Talk:Tensor-vector-scalar gravity

A modified gravity (MOG) has been published based on a symmetric pseudo-Riemannian metric and the Einstein-Hilbert action and an action formed from a skew symmetric third-rank tensor coupled to matter. This theory is called Metric-Skew-Tensor-Gravity (MSTG) [1]. A simpler version of this theory is based on an Einstein-Hilbert action and a second-rank skew symmetric tensor derived from the curl of a massive vector field called a phion field (particle). The gravitational "constant" G, the coupling "constant" and the effective mass of the phion field are described by spacetime dependent scalar fields in the action. This version of the theory is called Scalar-Vector-Tensor-Gravity (STVG) [2]. It can be proved that these theories are stable and are free from negative energy ghosts and tachyons (the Hamiltonian is bounded from below). The modified gravity theories are fully relativistic and generally covariant. The skew symmetric fields are interpreted as a "fifth force" in nature. The variation of the coupling constants and effective mass of the phion field can be understood in an asymptotically free quantum gravity scenario, using renormalization group (RG) flow techniques in which the constants are scale dependent and "run" with momentum and distance scale [3,1,2]. This scenario is analogous to the RG flow description of the running of coupling constants in the standard model of particle physics including quantum chromodynamics.

Both of these modified gravity theories lead to the same weak field consequences and determine the same modified acceleration law for weak gravitational fields. An extensive fitting to a large number of galaxy rotation curve data without exotic dark matter has been published [4]. When the photometric data describing the visible baryon matter disk, bulge and HI gas of galaxies is used, the fits only involve one free parameter -- the mass-to-light ratio <M/L>. An extensive fitting to x-ray galaxy clusters has also been published in which the fits to over 100 x-ray clusters is performed with effectively zero parameters without exotic dark matter [5]. The fits to the galaxy rotation curve data match closely the predictions of Milgrom's MOND formula [6] with a critical acceleration a_0. However, in contrast to STVG, MOND does not fit the x-ray cluster data without significant addition of dark matter. Moreover, the rotational velocity curves reduce at large distances from the galaxies (satellites) to their Kepler-Newtonian values. The modified gravity predicts lensing effects that agree with data without the need for unobserved dark matter. The theory can explain the Pioneer 10/11 anomalous acceleration data [7] if the anomaly has its origins in gravity. A fit to the available anomalous acceleration data for the Pioneer 10/11 spacecraft is obtained for a phenomenological representaion of the "running" constants and values of the associated parameters are shown to exist that are consistent with fifth force experimental bounds. An analysis of Kepler's third law for the varying gravitational constant, shows that the predicted anomalous acceleration is very small for the inner planets and grows to its observed value beyond Saturn's orbit. The predicted anomalous acceleration is consistent with all inner-planetary observations and with the JPL ephemerides data for the outer planets.

The cosmological consequences for MOG have been studied and the massive phion boson field is assumed to undergo a phase transition (spontaneous symmetry breaking) for a temperature below a critical value, T < T_c, generating an electrically neutral Bose-Einstein condensate (BEC) superfluid with zero viscosity and zero classical pressure [8]. This superfluid forms a second matter fluid in addition to the baryon-photon fluid before recombination. This allows for a fitting of the acoustic oscillation peaks observed in the cosmic microwave background (CMB) WMAP3 and combined world data. In particular, it predicts a third peak that cannot be obtained from only a baryon-photon fluid due to baryon drag. The BEC phion fluid produces a cosmological "dark" electrically neutral matter in addition to the visible baryons and photons. For the localized late-time galaxies and clusters of galaxies, the spontaneous symmetry breaking due to the non-vanishing vacuum expectation value of the phion field is relaxed and the BEC matter is dominated by visible baryon matter. The BEC matter only dominates over baryon and neutrino matter at large cosmological scales; in particular at the CMB surface of last scattering. In this way, the MOG describes a unified picture of the present data for the inner solar system, galaxies, clusters of galaxies and cosmology.

Recent published papers have described an inhomogeneous cosmology based on a spherically symmetric set of Einstein's field equations. Exact solutions of these equations for a matter dominated universe are described by the Lemaitre-Tolman-Bondi solutions. A large scale inhomogeneous enhancement at late times in the expanding universe can for an off-centered observer explain the "axis of evil" and the observed asymmetry of the anisotropy in the northern and southern celestial hemispheres [9]. It has also been shown that an explanation of the accelerating expansion of the universe can be obtained from the late-time exact inhomogeneous solution provided a suitable spatial volume averaging is performed over the data and the expression for the deceleration parameter q [10]. This can explain the acceleration of the universe without a quintessence "dark" energy or a cosmological constant and avoid the fine-tuned "coincidence" problem.

A new quantum field theory (QFT) and interpretation of the vacuum energy has been published in which the zero-point vacuum energy in relativistic QFT is shown to cancel due to the invariance of the vauum state with respect to a generalized dynamical charge conjugation operator The QFT is partly based on the work of Carl Bender and collaborators on non-Hermitian Hamiltonians. It incorporates a para-statistical Pauli exclusion pinciple for negative energy bosons in the vacuum, which stabilizises the vacuum and resolved the cosmological constant problem [11].

[1] J. W. Moffat, JCAP 0505 (2005) 003, astro-ph/0412195.

[2] J. W. Moffat, JCAP 0603 (2006) 004, gr-qc/0506021.

[3] M. Reuter and H. Weyer, JCAP 0412 (2004) 001, hep-th/0410119.

[4] J. R. Brownstein and J. W. Moffat, Astrophys.J. 636 (2006) 721-741, astro-ph/0506370.

[5] J. R. Brownstein and J. W. Moffat, Mon.Not.Roy.Astron.Soc. 367 (2006) 527-540,astro-ph/0507222.

[6] M. Milgrom, Astroph. J. 270, 365 (1983).

[7] J. R. Brownstein and J. W. Moffat, Class. Quantum Grav. 23 (2006) 3427-3436, gr-qc/0511026.

[8] J. W. Moffat, astro-ph/0602607.

[9] J. W. Moffat, JCAP 0510 (2005) 012, astro-ph/0502110.

[10] J. W. Moffat, JCAP 05 (2006) 001, astro-ph/0505326.

[11] J. W. Moffat, Phys.Lett. B627 (2005) 9-17, hep-th/0507020.