Ultra-local models of modified gravity without kinetic term

Abstract

We present a class of modified-gravity theories which we call ultra-local models. We add a scalar field, with negligible kinetic terms, to the Einstein-Hilbert action. We also introduce a conformal coupling to matter. This gives rise to a new screening mechanism which is not entirely due to the non-linearity of the scalar field potential or the coupling function but to the absence of the kinetic term. As a result this removes any fifth force between isolated objects in vacuum. The predictions of these models only depend on a single free function, as the potential and the coupling function are degenerate, with an amplitude given by a parameter $\alpha \lesssim 10^{-6}$, whose magnitude springs from requiring a small modification of Newton's potential astrophysically and cosmologically. This singles out a redshift $z_{\alpha }\sim {\alpha }^{-1/3}\gtrsim 100$ where the fifth force is the greatest. The cosmological background follows the $\Lambda$-CDM history within a $10^{-6}$ accuracy, while cosmological perturbations are significantly enhanced (or damped) on small scales, $k\gtrsim 2h{\mathrm{Mpc}}^{-1}$ at $z=0$. The spherical collapse and the halo mass function are modified in the same manner. We find that the modifications of gravity are greater for galactic or sub-galactic structures. We also present a thermodynamic analysis of the non-linear and inhomogeneous fifth-force regime where we find that the Universe is not made more inhomogeneous before $z_{\alpha }$ when the fifth force dominates, and does not lead to the existence of clumped matter on extra small scales inside halos for large masses while this possibility exists for masses $M\lesssim 10^{11}{M}_{\odot }$ where the phenomenology of ultra-local models would be most different from $\Lambda$-CDM.

40 pages, 23 figures, updated references

References in corpus (21)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• The Structure of Cold Dark Matter Halos
• Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space
• The String Dilaton and a Least Coupling Principle
• Cosmology and fundamental physics with the Euclid satellite
• Varying constants, Gravitation and Cosmology
• Progress in Lunar Laser Ranging Tests of Relativistic Gravity
• The Confrontation between General Relativity and Experiment
• Halo Mass Function and the Free Streaming Scale
• Modified-Source Gravity and Cosmological Structure Formation
• Dynamics and thermodynamics of a simple model similar to self-gravitating systems: the HMF model
• Modified Gravity Tomography
• Impact on the power spectrum of Screening in Modified Gravity Scenarios
• K-mouflage Cosmology: Formation of Large-Scale Structures
• Thermodynamics and dynamics of a 1-D gravitational system
• Structure Formation in Modified Gravity Scenarios
• Mass functions and bias of dark matter halos
• Dynamics of Supersymmetric Chameleons
• SUPER-Screening
• Supersymmetric chameleons and ultra-local models

Cited by in corpus (3)

• Goldstone models of modified gravity
• New Bounds on Dark Energy Induced Fifth Forces
• $R^2$ Dark Energy in the Laboratory