A Relativistic Origin for Early Cosm

Abstract

We propose an effective, relativistic mechanism for the early accelerated expansion of the Universe that does not require a fundamental inflaton field. Instead, we explore the consequences of a curvature–dependent suppression of local proper time in regimes of extreme spacetime curvature. Within the Einstein–Hilbert framework, and using a homogeneous and isotropic FRW geometry with a nontrivial lapse function, we introduce a phenomenological relation between the lapse and the spacetime curvature that is motivated by near–horizon time dilation and by the requirement that proper time nearly “freezes” in a high–curvature epoch. This “Relativistic Inflation via Clock-suppression” (RIC) produces a quasi–de Sitter background, with an effective equation of state close to w ≃ −1, without introducing a new scalar degree of freedom. Under the additional assumption that the RIC background can be embedded in the standard Effective Field Theory (EFT) of single-clock inflation with a canonical kinetic structure and sound speed cs ≃ 1, we show that the usual expressions for the scalar spectral index ns and tensor-to-scalar ratio r carry over with a generalized “slow-roll” parameter ϵRIC defined by the time variation of the Hubble rate in the curvature-suppressed regime. In this work, the EFT layer is treated as a post-processing framework applied to the RIC background, with assumptions stated explicitly. For a broad class of curvature–clock relations, we obtain ns ≃ 0.96 and predict a very small tensor amplitude r ≪ 10−2 , consistent with current CMB constraints and providing a clear target for future searches. We emphasize that our curvature–clock relation is phenomenological, not derived from a microscopic quantum gravity theory, and we discuss the limitations and testability of this approach. The framework significantly reduces model arbitrariness compared to generic inflaton potentials, while remaining falsifiable through the combination of scalar–tilt and tensor constraints.

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