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Register a new userMimetic Tensor-Vector-Scalar Cosmology: Unified Dark Energy, Dark Matter and Stiff Matter
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Phenomenological implications of the Mimetic Tensor-Vector-Scalar theory (MiTeVeS) are studied. The theory is an extension of the vector field model of mimetic dark matter, where a scalar field is also incorporated, and it is known to be free from ghost instability. In the absence of interactions between the scalar field and the vector field, the obtained cosmological solution corresponds to the General theory of Relativity (GR) with a minimally-coupled scalar field. However, including an interaction term between the scalar field and the vector field yields interesting dynamics. There is a shift symmetry for the scalar field with a flat potential, and the conserved Noether current, which is associated with the symmetry, behaves as a dark matter component. Consequently, the solution contains a cosmological constant, dark matter and a stiff matter fluid. Breaking the shift symmetry with a non-flat potential gives a natural interaction between dark energy and dark matter.
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For a scalar field $phi$ coupled to cold dark matter (CDM), we provide a general framework for studying the background and perturbation dynamics on the isotropic cosmological background. The dark energy sector is described by a Horndeski Lagrangian with the speed of gravitational waves equivalent to that of light, whereas CDM is dealt as a perfect fluid characterized by the number density $n_c$ and four-velocity $u_c^mu$. For a very general interacting Lagrangian $f(n_c, phi, X, Z)$, where $f$ depends on $n_c$, $phi$, $X=-partial^{mu} phi partial_{mu} phi/2$, and $Z=u_c^{mu} partial_{mu} phi$, we derive the full linear perturbation equations of motion without fixing any gauge conditions. To realize a vanishing CDM sound speed for the successful structure formation, the interacting function needs to be of the form $f=-f_1(phi, X, Z)n_c+f_2(phi, X, Z)$. Employing a quasi-static approximation for the modes deep inside the sound horizon, we obtain analytic formulas for the effective gravitational couplings of CDM and baryon density perturbations as well as gravitational and weak lensing potentials. We apply our general formulas to several interacting theories and show that, in many cases, the CDM gravitational coupling around the quasi de-Sitter background can be smaller than the Newton constant $G$ due to a momentum transfer induced by the $Z$-dependence in $f_2$.
The recent observation of the the gravitational wave event GW170817 and of its electromagnetic counterpart GRB170817A, from a binary neutron star merger, has established that the speed of gravitational waves deviates from the speed of light by less than one part in $10^{15}$. As a consequence, many extensions of General Relativity are inevitably ruled out. Among these we find the most relevant sectors of Horndeski gravity. In its original formulation, mimetic gravity is able to mimic cosmological dark matter, has tensorial perturbations that travel exactly at the speed of light but has vanishing scalar perturbations and this fact persists if we combine mimetic with Horndeski gravity. In this work, we show that implementing the mimetic gravity action with higher-order terms that break the Horndeski structure yields a cosmological model that satisfies the constraint on the speed of gravitational waves and mimics both dark energy and dark matter with a non-vanishing speed of sound. In this way, we are able to reproduce the $Lambda$CDM cosmological model without introducing particle cold dark matter.
We derive the non-relativistic limit of a massive vector field. We show that the Cartesian spatial components of the vector behave as three identical, non-interacting scalar fields. We find classes of spherical, cylindrical, and planar self-gravitating vector solitons in the Newtonian limit. The gravitational properties of the lowest-energy vector solitons$mathrm{-}$the gravitational potential and density field$mathrm{-}$depend only on the net mass of the soliton and the vector particle mass. In particular, these self-gravitating, ground-state vector solitons are independent of the distribution of energy across the vector field components, and are indistinguishable from their scalar-field counterparts. Fuzzy Vector Dark Matter models can therefore give rise to halo cores with identical observational properties to the ones in scalar Fuzzy Dark Matter models. We also provide novel hedgehog vector soliton solutions, which cannot be observed in scalar-field theories. The gravitational binding of the lowest-energy hedgehog halo is about three times weaker than the ground-state vector soliton. Finally, we show that no spherically symmetric solitons exist with a divergence-free vector field.
Here we generalize ideas of unified Dark Matter Dark Energy in the context of Two Measure Theories and of Dynamical space time Theories. In Two Measure Theories one uses metric independent volume elements and this allows to construct unified Dark Matter Dark Energy, where the cosmological constant appears as an integration constant associated to the equation of motion of the measure fields. The Dynamical space time Theories generalize the Two Measure Theories by introducing a vector field whose equation of motion guarantees the conservation of a certain Energy Momentum tensor, which may be related, but in general is not the same as the gravitational Energy Momentum tensor. We propose two formulations of this idea: I - by demanding that this vector field be the gradient of a scalar, II - by considering the dynamical space field appearing in another part of the action. Then the Dynamical space time Theory becomes a theory of Diffusive Unified Dark Energy and Dark Matter. These generalizations produce non conserved energy momentum tensors instead of conserved energy momentum tensors which leads at the end to a formulation of interacting DE-DM dust models in the form of a diffusive type interacting Unified Dark Energy and Dark Matter scenario. We solved analytically the theories for perturbative solution and asymptotic solution, and we show that the $Lambda$CDM is a fixed point of these theories at large times. Also a preliminary argument about the good behavior of the theory at the quantum level is proposed for both theories.
We study the cosmology on the Friedmann-Lemaitre-Robertson-Walker background in scalar-vector-tensor theories with a broken $U(1)$ gauge symmetry. For parity-invariant interactions arising in scalar-vector-tensor theories with second-order equations of motion, we derive conditions for the absence of ghosts and Laplacian instabilities associated with tensor, vector, and scalar perturbations at linear order. This general result is applied to the computation of the primordial tensor power spectrum generated during inflation as well as to the speed of gravity relevant to dark energy. We also construct a concrete inflationary model in which a temporal vector component $A_0$ contributes to the dynamics of cosmic acceleration besides a scalar field $phi$ through their kinetic mixings. In this model, we show that all the stability conditions of perturbations can be consistently satisfied during inflation and subsequent reheating.
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