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Register a new userSuppressed cosmic growth in coupled vector-tensor theories
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We study a coupled dark energy scenario in which a massive vector field $A_{mu}$ with broken $U(1)$ gauge symmetry interacts with the four-velocity $u_c^{mu}$ of cold dark matter (CDM) through the scalar product $Z=-u_c^{mu} A_{mu}$. This new coupling corresponds to the momentum transfer, so that the background vector and CDM continuity equations do not have explicit interacting terms analogous to the energy exchange. Hence the observational preference of uncoupled generalized Proca theories over the $Lambda$CDM model can be still maintained at the background level. Meanwhile, the same coupling strongly affects the evolution of cosmological perturbations. While the effective sound speed of CDM vanishes, the propagation speed and no-ghost condition of a longitudinal scalar of $A_{mu}$ and the CDM no-ghost condition are subject to nontrivial modifications by the $Z$ dependence in the Lagrangian. We propose a concrete dark energy model and show that the gravitational interaction on scales relevant to the linear growth of large-scale structures can be smaller than the Newton constant at low redshifts. This leads to the suppression of growth rates of both CDM and total matter density perturbations, so our model allows an interesting possibility for reducing the tension of matter density contrast $sigma_8$ between high- and low-redshift measurements.
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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.
In scalar-vector-tensor (SVT) theories with parity invariance, we perform a gauge-ready formulation of cosmological perturbations on the flat Friedmann-Lema^{i}tre-Robertson-Walker (FLRW) background by taking into account a matter perfect fluid. We derive the second-order action of scalar perturbations and resulting linear perturbation equations of motion without fixing any gauge conditions. Depending on physical problems at hand, most convenient gauges can be chosen to study the development of inhomogeneities in the presence of scalar and vector fields coupled to gravity. This versatile framework, which encompasses Horndeski and generalized Proca theories as special cases, is applicable to a wide variety of cosmological phenomena including nonsingular cosmology, inflation, and dark energy. By deriving conditions for the absence of ghost and Laplacian instabilities in several different gauges, we show that, unlike Horndeski theories, it is possible to evade no-go arguments for the absence of stable nonsingular bouncing/genesis solutions in both generalized Proca and SVT theories. We also apply our framework to the case in which scalar and vector fields are responsible for dark energy and find that the separation of observables relevant to the evolution of matter perturbations into tensor, vector, and scalar sectors is transparent in the unitary gauge. Unlike the flat gauge chosen in the literature, this result is convenient to confront SVT theories with observations associated with the cosmic growth history.
We investigate a dark energy scenario in which a canonical scalar field $phi$ is coupled to the four velocity $u_{c}^{mu}$ of cold dark matter (CDM) through a derivative interaction $u_{c}^{mu} partial_{mu} phi$. The coupling is described by an interacting Lagrangian $f(X, Z)$, where $f$ depends on $X=-partial^{mu} phi partial_{mu} phi/2$ and $Z=u_{c}^{mu} partial_{mu} phi$. We derive stability conditions of linear scalar perturbations for the wavelength deep inside the Hubble radius and show that the effective CDM sound speed is close to 0 as in the standard uncoupled case, while the scalar-field propagation speed is affected by the interacting term $f$. Under a quasi-static approximation, we also obtain a general expression of the effective gravitational coupling felt by the CDM perturbation. We study the late-time cosmological dynamics for the coupling $f propto X^{(2-m)/2}Z^m$ and show that the gravitational coupling weaker than the Newton constant can be naturally realized for $m>0$ on scales relevant to the growth of large-scale structures. This allows the possibility for alleviating the tension of $sigma_8$ between low- and high-redshift measurements.
In scalar-vector-tensor theories with $U(1)$ gauge invariance, it was recently shown that there exists a new type of hairy black hole (BH) solutions induced by a cubic-order scalar-vector interaction. In this paper, we derive conditions for the absence of ghosts and Laplacian instabilities against odd-parity perturbations on a static and spherically symmetric background for most general $U(1)$ gauge-invariant scalar-vector-tensor theories with second-order equations of motion. We apply those conditions to hairy BH solutions arising from the cubic-order coupling and show that the odd-parity stability in the gravity sector is always ensured outside the event horizon with the speed of gravity equivalent to that of light. We also study the case in which quartic-order interactions are present in addition to the cubic coupling and obtain conditions under which black holes are stable against odd-parity perturbations.
A stationary and spherically symmetric black hole (For example, Reissner-Nordstrom black hole or Kerr-Newman black hole) has at most one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? De Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves.
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