Abstract
AbstractThe generalized SU(2) Proca theory (GSU2P) is a variant of the well known generalized Proca theory where the vector field belongs to the Lie algebra of the SU(2) group of global transformations under which the action is made invariant. New interesting possibilities arise in this framework because of the existence of new interactions of purely non‐Abelian character and new configurations of the vector field resulting in spatial spherical symmetry and the cosmological dynamics being driven by the propagating degrees of freedom. We study the 2D phase space of the system that results when the cosmic triad configuration is employed in the Friedmann–Lemaitre–Robertson–Walker background and find an attractor curve whose attraction basin both covers almost all the allowed region and does not include a Big‐Bang singularity. Such an attractor curve corresponds to a primordial inflationary solution that has the following characteristic properties: 1) it is a de Sitter solution whose Hubble parameter is regulated by a generalized version of the SU(2) group coupling constant, 2) it is constant‐roll including, as a limiting case, the slow‐roll variety, 3) a number of e‐folds is easily reached, 4) it has a graceful exit into a radiation dominated period powered by the canonical kinetic term of the vector field and the Einstein–Hilbert term. The free parameters of the action are chosen such that the tensor sector of the theory is the same as that of general relativity at least up to second‐order perturbations, thereby avoiding the presence of ghost and Laplacian instabilities in the tensor sector as well as making the gravity waves propagate at light speed. This is a proof of concept of the interesting properties that could be found in this scenario when the coupling constants be replaced by general coupling functions and more terms be discovered in the GSU2P.
Highlights
Unless the evidence [1, 2, 3, 4] that General Relativity (GR) is non-perturbatively renormalizable becomes decisive, Einstein gravity continues to be an effective theory [5, 6]
One procedure general enough to produce these constraints, at least those primary, is to degenerate the kinetic Lagrangian. This procedure has been applied when the additional gravitational degree of freedom is of scalar nature, giving existence to the so called Degenerate Higher-Order Scalar-Tensor theory (DHOST) [17, 18, 19, 20], and when such a degree of freedom is of vector nature, giving existence to the so called Extended Vector-Tensor theory (EVT) [21]
In order to get a clear picture of what could happen in the most general situation, we have notoriously reduced the number of free parameters by analyzing the perturbative tensor sector of the theory and imposing conditions so that it takes the form shown in GR, at least up to second order
Summary
Unless the evidence [1, 2, 3, 4] that General Relativity (GR) is non-perturbatively renormalizable becomes decisive, Einstein gravity continues to be an effective theory [5, 6]. Such reconstruction paid careful attention to the covariantization process so that the beyond SU(2) Proca terms (parts of what would be an extended version of the GSU2P) were unveiled following the technique devised in Ref [60] It is the purpose of this paper to investigate the cosmological implications of the GSU2P, on the primordial inflationary period. The ghost and Laplacian instabilities problems in the tensor sector are solved while making the gravity waves propagate at light speed This is more than what is required in a perturbative analysis but perfectly fits our intention of easying the work and uncovering some interesting aspects of the dynamics that are likely present in the most general situation. The sign convention is the (+++) according to Misner, Thorne, and Wheeler [66]
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