Modified Einstein and Finsler Like Theories on Tangent Lorentz Bundles

We study modifications of general relativity, GR, with nonlinear dispersion relations which can be geometrized on tangent Lorentz bundles. Such modified gravity theories, MGTs, can be modeled by gravitational Lagrange density functionals $f(\mathbf{R},\mathbf{T},F)$ with generalized/ modified scalar curvature $\mathbf{R}$, trace of matter field tensors $\mathbf{T}$ and modified Finsler like generating function $F$. In particular, there are defined extensions of GR with extra dimensional "velocity/ momentum" coordinates. For four dimensional models, we prove that it is possible to decouple and integrate in very general forms the gravitational fields for $f(\mathbf{R},\mathbf{T},F)$-modified gravity using nonholonomic 2+2 splitting and nonholonomic Finsler like variables $F$. We study the modified motion and Newtonian limits of massive test particles on nonlinear geodesics approximated with effective extra forces orthogonal to the four--velocity. We compute the constraints on the magnitude of extra-accelerations and analyze perihelion effects and possible cosmological implications of such theories. We also derive the extended Raychaudhuri equation in the framework of a tangent Lorentz bundle. Finally, we speculate on effective modelling of modified theories by generic off-diagonal configurations in Einstein and/or MGTs and Finsler gravity. We provide some examples for modified stationary (black) ellipsoid configurations and locally anisotropic solitonic backgrounds.Comment: latex2e, 20 pages; version accepted to IJMPD; changed title and modifications following requests of refere

Testing gravity with non-Gaussianity

We show that modified gravity presents distinctive nonlinear features on the Cosmic Microwave Background (CMB) anisotropies comparing with General Relativity (GR). We calculate the contribution to the CMB non-Gaussianity from nonlinear Sachs-Wolfe effect in $f(R)$ gravity and show that, contrary to GR's contribution which is typically $\lesssim \mathcal{O}(1)$, the contribution in $f(R)$ gravity is sensitive to the nonlinear structure of $f(R)$ and can be large in principle. Optimistically, this gives an alternative origin for the possibly observed large CMB non-Gaussianities besides the primordial ones. On the other hand, such nonlinear features can be employed to provide a new cosmological test of $f(R)$ or other modified theories of gravitation, which is unique and independent of previously known tests.Comment: 4 pages, 1 figure, v2 to match the published versio

Constraining Modified Gravity with Euclid

Future proposed satellite missions as Euclid can offer the opportunity to test general relativity on cosmic scales through mapping of the galaxy weak lensing signal. In this paper we forecast the ability of these experiments to constrain modified gravity scenarios as those predicted by scalar-tensor and $f(R)$ theories. We found that Euclid will improve constraints expected from the PLANCK satellite on these modified gravity models by two orders of magnitude. We discuss parameter degeneracies and the possible biases introduced by modified gravity

Inference in Regression Models with Many Regressors

We investigate the behavior of various standard and modified F, LR and LM tests in linear homoskedastic regressions, adapting an alternative asymptotic framework where the number of regressors and possibly restrictions grows proportionately to the sample size. When restrictions are not numerous, the rescaled classical test statistics are asymptotically chi-squared irrespective of whether there are many or few regressors. However, when restrictions are numerous, standard asymptotic versions of classical tests are invalid. We propose and analyze asymptotically valid versions of the classical tests, including those that are robust to the numerosity of regressors and restrictions. The local power of all asymptotically valid tests under consideration turns out to be equal. The "exact" F test that appeals to critical values of the F distribution is also asymptotically valid and robust to the numerosity of regressors and restrictions.Alternative asymptotic theory, linear regression, test size, test power, F test, Wald test, Likelihood Ratio test, Lagrange Multiplier test

Modified f(G) gravity models with curvature-matter coupling

A modified f(G) gravity model with coupling between matter and geometry is proposed, which is described by the product of the Lagrange density of the matter and an arbitrary function of the Gauss-Bonnet term. The field equations and the equations of motion corresponding to this model show the non-conservation of the energy-momentum tensor, the presence of an extra-force acting on test particles and the non-geodesic motion. Moreover, the energy conditions and the stability criterion at de Sitter point in the modified f(G) gravity models with curvature-matter coupling are derived, which can degenerate to the well-known energy conditions in general relativity. Furthermore, in order to get some insight on the meaning of these energy conditions, we apply them to the specific models of f(G) gravity and the corresponding constraints on the models are given. In addition, the conditions and the candidate for late-time cosmic accelerated expansion in the modified f(G) gravity are studied by means of conditions of power-law expansion and the equation of state of matter less than -1/ 3 .Comment: 13 pages, 4 figure

