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Register a new userLimitations of cosmography in extended theories of gravity
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Added by
Alvaro De La Cruz-Dombriz
Publication date
2016
fields
Physics
and research's language is
English
Authors
Alvaro de la Cruz-Dombriz
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The cosmographic approach, which only relies upon the homogeneity and isotropy of the Universe on large scales, has become an essential tool in dealing with an increasing number of theoretical possibilities for explaining the late-time acceleration of the Universe, ranging from Modified Gravity theories to Dark Energy alternatives passing from testing the cosmological concordance Lambda-CDM model. Despite its generality, we show that this method has a number of shortcomings when trying to adequately reconstruct theories with higher-order derivatives in either the gravitational or the matter sector. Herein some paradigmatic examples of such an inability, explanations of the limitations and prospective cures will be presented.
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Cosmography is an ideal tool to investigate the cosmic expansion history of the Universe in a model-independent way. The equations of motion in modified theories of gravity are usually very complicated; cosmography may select practical models without imposing arbitrary choices a priori. We use the model-independent way to derive $f(z)$ and its derivatives up to fourth order in terms of measurable cosmographic parameters. We then fit those functions into the luminosity distance directly. We perform the MCMC analysis by considering three different sets of cosmographic functions. Using the largest supernovae Ia Pantheon sample, we derive the constraints on the Hubble constant $H_0$ and the cosmographic functions, and find that the former two terms in Taylor expansion of luminosity distance work dominantly in $f(Q)$ gravity.
In the context of extended Teleparallel gravity theories with a 3+1 dimensions Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological solutions. In particular when applied to a Friedmann-Lema^itre-Robertson-Walker geometry in four-dimensional spacetime with standard fluids exclusively. We study different types of gravitational Lagrangians and reconstruct solutions provided by analytical expressions for either the cosmological scale factor or the Hubble parameter. We also show that it is possible to find Lagrangians of this type without a cosmological constant such that the behaviour of the LCDM model is precisely mimicked. The new Lagrangians may also lead to other phenomenological consequences opening up the possibility for new theories to compete directly with other extensions of General Relativity.
The intriguing choice to treat alternative theories of gravity by means of the Palatini approach, namely elevating the affine connection to the role of independent variable, contains the seed of some interesting (usually under-explored) generalizations of General Relativity, the metric-affine theories of gravity. The peculiar aspect of these theories is to provide a natural way for matter fields to be coupled to the independent connection through the covariant derivative built from the connection itself. Adopting a procedure borrowed from the effective field theory prescriptions, we study the dynamics of metric-affine theories of increasing order, that in the complete version include invariants built from curvature, nonmetricity and torsion. We show that even including terms obtained from nonmetricity and torsion to the second order density Lagrangian, the connection lacks dynamics and acts as an auxiliary field that can be algebraically eliminated, resulting in some extra interactions between metric and matter fields.
The debate on gravity theories to extend or modify General Relativity is very active today because of the issues related to ultra-violet and infra-red behavior of Einsteins theory. In the first case, we have to address the Quantum Gravity problem. In the latter, dark matter and dark energy, governing the large scale structure and the cosmological evolution, seem to escape from any final fundamental theory and detection. The state of art is that, up to now, no final theory, capable of explaining gravitational interaction at any scale, has been formulated. In this perspective, many research efforts are devoted to test theories of gravity by space-based experiments. Here we propose straightforward tests by the GINGER experiment, which, being Earth based, requires little modeling of external perturbation, allowing a thorough analysis of the systematics, crucial for experiments where sensitivity breakthrough is required. Specifically, we want to show that it is possible to constrain parameters of gravity theories, like scalar-tensor or Horava-Lifshitz gravity, by considering their post-Newtonian limits matched with experimental data. In particular, we use the Lense-Thirring measurements provided by GINGER to find out relations among the parameters of theories and finally compare the results with those provided by LARES and Gravity Probe-B satellites.
This Thesis is devoted to the study of Metric-Affine Theories of Gravity and Applications to Cosmology. The thesis is organized as follows. In the first Chapter we define the various geometrical quantities that characterize a non-Riemannian geometry. In the second Chapter we explore the MAG model building. In Chapter 3 we use a well known procedure to excite torsional degrees of freedom by coupling surface terms to scalars. Then, in Chapter 4 which seems to be the most important Chapter of the thesis, at least with regards to its use in applications, we present a step by step way to solve for the affine connection in non-Riemannian geometries, for the first time in the literature. A peculiar f(R) case is studied in Chapter 5. This is the conformally (as well as projective invariant) invariant theory f(R)=a R^{2} which contains an undetermined scalar degree of freedom. We then turn our attention to Cosmology with torsion and non-metricity (Chapter 6). In Chapter 7, we formulate the necessary setup for the $1+3$ splitting of the generalized spacetime. Having clarified the subtle points (that generally stem from non-metricity) in the aforementioned formulation we carefully derive the generalized Raychaudhuri equation in the presence of both torsion and non-metricity (along with curvature). This, as it stands, is the most general form of the Raychaudhuri equation that exists in the literature. We close this Thesis by considering three possible scale transformations that one can consider in Metric-Affine Geometry.
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