Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

f(R) theories

Extended Theories of Gravity

Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution

One century after its formulation, Einstein's general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

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Testing general relativity with present and future astrophysical observations

We review the problem of dark energy, including a survey of theoretical models and some aspects of numerical studies

Dark Energy

We consider the early time cosmology of fðRÞ theories in Palatini formalism and study the conditions that guarantee the existence of homogeneous and isotropic models that avoid the big bang singularity. We show that for such models the big bang singularity can be replaced by a cosmic bounce without violating any energy condition. In fact, the bounce is possible even for pressureless dust. We give a characterization of such models and discuss their dynamics in the region near the bounce. We also find that power-law Lagrangians with a finite number of terms may lead to nonsingular universes, which contrasts with the infinite-series Palatini fðRÞ Lagrangian that one needs to fully capture the effective dynamics of loop quantum cosmology. We argue that these models could also avoid the formation of singularities during stellar gravitational collapse. DOI: 10.1103/PhysRevD.80.024016

http://digital.csic.es/bitstream/10261/16694/3/Bouncing_cosmologies.pdf

Bouncing cosmologies in Palatini f(R) gravity

We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini f(R) and f(R,R{sub {mu}{nu}R}{sup {mu}{nu}}) theories of gravity with a perfect fluid and consider the existence of nonsingular bouncing solutions in the early universe. We find that all f(R) models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model R+aR{sup 2}/R{sub P}+R{sub {mu}{nu}R}{sup {mu}{nu}/}R{sub P} exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for a 1) sources of matter/energy or extra degrees of freedom.

/pdf/isotropic-and-anisotropic-bouncing-cosmologies-in-palatini-4ydujoo1c8.pdf

Isotropic and Anisotropic Bouncing Cosmologies in Palatini Gravity

Terrestrial diatom communities are dynamic, partially unknown and potential bioindicators of the soil ecological quality. Many different sampling methods for soil algae can be found in the literature. However, so far none of them have been tested for their performance with soil diatom communities and given recommendations for obtaining a representative diatom sample for bioindication purposes. The aim of this study was to develop a standardized sampling protocol for terrestrial diatoms and test the spatial variability of the communities to ensure the representativeness of the samples obtained. Sampling was performed in four different sampling sites in the Attert River basin (NW Luxembourg), using metal cylinders (O 5.6 cm) to extract soil cores. Our objective was to determine whether a single cylinder or a mix of several is needed to obtain a representative sample of the community of a certain site. Different statistical analyses (ANOVA, PerMANOVA and Mantel test) have been carried out to assess the reliability of the sampling method and give some recommendations for a routine sampling. Inside each site, no differences were found between single and mixed samples for their species composition or diatom-based quality index values. However, the species richness and diversity had significant differences in the only natural (forest) sampled site. The method here presented has proven to be useful for obtaining representative soil diatom samples and its use is recommended following the advices presented in this work.

A standard method for the routine sampling of terrestrial diatom communities for soil quality assessment

We show that there exist modified theories of gravity in which the metric satisfies second-order equations and in which the Big Bang singularity is replaced by a cosmic bounce without violating any energy condition. In fact, the bounce is possible even for presureless dust. We give a characterization of such theories, which are formulated in the Palatini formalism, and discuss their dynamics in the region near the bounce. We consider spatially flat and non-flat homogeneous and isotropic universes.

Avoiding the Big Bang Singularity with Palatini f(R) Theories

With 44 figures and 2 tables Abstract: The analysis of samples taken in different aerial microhabitats in Europe (Germany and Luxembourg) revealed the presence of a new and interesting small-celled naviculoid diatom species. Based on detailed light and scanning electron microscopy, one taxon previously misidentified as Sellaphora saugerresii is here described as Mayamaea petersenii sp. nov. The ecological preferences and a detailed analysis of its frustule ultrastructure lead to propose its generic placement in Mayamaea, followed by a discussion concerning key characters of the genera Sellaphora, Eolimna and Chamaepinnularia.

Carlos Barragán

Papers

Bouncing cosmologies in Palatini f(R) gravity

Isotropic and Anisotropic Bouncing Cosmologies in Palatini Gravity

A standard method for the routine sampling of terrestrial diatom communities for soil quality assessment

Avoiding the Big Bang Singularity with Palatini f(R) Theories

Mayamaea petersenii sp. nov., a new diatom from European aerial habitats and a brief appraisal on the morphological diversity of the genus