2014/01/01 by L Reverberi, Reverberi, Lorenzo
Earth and Planetary Sciences · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1406.6943
openalex publication_date 2014/01/01 · openalex created_date 2022/09/11 · openalex updated_date 2026/07/28
Among modified theories of gravitation, f (R) theories are possibly the \nmost straightforward and “natural” purely geometric extension of GR. The \nfirst appearance of modified gravity theories dates back to the 1920’s [1, 2], \nalthough their relevance and popularity vastly increased about 40 years \nago, when pioneering works [3–5] showed the possibility of generating the \nearly inflationary period with quadratic theories, which arise naturally from \nquantum corrections in curved spacetime. \nAfter the discovery of the cosmic acceleration [6–9], new life was infused \ninto f (R) theories, sparked by the early works [10–14]. These models were \nsoon realised to suffer from severe instabilities [15, 16], because the additional \nscalar degree of freedom acquires an imaginary mass. During the \nfollowing years, an impressive amount of work was directed to determining \nthe cosmological viability conditions of f (R) models [17–26]. Clearly, despite \nthe conceptual simplicity of f (R) theories, the additional dynamics and the \nhigher-order equations make it difficult – and fun – to come up with “good” \nmodels to model dark energy. \nFurthermore, these models must be tested in a variety of cosmological and \nastrophysical situations, and may lead to important detectable signatures \nwhich could in principle be observed soon. As important as inventing new \nmodels is, finding new ways to constrain and even exclude them is no \nsmaller task. It is believed that f (R) models can be considered as low-energy \nphenomenological limits of some more fundamental theory such as string \ntheory, etc. [27–29]. Every step towards the “right” f (R) model may very \nwell be a step towards the “right” theory of quantum gravity, so there is no \noverestimating the relevance of any result in this direction. This has been \nprecisely the intent of my work. \nChapter 1 is devoted to introducing the vacuum energy problem. After \na brief review of the standard cosmological scenario and of the main observational \nindications for a vacuum energy component, I present a few \nof the most important theoretical models proposed to explain the cosmic \nacceleration, from both the modified matter (dark energy) and modified \ngravity standpoints. \nIn Chapter 2, I study the radiation-dominated epoch in R + R2 gravity, \ndiscussing the modified curvature dynamics analytically and numerically. \nThe curvature scalar exhibits fast oscillations around some power-law behaviour \nwhich may or may not correspond to the standard GR solution. These curvature oscillations are however damped due to gravitational particle production \neffects, so that eventually the solutions relax to the GR ones, but with \nan additional relic density of gravitationally produced particles which can in \nprinciple give some imprint on the cosmological evolution and perhaps even \nmake up an effective mechanism to produce dark matter. \nIn Chapter 3, I investigate the formation of curvature singularities inside \nastronomical contracting systems within the framework of two recently \nproposed f (R) models [30, 31], studying the problem analytically and comparing \nmy estimates with exact numerical results. I show that such infinite-R, \nfinite-r singularities can arise in a number of physically reasonable systems, \nand derived the time scales for this to happen. \nNaturally, as R approaches infinity, one expects high-curvature effects \nto come into play. In Chapter 4, I study the curvature evolution in the \nmodels [30, 31] with the addition of an R2 term (irrelevant for cosmology, \nbut important for large R). I show that this term prevents the formation of \nthe curvature singularity while still allowing R to reach very large values, \nand in turn may lead to strong particle production. I calculate the particle \nproduction rate, which depends on both physical properties of the system \nand on model parameters. These high-energy cosmic rays could in principle \nbe detectable and, if observed, would represent a unique model-dependent \nsignature. Some unexplained features in the cosmic ray spectrum, e.g. \nthe so-called “ankle” [32–35], might find a fascinating explanation in this \nframework. \nIn Chapter 5, I discuss another interesting and unexpected consequence of \nthese high-R solutions, namely the possibility of gravitational repulsion in \ncontracting systems. 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