Verlindes heuristic argument for the interpretation of the standard Newtonian gravitational force as an entropic force is generalized by the introduction of a minimum temperature (or maximum wave length) for the microscopic degrees of freedom on the holographic screen. With the simplest possible setup, the resulting gravitational acceleration felt by a test mass m from a point mass M at a distance R is found to be of the form of the modified Newtonian dynamics (MOND) as suggested by Milgrom. The corresponding MOND-type acceleration constant is proportional to the minimum temperature, which can be interpreted as the Unruh temperature of an emerging de-Sitter space. This provides a possible explanation of the connection between local MOND-type two-body systems and cosmology.
We study the statistical mechanics of binary systems under gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems, in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of physical parameters of the binary system.
We review the effective field theory of modified gravity in which the Lagrangian involves three dimensional geometric quantities appearing in the 3+1 decomposition of space-time. On the flat isotropic cosmological background we expand a general action up to second order in the perturbations of geometric scalars, by taking into account spatial derivatives higher than two. Our analysis covers a wide range of gravitational theories-- including Horndeski theory/its recent generalizations and the projectable/non-projectab
Using a perturbative approach we solve stellar structure equations for low-density (solar-type) stars whose interior is described with a polytropic equation of state in scenarios involving a subset of modified gravity theories. Rather than focusing on particular theories, we consider a model-independent approach in which deviations from General Relativity are effectively described by a single parameter $xi$. We find that for length scales below those set by stellar General Relativistic radii the modifications introduced by modified gravity can affect the computed values of masses and radii. As a consequence, the stellar luminosity is also affected. We discuss possible further implications for higher density stars and observability of the effects before described.
Screened modified gravity (SMG) is a kind of scalar-tensor theories with screening mechanisms, which can generate screening effect to suppress the fifth force in high density environments and pass the solar system tests. Meanwhile, the potential of scalar field in the theories can drive the acceleration of the late universe. In this paper, we calculate the parameterized post-Newtonian (PPN) parameters $gamma$ and $beta$, the effective gravitational constant $G_{rm eff}$ and the effective cosmological constant $Lambda$ for SMG with a general potential $V$ and coupling function $A$. The dependence of these parameters on the model parameters of SMG and/or the physical properties of the source object are clearly presented. As an application of these results, we focus on three specific theories of SMG (chameleon, symmetron and dilaton models). Using the formulae to calculate their PPN parameters and cosmological constant, we derive the constraints on the model parameters by combining the observations on solar system and cosmological scales.
I review the history and development of Modified Newtonian Dynamics (MOND) beginning with the phenomenological basis as it existed in the early 1980s. I consider Milgroms papers of 1983 introducing the idea and its consequences for galaxies and galaxy groups, as well as the initial reactions, both negative and positive. The early criticisms were primarily on matters of principle, such as the absence of conservation laws and perceived cosmological problems; an important step in addressing these issues was the development of the Lagrangian-based non-relativistic theory of Bekenstein and Milgrom. This theory led to the development of a tentative relativistic theory that formed the basis for later multi-field theories of gravity. On an empirical level the predictive success of the idea with respect to the phenomenology of galaxies presents considerable challenges for cold dark matter. For MOND the essential challenge remains the absence of a generally accepted theoretical underpinning of the idea and, thus, cosmological predictions. I briefly review recent progress in this direction. Finally I discuss the role and sociology of unconventional ideas in astronomy in the presence of a strongly entrenched standard paradigm.