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Register a new userCan Gravity Probe B usefully constrain torsion gravity theories?
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In most theories of gravity involving torsion, the source for torsion is the intrinsic spin of matter. Since the spins of fermions are normally randomly oriented in macroscopic bodies, the torsion generated is normally negligible. However, in a recent paper, Mao et al. point out that there is a class of theories in which the angular momentum of macroscopic spinning bodies generates a significant amount of torsion. They argue that by the principle of action equals reaction, one would expect the angular momentum of test bodies to couple to a background torsion field, and therefore the precession of the GPB gyroscopes should be affected in these theories by the torsion generated by the Earth. We show that in fact the principle of action equals reaction does not apply to these theories. We examine in detail a generalization of the Hayashi-Shirafuji theory suggested by Mao et al. called Einstein-Hayashi-Shirafuji theory. There are a variety of differe
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In this manuscript we will present the theoretical framework of the recently proposed infinite derivative theory of gravity with a non-symmetric connection. We will explicitly derive the field equations at the linear level and obtain new solutions with a non-trivial form of the torsion tensor in the presence of a fermionic source, and show that these solutions are both ghost and singularity-free.
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.
We consider f(R) modified gravity theories in the metric variation formalism and attempt to reconstruct the function f(R) by demanding a background LCDM cosmology. In particular we impose the following requirements: a. A background cosmic history H(z) provided by the usual flat LCDM parametrization though the radiation (w_eff=1/3), matter (w_eff=0) and deSitter (w_eff=-1) eras. b. Matter and radiation dominate during the `matter and `radiation eras respectively i.e. Omega_m =1 when w_eff=0 and Omega_r=1 when w_eff=1/3. We have found that the cosmological dynamical system constrained to obey the LCDM cosmic history has four critical points in each era which correspondingly lead to four forms of f(R). One of them is the usual general relativistic form f(R)=R-2Lambda. The other three forms in each era, reproduce the LCDM cosmic history but they do not satisfy requirement b. stated above. Only one of these forms (different from general relativity) is found to be an attractor of the dynamical cosmological evolution. It has (Omega_DE=1, Omega_r=0, Omega_m=0) throughout the evolution. Its phase space trajectory is numerically obtained.
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