A cyclic scale-invariance universe with negative variable cosmological constant

TL;DR

This work probes the sign problem of the cosmological constant in cyclic cosmology by adopting a negative, time-varying Λ(H) within a scale-invariance gravity framework. It uses a periodic deceleration parameter $q(t)=m\cos kt-1$ and derives a corresponding scale factor and modified Friedmann equations that yield $p$, $\rho$, and $\omega$ with Quintom-type behavior and periodic AdS minima separated by a barrier. The analysis shows AdS–dS transitions emerge through a sign flip of Λ within each cycle, driven by a nontrivial interplay between the kinetic term $K$, potential $V$, and the scalar field $\phi(t)$, where both $K$ and $V$ change sign. Nonlinear energy conditions are satisfied across cycles, and the work summarizes observational and theoretical support for negative Λ as a viable component of late-time acceleration.

Abstract

The AdS vacuum corresponds to a negative cosmological constant $Λ$. While it is well-motivated theoretically, There has always been controversy over its actual existence. The AdS-dS transition is corresponding to a sign switching $Λ$. We have proposed an ansatz for a negative time-varying cosmological constant $Λ(H)$ as a function of Hubble parameter $H$, and used it in constructing a periodic model with no future singularity in a scale-invariance gravity. With the proposed Ansatz for negative $Λ$, The model leads to a physically acceptable cosmic description, while we get unphysical parameters with the positive and zero values of $Λ$. The model reveals a Quintom behavior with a sign flipping of cosmic pressure during each period. The non-conventional mechanism of negative $Λ$ that are expected to address the late-time acceleration has been revisited.

Figures (3)

• Figure 1: Evolution of $\rho$, $p$, $\omega$ and $Q$. Same behavior repeats periodically for each cycle.
• Figure 2: Plots of $K$, $V$, $Q$, and the sum $V+Q$. The time evolution of the scalar and quantum potentials with the expected Anti-de Sitter (AdS) minima separated by a potential barrier with positive energy. Both $V$ and $K$ undergoes a sign change in each cycle. The minimum in $V(t)$ corresponds to the epoch when the field has reached its vacuum state, which physically means the universe’s dark-energy density has become constant. In general, the cyclic behavior may be obtained when a scalar field with a negative potential or a negative cosmological constant is introduced into a non-singular cosmological model, leading to a recollapse at some point in the evolution loop
• Figure 3: (c) Classical energy conditions: DEC is always satisfied while WEC is valid for half cycle. SEC is valid only at the start of the cycle during the decelerating era. (d) Nonlinear energy conditions: FEC is partially satisfied, DETEC and TOSEC are satisfied all the time.