MuñozCasta.Vacuum energy and the Topology of the Universe.-3. M. BORDAG and I. Pirozhenko.The Low Temperature Corrections to the Casimir Force Between a Sphereand a Plane.- 4. I. BREVIK.Casimir Effect for the Piecewise Uniform String.- 5. I.L. BUCHBINDER, N.G. Pletnev and I.B. Samsonov.N= 2and N= 4Supersymmetric LowEnergy Effective Actions in Three Dimensions.- 6. M. CHAICHIAN.Colour Confinement, the GotoImamuraSchwinger Term and Renormalization Group.- 7. J. GOMIS.NonCentral Extensions of (Super) Poincaré Algebra and (Susy) Electromagnetic Backgrounds.-8. K. A. MILTON, J. Wagner, P. Parashar, I. CaveroPeláez, I. Brevik and S. A. Ellingsen.Multiple Scattering: Dispersion, Temperature Dependence, and Annular Pistons.-Part II Gravity and Cosmology.-9. M. BOUHMADILÓPEZ.Brane Cosmology with an f(R)Contribution.- 10. S. CAPOZZIELLO.f(R)Gravity Matched with Large Scale Structure and Cosmological Observations.- 11. S. CARLONI.An Analysis of the Phase Space of HoavaLifshitz Cosmologies.- 12. C. CORDA.Gravitational Waves Astronomy: a Cornerstone for Gravitational Theories.- 13. R. DI CRISCIENZO, L. Vanzo and S. Zerbini.HamiltonJacobi Method and Gravitation.- 14. K. N. Ananda, S. Carloni and P. K. S. DUNSBY.A Characteristic Signature of Fourth Order Gravity.- 15. V. FARAONI.Horizons and Singularity in Clifton's Spherical Solution of f(R)vacuum.- 16. R. GARATTINI.Gravitational Zero Point Energy and the Induced Cosmological Constant.- 17. P. GONZALEZDÍAZ.Lensing Effects in Ringholes and the Multiverse Black Holes.- 18. L. LUSANNA.Hamiltonian ADM Gravity in NonHarmonic Gauges with Well Defined NonEuclidean 3Spaces:How Much Darkness can be Explained as a Relativistic Inertial Effect?-19. J. Beltrán and A. LÓPEZ MAROTO.Dark Energy and Cosmic Magnetic Fields: Electromagnetic Relics from Inflation.- 20. N. Carlevaro, G. MONTANI and M. Lattanzi.On the Viability of NonAnalytical f(R)Theory.- 21. S. NOJIRI.Towards the Unification of LateTime Acceleration and Inflation by kEssence Model.- 22. N. Deruelle and M. SASAKI. Conformal Equivalence in Classical Gravity: the Example of Veiled General Relativity.- 23. L. SEBASTIANI.FiniteTime Singularities in Modified f(R;G)Gravity and Singularity Avoidance.- 24. P. J. SILVA.Asymptotic Darkness in HoavaLifshitz Gravity.- 25. C. F. SOPUERTA and N. Yunes.Testing Modified Gravity with Gravitational Wave Astronomy.- 26. P. K. TOWNSEND.Gravitons in Flatland.- 27. M. M. SheikhJabbari and A. TUREANU.Very Special Relativity and Noncommutative SpaceTime.-Part III Zeta Functions in Physics and Mathematics.-28. G. Fucci, K. KIRSTEN and P. Morales.Pistons Modelled by Potentials.- 29. V. Moretti.Localfunctions, stressenergy tensor, field fluctuations, and all that, in curved static spacetime.- 30. V. Muñoz and R. PÉREZMARCO.Ergodic Solenoidal Geometry.- 31. A. VOROS.ZetaRegularization and Exact WKB Method for a General 1D Schrödinger equation.- 32. G. Cognola and S. ZERBINI.Generalized Zeta Function Regularization and the Multiplicative Anomaly.-Part IV Nonstandard approaches.-33. R. M. SANTILLI.Isominkowskian Geometry for Interior Dynamical Problems.- 34. L. YING.Nuclear Fusion Drives Cosmic Expansion.-Index