CONSTRUCTION OF MINIMAL THEORY OF MASS-VARYING MASSIVE GRAVITY AND ITS COSMOLOGICAL CONSEQUENCES - Khoirul Falah, Ahmad
Over the past two decades, the phenomena of the accelerating Universe have remained an open problem in the study of cosmology and theoretical physics. Standard arguments that are anchored on the role of cosmological constant also suffer from new problems which no less complicated. Moreover, speculations regarding the initial conditions of the expanding Universe—commonly associated with cosmological inflation scenarios—are currently undergoing empirical examination. Indeed, the general picture of inflationary mechanisms and characteristics is wellunderstood. However, a further substantial framework to explain detailed corresponding dynamics remains a subject worthy of exploration and development. This Dissertation proposes a new construction, i.e. the minimal theory of massvarying massive gravity (MTMVMG) as a novel theoretical framework conceived to shed light on these phenomena and speculations. The MTMVMG per se is a part of modified gravity classes based on the effective field theory of mass-varying gravitons through the minimalism program à la De Felice and Mukohyama. Consequently, Lorentz symmetry is explicitly broken and reduced to the spatial rotation invariance in the hypersurface. Furthermore, MTMVMG possesses three degrees of freedom, consistent with the theory of constant-mass gravity without Lorentz invariance, or equivalent to the theory of massless gravity coupled scalar field with Lorentz invariance. To uncover the cosmological aspects in MTMVMG, this Dissertation employs two analytical approaches, namely (i) dynamical system analysis and (ii) cosmological perturbation theory. From the dynamical system analysis, MTMVMG offers a cosmological description that fits the criteria of the early-time, intermediate, and late-time Universes. In the early-time, the expansion of the Universe was described by a cosmic inflation where the scale factor followed a power-law form. In the latetime, the acceleration of the Universe is driven by graviton mass that behaves as a cosmological-constant-like term or by external scalar field sectors—with gravitons can be massive or massless—that act similarly to the quintessence. On the other hand, from the cosmological perturbation theory, the construction of MTMVMG has tensor- and scalar-type active modes that propagates three degrees of freedom as described in the background. Thanks to the ansätze solution and some certain conditions, the construction is also free from various pathologies such as nonlinear ghost modes, gradient instability, and tachyon modes. The late-time accelerating Universe can be well-modeled through the application of psi-four form to the selfinteraction potential. Furthermore, the study of early-time expansion shows that de Sitter geometry—as a standard analytical framework to inflationary scenarios—can be constructed without the necessary to the slow-roll approximation. Remarkably, the MTMVMG cosmology establishes a relationship between the tensor-to-scalar ratio parameter and the scalar mode spectral index, which relatively overlaps with current observational constraints in Planck 2018 release. This Dissertation shows that MTMVMG has a promising avenue for advancing our understanding of the accelerating Universe and cosmological dynamics.