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Register a new userA cosmological dust model with extended f(chi) gravity
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Introducing a fundamental constant of nature with dimensions of acceleration into the theory of gravity makes it possible to extend gravity in a very consistent manner. At the non-relativistic level a MOND-like theory with a modification in the force sector is obtained, which is the limit of a very general metric relativistic theory of gravity. Since the mass and length scales involved in the dynamics of the whole universe require small accelerations of the order of Milgroms acceleration constant a_0, it turns out that the relativistic theory of gravity can be used to explain the expansion of the universe. In this work it is explained how to use that relativistic theory of gravity in such a way that the overall large-scale dynamics of the universe can be treated in a pure metric approach without the need to introduce dark matter and/or dark energy components.
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In this article we perform a second order perturbation analysis of the gravitational metric theory of gravity $ f(chi) = chi^{3/2} $ developed by Bernal et al. (2011). We show that the theory accounts in detail for two observational facts: (1) the phenomenology of flattened rotation curves associated to the Tully-Fisher relation observed in spiral galaxies, and (2) the details of observations of gravitational lensing in galaxies and groups of galaxies, without the need of any dark matter. We show how all dynamical observations on flat rotation curves and gravitational lensing can be synthesised in terms of the empirically required metric coefficients of any metric theory of gravity. We construct the corresponding metric components for the theory presented at second order in perturbation, which are shown to be perfectly compatible with the empirically derived ones. It is also shown that under the theory being presented, in order to obtain a complete full agreement with the observational results, a specific signature of Riemanns tensor has to be chosen. This signature corresponds to the one most widely used nowadays in relativity theory. Also, a computational program, the MEXICAS (Metric EXtended-gravity Incorporated through a Computer Algebraic System) code, developed for its usage in the Computer Algebraic System (CAS) Maxima for working out perturbations on a metric theory of gravity, is presented and made publicly available.
We investigate the cosmological perturbations in f(T) gravity. Examining the pure gravitational perturbations in the scalar sector using a diagonal vierbien, we extract the corresponding dispersion relation, which provides a constraint on the f(T) ansatzes that lead to a theory free of instabilities. Additionally, upon inclusion of the matter perturbations, we derive the fully perturbed equations of motion, and we study the growth of matter overdensities. We show that f(T) gravity with f(T) constant coincides with General Relativity, both at the background as well as at the first-order perturbation level. Applying our formalism to the power-law model we find that on large subhorizon scales (O(100 Mpc) or larger), the evolution of matter overdensity will differ from LCDM cosmology. Finally, examining the linear perturbations of the vector and tensor sectors, we find that (for the standard choice of vierbein) f(T) gravity is free of massive gravitons.
We perform a detailed dynamical analysis of various cosmological scenarios in extended (varying-mass) nonlinear massive gravity. Due to the enhanced freedom in choosing the involved free functions, this cosmological paradigm allows for a huge variety of solutions that can attract the universe at late times, comparing to scalar-field cosmology or usual nonlinear massive gravity. Amongst others, it accepts quintessence, phantom, or cosmological-constant-like late-time solutions, which moreover can alleviate the coincidence problem. These features seem to be general and non-sensitive to the imposed ansantzes and model parameters, and thus extended nonlinear massive gravity can be a good candidate for the description of nature.
We investigate the cosmological observational test of the extended quintessence model, i.e. a scalar-tensor gravity model with a scalar field potential serving as dark energy, by using the Planck 2018 cosmic microwave background (CMB) data, together with the baryon acoustic oscillations (BAO) and redshift-space distortion (RSD) data. As an example, we consider the model with a Brans-Dicke kinetic term $frac{omega(phi)}{phi} phi_{;mu} phi^{;mu} $ and a quadratic scalar potential $V (phi) = A + B (phi - phi_0) + frac{C}{2} (phi - phi_0)^2$, which reduces to general relativity (GR) in the limit $omega(phi) to infty$, and the cosmological constant in the limit $B=C=0$. In such a model the scalar field typically rolls down the potential and oscillates around the minimum of $V (phi)$. We find that the model parameter estimate for the CMB+BAO+RSD data set is given by $lg alpha = -3.6 _{-0.54}^{+0.66}~ (68%)$, corresponding to $ 3.8 times 10^5 < omega_0 < 9.5 times 10^7~ (68%)$, and $lg C = 4.9 pm 1.4~ (68%) $. However, the GR $Lambda$CDM model can fit the data almost as good as this extended quintessence model, and is favored by the Akaike information criterion (AIC). The variation of the gravitational constant since the epoch of Recombination is constrained to be $0.97 < G_{rm rec}/G_0 < 1.03~ (1 sigma)$. In light of recent report that the CMB data favors a closed universe, we consider the case with non-flat geometry in our fit, and find that the mean value of $Omega_k$ shifts a little bit from $-0.049$ to $-0.036$, and the parameters in our model are not degenerate with $Omega_k$.
Based on thermodynamics, we discuss the galactic clustering of expanding Universe by assuming the gravitational interaction through the modified Newtons potential given by $f(R)$ gravity. We compute the corrected $N$-particle partition function analytically. The corrected partition function leads to more exact equations of states of the system. By assuming that system follows quasi-equilibrium, we derive the exact distribution function which exhibits the $f(R)$ correction. Moreover, we evaluate the critical temperature and discuss the stability of the system. We observe the effects of correction of $f(R)$ gravity on the power law behavior of particle-particle correlation function also. In order to check feasibility of an $f(R)$ gravity approach to the clustering of galaxies, we compare our results with an observational galaxy cluster catalog.
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