Non-analytical power law correction to the Einstein-Hilbert action: gravitational wave propagation

We analyze the features of the Minkowskian limit of a particular non-analytical f(R) model, whose Taylor expansion in the weak field limit does not hold, as far as gravitational waves (GWs) are concerned. We solve the corresponding Einstein equations and we find an explicit expression of the modified GWs as the sum of two terms, i.e. the standard one and a modified part. As a result, GWs in this model are not transverse, and their polarization is different from that of General Relativity. The velocity of the GW modified part depends crucially on the parameters characterizing the model, and it mostly results much smaller than the speed of light. Moreover, this investigation allows one to further test the viability of this particular f(R) gravity theory as far as interferometric observations of GWs are concerned.Comment: 18 pages, 3 figure

Using approximate roots for irreducibility and equi-singularity issues in K[[x]][y]

We provide an irreducibility test in the ring K[[x]][y] whose complexity is quasi-linear with respect to the valuation of the discriminant, assuming the input polynomial F square-free and K a perfect field of characteristic zero or greater than deg(F). The algorithm uses the theory of approximate roots and may be seen as a generalization of Abhyankhar's irreducibility criterion to the case of non algebraically closed residue fields. More generally, we show that we can test within the same complexity if a polynomial is pseudo-irreducible, a larger class of polynomials containing irreducible ones. If $F$ is pseudo-irreducible, the algorithm computes also the valuation of the discriminant and the equisingularity types of the germs of plane curve defined by F along the fiber x=0.Comment: 51 pages. Title modified. Slight modifications in Definition 5 and Proposition 1

Asphalt Mixture with Scrap Tire Rubber and Nylon Fiber from Waste Tires: Laboratory Performance and Preliminary M‐E Design Analysis

Scrap tire rubber and nylon fiber are waste materials that could potentially be recycled and used to improve the mechanical properties of asphalt pavement. The objective of this research was to investigate the properties of scrap tire rubber and nylon fiber (R‐F) modified warm mix asphalt mixture (WMA). The high‐temperature performance was estimated by the Hamburg wheel-tracking testing (HWTT) device. The low‐temperature cracking performance was evaluated by the disk‐shaped compact tension (DCT) test and the indirect tensile strength (IDT) test. The stress and strain relationship was assessed by the dynamic modulus test at various temperatures and frequencies. The extracted asphalt binder was evaluated by the dynamic shear rheometer (DSR). Pavement distresses were predicted by pavement mechanistic‐empirical (M‐E) analysis. The test results showed that: (1) The R‐F modified WMA had better high‐temperature rutting performance. The dynamic modulus of conventional hot mix asphalt mixture (HMA) was 21.8% ~ 103% lower than R‐ F modified WMA at high temperatures. The wheel passes and stripping point of R‐F modified WMA were 2.17 and 5.8 times higher than those of conventional HMA, respectively. Moreover, the R‐F modified warm mix asphalt had a higher rutting index than the original asphalt. (2) R‐F modified WMA had better cracking resistance at a low temperature. The failure energy of the R‐F modified WMA was 24.3% higher than the conventional HMA, and the fracture energy of the R‐F modified WMA was 7.7% higher than the conventional HMA. (3) The pavement distress prediction results showed the same trend compared with the laboratory testing performance in that the R‐F modified WMA helped to improve the IRI, AC cracking, and rutting performance compared with the conventional HMA. In summary, R‐F modified WMA can be applied in pavement construction

Implications of the Holst term in a f(R)f(R) theory with torsion

We analyze a modified $f(R)$ theory of gravity in the Palatini formulation, when an Holst term endowed with a dynamical Immirzi field is included. We study the basic features of the model, especially in view of liminating the torsion field via the Immirzi field and the scalar-tensor degrees of freedom of the $f(R)$ model. The main task of this study is the investigation of the morphology of the gravitational wave polarization when their coupling to a circle of test particles is considered. We first observe that the dynamics of the scalar mode of the $f(R)$ Lagrangian is frozen out, since its first order term identically vanishes. This allows a detailed characterization of the linearized theory, which outlines the emergence of a modified Newtonian potential in the static limit, and when time independence is relaxed a standard gravitational wave plus the scalar wave associated to the Immirzi field. Investigating the effect of the coupling of this scalar-tensor wave on a circle of test particles, we arrive to define two effective gravitational polarizations, corresponding to an equivalent phenomenological wave, whose morphology is anomalous with respect the standard case of General Relativity. In fact, the particle circle suffers modifications as it was subjected to modified plus and cross modes, whose specific features depend on the model free parameters and are, in principle, detectable via a data analysis procedure.Comment: 8 pages, 4 figures, accepted for publication in Physical Review