New cosmological solutions in massive gravity

Abstract

We find new, simple cosmological solutions with flat, open, and closed spatial geometries, contrary to the previous wisdom that only the open model is allowed. The metric and the Stückelberg fields are given explicitly, showing nontrivial configurations of the Stückelberg in the usual FriedmannLemaître-Robertson-Walker coordinates. The solutions exhibit self-acceleration, while being free from ghost instabilities. Our solutions can accommodate inhomogeneous dust collapse represented by the Lemaître-Tolman-Bondi metric as well. Thus, our results can be used not only to describe homogeneous and isotropic cosmology but also to study gravitational collapse in massive gravity.It is very intriguing to explore whether or not the graviton can have a mass. The first attempt to add a mass term to the gravity action was made by Fierz and Pauli [1], who considered the quadratic action for the graviton h µν in flat space with the mass termThe linear theory with the Fierz-Pauli mass term is ghost-free. However, the theory does not reproduce general relativity in the massless limit m → 0. The extra three degrees of freedom in a massive spin 2 survive even in this limit, and therefore the prediction for light bending is away from that of general relativity, which clearly contradicts solar-system tests. This is called the vDVZ discontinuity [2]. As pointed out by Vainshtein [3], the discontinuity can in fact be cured by going beyond the linear theory. Massive gravity has a new length scale called the Vainshtein radius, below which the nonlinearities of the theory come in and the effect of the extra degrees of freedom is screened safely. The Vainshtein radius becomes larger as m gets smaller, and thereby a smooth massless limit is attained.However, the very nonlinearities turned out to cause another trouble. Boulware and Deser argued that there appears a sixth scalar degree of freedom at nonlinear order, which has a wrong sign kinetic term, i.e., the sixth mode is a ghost [4]. The ghost issue was emphasized in the effective field theory approach in Ref. [5]. The presence of the Boulware-Deser (BD) ghost has hindered us from constructing a consistent theory of massive gravity.Recently, a theoretical breakthrough in this field has been made. Adding higher-order self-interaction terms and tuning appropriately their coefficients, de Rham and collaborators successfully eliminated the dangerous scalar mode from the theory in the decoupling limit [6,7]. Then, Hassan and Rosen established a complete proof that the theory does not suffer from the BD ghost instability to all orders in perturbations and away from the decoupling limit [8]. Thus, there certainly exists a nonlinear theory of massive gravity that is free of the BD ghost.In addition to the theoretical interests described above, the mystery of the accelerated expansion of the Universe [9] motivates massive gravity theories as a possible alternative to dark energy. Since the attractive force mediated by a massive graviton is Yukawa-suppressed by a factor e −mr , massive gravity t...

Nonlinear stability of cosmological solutions in massive gravity

“…For instance, there are such known solutions [13,[34][35][36][37][38][39], where the background dynamics is FLRW-like (or reduces to FLRW through cosmological Vainshtein mechanism [13]) while the Stückelberg sector is contaminated by spatial inhomogeneities. In principle, these may also evade the FLRW ghost, although in the lack of symmetry, the stability analysis of perturbations becomes technically challenging (although see [40]).…”

Beyond the cosmological standard model

“…In [217,218], de Rham, Gabadadze and Tolley (dRGT) found a loophole and constructed a theory that is free of this pathological sixth mode (this was shown conclusively in [634]). Much work has gone into studying this massive gravity theory: for example studies of cosmological solutions [635][636][637][638][639][640][641][642][643][644][645][646] and black holes [638,[647][648][649][650][651][652] have been undertaken. The theory can also be cast in a vielbein language, as opposed to as a theory of a metric [216,[653][654][655][656][657].…”

A study of universal thermodynamics in massive gravity: modified entropy on the horizons

“…Recently, de Rham, Gabadadze and Tolley (dGRT) formulated a nonlinear massive gravity theory which is free from BD ghost [35]. Subsequently, various cosmological solutions [36][37][38][39][40][41][42][43] have been evaluated using dGRT-massive gravity theory. To ensure that no ghost appears in the decoupling limit, the total action takes the form [35] …”