We consider the recently estimated corrections \Delta\dot\varpi to the Newtonian/Einsteinian secular precessions of the longitudes of perihelia \varpi of several planets of the Solar System in order to evaluate whether they are compatible with the predicted precessions due to models of long-range modified gravity put forth to account for certain features of the rotation curves of galaxies without resorting to dark matter. In particular, we consider a logarithmic-type correction and a f(R) inspired power-law modification of the Newtonian gravitational potential. The results obtained by taking the ratio of the apsidal rates for different pairs of planets show that the modifications of the Newtonian potentials examined in this paper are not compatible with the secular extra-precessions of the perihelia of the Solar System's planets estimated by E.V. Pitjeva as solve-for parameters processing almost one century of data with the latest EPM ephemerides.
Deep Dive into Solar System tests of some models of modified gravity proposed to explain galactic rotation curves without dark matter.
We consider the recently estimated corrections \Delta\dot\varpi to the Newtonian/Einsteinian secular precessions of the longitudes of perihelia \varpi of several planets of the Solar System in order to evaluate whether they are compatible with the predicted precessions due to models of long-range modified gravity put forth to account for certain features of the rotation curves of galaxies without resorting to dark matter. In particular, we consider a logarithmic-type correction and a f(R) inspired power-law modification of the Newtonian gravitational potential. The results obtained by taking the ratio of the apsidal rates for different pairs of planets show that the modifications of the Newtonian potentials examined in this paper are not compatible with the secular extra-precessions of the perihelia of the Solar System’s planets estimated by E.V. Pitjeva as solve-for parameters processing almost one century of data with the latest EPM ephemerides.
Dark matter and dark energy are, possibly, the most severe theoretical issues that modern astrophysics and cosmology have to face, since the available observations seem to question the model of gravitational interaction on a scale larger than the Solar System. In fact, the data coming from the galactic rotation curves of spiral galaxies (Binney and Tremaine 1987) cannot be explained on the basis of Newtonian gravity or General Relativity (GR) if one does not introduce invisible dark matter compensating for the observed inconsistency of the Newtonian dynamics of stars. Likewise, since 1933, when Zwicky (1933) studied the velocity dispersion in the Coma cluster, there is the common agreement on the fact that the dynamics of cluster of galaxies is poorly understood on the basis of Newtonian gravity or GR (Peebles 1993;Peacock 1999) if the dark matter is not taken into account. In order to reconcile theoretical models with observations, the existence of a peculiar form of matter is postulated, the so called dark matter, which is supposed to be a cold and pressureless medium, whose distribution is that of a spherical halo around the galaxies. On the other hand, a lot of observations, such as the light curves of the type Ia supernovae and the cosmic microwave background (CMB) experiments (Riess et al. 1998;Perlmutter et al. 1999;Tonry et al. 2003;Bennet et al. 2003), firmly state that our Universe is now undergoing a phase of accelerated expansion. Actually, the present acceleration of the Universe cannot be explained, within GR, unless the existence of a cosmic fluid having exotic equation of state is postulated: the so-called dark energy.
The main problem dark matter and dark energy bring about is understanding their nature, since they are introduced as ad hoc gravity sources in a well defined model of gravity, i.e. GR (or Newtonian gravity). Of course, another possibility exists: GR (and its approximation, Newtonian gravity) is unfit to deal with gravitational interaction at galactic, intergalactic and cosmological scales. The latter viewpoint, led to the introduction of various modifications of gravity (Nojiri and Odintsov 2007;Esposito-Farèse 2008).
However, we must remember that, even though there are problems with galaxies and clusters dynamics and cosmological observations, GR is in excellent agreement with the Solar System experiments (see Will (2006) and Damour (2006)): hence, every theory that aims at explaining the large scale dynamics and the accelerated expansion of the Universe, should reproduce GR at the Solar System scale, i.e. in a suitable weak field limit. So, the viability of these modified theories of gravity at Solar System scale should be studied with great care.
In this paper we wish to quantitatively deal with such a problem by means of the secular (i.e. averaged over one orbital revolution) precessions of the longitudes of the perihelia ̟ of some planets of the Solar System (see also (Iorio 2007a,b)) in the following way. Generally speaking, let LRMOG (Long-Range Modified Model of Gravity) be a given exotic model of modified gravity parameterized in terms of, say, K, in a such a way that K = 0 would imply no modifications of gravity at all. Let P(LRMOG) be the prediction of a certain effect induced by such a model like, e.g., the secular precession of the perihelion of a planet. For all the exotic models considered it turns out that
where g is a function of the system’s orbital parameters a (semimajor axis) and e (eccentricity); such g is a peculiar consequence of the model LRMOG (and of all other models of its class with the same spatial variability). Now, let us take the ratio of P(LRMOG) for two different systems A and B, e.g. two Solar System’s planets:
but we still have a prediction that retains a peculiar signature of that model, i.e. g A /g B .
Of course, such a prediction is valid if we assume K is not zero, which is just the case both theoretically (LRMOG is such that should K be zero, no modifications of gravity at all occurred) and observationally because K is usually determined by other independent long-range astrophysical/cosmological observations. Otherwise, one would have the meaningless prediction 0/0. The case K = 0 (or K ≤ K) can be, instead, usually tested by taking one perihelion precession at a time, as already done, e.g., by Iorio (2007a,b).
If we have observational determinations O for A and B of the effect considered above such that they are affected also 1 by LRMOG (it is just the case for the purely phenomenologically estimated corrections to the standard Newton-Einstein perihelion precessions, since LRMOG has not been included in the dynamical force models of the ephemerides adjusted to the planetary data in the least-square parameters’ estimation process by Pitjeva (Pitjeva 2005a(Pitjeva ,b, 2006b))
within the errors, LRMOG survives (and the use of the single perihelion precessions can be used to put upper bounds on K). Otherwise, LRMOG is ruled out.
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