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Register a new userConformally Coupled Induced Gravity as an Infrared Fixed Point
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Yongsung Yoon
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We have found that the conformally coupled induced gravity can be an infrared fixed point of induced gravity with Yukawa couplings with matter. The late time cosmology with a uniform mean matter distribution can be described by the conformally coupled induced gravity, which has an emergent global conformal symmetry in the cosmic scale. Aiming to resolve the puzzles for the dark energy, we have obtained exact cosmological equations and determined the dark energy density, the matter density, and the jerk parameter in the present universe based on the recent observational cosmic expansion data for $a/H^{2}$.
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It is found that conformally coupled induced gravity with gradient torsion gives a dilaton gravity in Riemann geometry. In the Einstein frame of the dilaton gravity the conformal symmetry is hidden and a non-vanishing cosmological constant is not plausible due to the constraint of the conformal coupling.
In the present work we revisit a model consisting of a scalar field with a quartic self-interaction potential non-minimally (conformally) coupled to gravity [1]. When the scalar field vacuum is in a broken symmetry state, an effective gravitational constant emerges which, in certain regimes, can lead to gravitational repulsive effects when only ordinary radiation is coupled to gravity. In this case, a bouncing universe is shown to be the only cosmological solution admissible by the field equations when the scalar field is in such a broken symmetry state.
In this work by using a numerical analysis, we investigate in a quantitative way the late-time dynamics of scalar coupled $f(R,mathcal{G})$ gravity. Particularly, we consider a Gauss-Bonnet term coupled to the scalar field coupling function $xi(phi)$, and we study three types of models, one with $f(R)$ terms that are known to provide a viable late-time phenomenology, and two Einstein-Gauss-Bonnet types of models. Our aim is to write the Friedmann equation in terms of appropriate statefinder quantities frequently used in the literature, and we numerically solve it by using physically motivated initial conditions. In the case that $f(R)$ gravity terms are present, the contribution of the Gauss-Bonnet related terms is minor, as we actually expected. This result is robust against changes in the initial conditions of the scalar field, and the reason is the dominating parts of the $f(R)$ gravity sector at late times. In the Einstein-Gauss-Bonnet type of models, we examine two distinct scenarios, firstly by choosing freely the scalar potential and the scalar Gauss-Bonnet coupling $xi(phi)$, in which case the resulting phenomenology is compatible with the latest Planck data and mimics the $Lambda$-Cold-Dark-Matter model. In the second case, since there is no fundamental particle physics reason for the graviton to change its mass, we assume that primordially the tensor perturbations propagate with the speed equal to that of lights, and thus this constraint restricts the functional form of the scalar coupling function $xi(phi)$, which must satisfy the differential equation $ddot{xi}=Hdot{xi}$.
We consider modifications of general relativity characterized by a special noncovariant constraint on metric coefficients, which effectively generates a perfect-fluid type of matter stress tensor in Einstein equations. Such class of modified gravity models includes recently suggested generalized unimodular gravity (GUMG) theory and its simplest version -- unimodular gravity (UMG). We make these gravity models covariant by introducing four Stueckelberg fields and show that in the case of generalized unimodular gravity three out of these fields dynamically decouple. This means that the covariant form of generalized unimodular gravity is dynamically equivalent to k-essence theory with a specific Lagrangian which can be reconstructed from the parameters of GUMG theory. We provide the examples, where such reconstruction can be done explicitly, and briefly discuss theories beyond GUMG, related to self-gravitating media models. Also we compare GUMG k-inflation with cuscuton models of dynamically inert k-essence field and discuss motivation for GUMG coming from effective field theory.
We use the ideas of entropic gravity to derive the FRW cosmological model and show that for late time evolution we have an effective cosmological constant. By using the first law of thermodynamics and the modified entropy area relationship derived from the supersymmetric Wheeler-DeWitt equation of the Schwarzschild black hole, we obtain modifications to the Friedmann equations that in the late time regime gives an effective positive cosmological constant. Therefore, this simple model can account for the dark energy component of the universe by providing an entropic origin to the cosmological constant $Lambda$.
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