Search Results (4)

We resume our analysis of Newtonian Fractional-Dimension Gravity (NFDG), an alternative gravitational model that does not require the dark matter (DM) paradigm. We add three more galaxies (NGC 6946, NGC 3198, NGC 2841) to the catalog of those studied with NFDG methods. Once again, NFDG can successfully reproduce the observed rotation curves by using a variable fractional dimension $D\left(R\right)$, as with the nine other galaxies previously studied with these methods. In addition, we introduce a mass-dimension field equation for our model, which is capable of deriving the fractional mass dimension $D_m\left(R\right)$ from a single equation, as opposed to the previous $D\left(R\right)$, which was obtained simply by matching the experimental rotational velocity data for each galaxy. While the NFDG predictions computed with this new $D_m\left(R\right)$ dimension are not as accurate as those based on the original $D\left(R\right)$, they nevertheless confirm the validity of our fractional-dimension approach. Three previously studied galaxies (NGC 7814, NGC 6503, NGC 3741) were analyzed again with these new methods, and their structure was confirmed to be free from any dark matter components. Full article

Our main goal here is to conduct a comparative analysis between the well-known MOND theory and a more recent model called the $\kappa$-model. An additional connection, between the $\kappa$-model and two other novel MOND-type theories, Newtonian Fractional-Dimension Gravity (NFDG) and Refracted Gravity (RG), is likewise presented. All these models are built to overtake the DM paradigm, or at least to strongly reduce the dark matter content. Whereas they rely on different formalisms, however, all four seem to suggest that the universal parameter, $a_0$, appearing in MOND theory could intrinsically be correlated to either the sole baryonic mean mass density (RG and $\kappa$-model) and/or to the dimension of the object under consideration (NFDG and $\kappa$-model). We then confer to parameter $a_0$ a more flexible status of multiscale parameter, as required to explain the dynamics together in galaxies and in galaxy clusters. Eventually, the conformal gravity theory (CFT) also seems to have some remote link with the $\kappa$-model, even though the first one is an extension of general relativity, and the second one is Newtonian in essence. The $\kappa$-model has been tested on a small sample of spiral galaxies and in galaxy clusters. Now, we test this model on a large sample of galaxies issued from the SPARC database. Full article

We apply Newtonian fractional-dimension gravity (NFDG), an alternative gravitational model, to some notable cases of galaxies with little or no dark matter. In the case of the ultra-diffuse galaxy AGC 114905, we show that NFDG methods can effectively reproduce the observed rotation curve using a variable fractional dimension $D\left(R\right)$, as was performed for other galaxies in previous studies. For AGC 114905, we obtain a variable dimension in the range $D\approx$ 2.2–3.2, but our fixed D = 3 curve can still fit all the experimental data within their error bars. This confirms other studies indicating that the dynamics of this galaxy can be described almost entirely by the baryonic mass distribution alone. In the case of NGC 1052-DF2, we use an argument based on the NFDG extension of the virial theorem applied to the velocity dispersion of globular clusters showing that, in general, discrepancies between observed and predicted velocity dispersions can be attributed to an overall fractal dimension $D<3$ of the astrophysical structure considered, and not to the presence of dark matter. For NGC 1052-DF2, we estimate $D\approx 2.9$, thus confirming that this galaxy almost follows standard Newtonian behavior. We also consider the case of the Bullet Cluster merger (1E0657-56), assumed to be one of the strongest proofs of dark matter existence. A simplified but effective NFDG model of the collision shows that the observed infall velocity of this merger can be explained by a fractional dimension of the system in the range $D\simeq$ 2.4–2.5, again, without using any dark matter. Full article

This paper presents a relativistic version of Newtonian Fractional-Dimension Gravity (NFDG), an alternative gravitational model recently introduced and based on the theory of fractional-dimension spaces. This extended version—Relativistic Fractional-Dimension Gravity (RFDG)—is based on other existing theories in the literature and might be useful for astrophysical and cosmological applications. In particular, in this work, we review the mathematical theory for spaces with non-integer dimensions and its connections with the non-relativistic NFDG. The Euler–Lagrange equations for scalar fields can also be extended to spaces with fractional dimensions, by adding an appropriate weight factor, and then can be used to generalize the Laplacian operator for rectangular, spherical, and cylindrical coordinates. In addition, the same weight factor can be added to the standard Hilbert action in order to obtain the field equations, following methods used for scalar-tensor models of gravity, multi-scale spacetimes, and fractional gravity theories. We then apply the field equations to standard cosmology and to the Friedmann-Lemaître-Robertson-Walker metric. Using a suitable weight $v_t\left(t\right)$, depending on the synchronous time t and on a single time-dimension parameter ${\alpha }_t$, we extend the Friedmann equations to the RFDG case. This allows for the computation of the scale factor $a\left(t\right)$ for different values of the fractional time-dimension ${\alpha }_t$ and the comparison with standard cosmology results. Future additional work on the subject, including studies of the cosmological late-time acceleration, type Ia supernovae data, and related dark energy theory will be needed to establish this model as a relativistic alternative theory of gravity. Full article