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Cosmology, Quantum Vacuum and Zeta Functions

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.
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Table of Contents

Part I QFT and the Casimir Effect.- 1. I. Ya. AREF'EVA. Colliding Hadrons as Cosmic Membranes and Possible Signatures of Lost Momentum.- 2. M. ASOREY, I. Cavero-Pelaez and J. M. Munoz-Casta. Vacuum energy and the Topology of the Universe.-3. M. BORDAG and I. Pirozhenko. The Low Temperature Corrections to the Casimir Force Between a Sphere and a Plane.- 4. I. BREVIK. Casimir Effect for the Piecewise Uniform String.- 5. I.L. BUCHBINDER, N.G. Pletnev and I.B. Samsonov. N = 2 and N = 4 Supersymmetric Low-Energy Effective Actions in Three Dimensions.- 6. M. CHAICHIAN. Colour Confinement, the Goto-Imamura-Schwinger Term and Renormalization Group.- 7. J. GOMIS. Non-Central Extensions of (Super) Poincare Algebra and (Susy) Electromagnetic Backgrounds.- 8. K. A. MILTON, J. Wagner, P. Parashar, I. Cavero-Pelaez, I. Brevik and S. A. Ellingsen. Multiple Scattering: Dispersion, Temperature Dependence, and Annular Pistons.- Part II Gravity and Cosmology.- 9. M. BOUHMADI-LOPEZ. 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 Horava-Lifshitz Cosmologies.- 12. C. CORDA. Gravitational Waves Astronomy: a Cornerstone for Gravitational Theories.- 13. R. DI CRISCIENZO, L. Vanzo and S. Zerbini. Hamilton-Jacobi 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. GONZALEZ-DIAZ. Lensing Effects in Ringholes and the Multiverse Black Holes.- 18. L. LUSANNA. Hamiltonian ADM Gravity in Non-Harmonic Gauges with Well Defined Non-Euclidean 3-Spaces: How Much Darkness can be Explained as a Relativistic Inertial Effect?- 19. J. Beltran and A. LOPEZ MAROTO. Dark Energy and Cosmic Magnetic Fields: Electromagnetic Relics from Inflation.- 20. N. Carlevaro, G. MONTANI and M. Lattanzi. On the Viability of Non-Analytical f(R)-Theory.- 21. S. NOJIRI. Towards the Unification of Late-Time Acceleration and Inflation by k-Essence Model.- 22. N. Deruelle and M. SASAKI. Conformal Equivalence in Classical Gravity: the Example of "Veiled" General Relativity.- 23. L. SEBASTIANI. Finite-Time Singularities in Modified f(R;G)-Gravity and Singularity Avoidance.- 24. P. J. SILVA. Asymptotic Darkness in Horava-Lifshitz 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. Sheikh-Jabbari and A. TUREANU. Very Special Relativity and Noncommutative Space-Time.- Part III Zeta Functions in Physics and Mathematics.-28. G. Fucci, K. KIRSTEN and P. Morales. Pistons Modelled by Potentials.- 29. V. Moretti. Local ζ-functions, stress-energy tensor, field fluctuations, and all that, in curved static spacetime.- 30. V. Munoz and R. PEREZ-MARCO. Ergodic Solenoidal Geometry.- 31. A. VOROS. Zeta-Regularization and Exact WKB Method for a General 1D Schroedinger equation.- 32. G. Cognola and S. ZERBINI. Generalized Zeta Function Regularization and the Multiplicative Anomaly.- Part IV Non-standard approaches.- 33. R. M. SANTILLI. Isominkowskian Geometry for Interior Dynamical Problems.- 34. L. YING. Nuclear Fusion Drives Cosmic Expansion.- Index


From the reviews: "This book in part is about on some technology concerning the local zeta function applied to quantum field theory in curved static (thermal) spacetime to regularize the stress energy tensor and the field fluctuations. ... I find this book extremely useful and important, because it signifies the beauty of a mathematical technique in physics in general. I recommend this book for you it is an amazing reading!" (Philosophy, Religion and Science Book Reviews,, January, 2014)

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