[Paper Review] The Lifetime of the Universe

Don N. Page|arXiv (Cornell University)|Sep 30, 2005

Cosmology and Gravitation Theories3 citations

TL;DR

This paper derives lower and upper bounds on the future lifetime of the universe using observational data on dark energy and theoretical assumptions about scalar field potentials. Assuming a non-convex dark energy potential, it finds a lower bound of 26 billion years; assuming exponential or power-law expansion, it sets upper bounds of ~10^60 years or e^{10^50} years, respectively, based on observer survival constraints in a multiverse framework.

ABSTRACT

Current observations of the fraction of dark energy and a lower limit on its tension, coupled with an assumption of the non-convexity of the dark energy potential, are used to derive a lower limit of 26 billion years for the future age of the universe. Conversely, our ordered observations, coupled with an assumption that observers are smaller than the universe, are used to argue for an upper limit of about e^10^50 years if the universe eventually undergoes power-law expansion, and an upper limit of only about 10^60 years left for our universe if it continues to expand exponentially at the current rate.

Motivation & Objective

• To establish a lower bound on the future lifetime of the universe using current dark energy observations and the assumption of a non-convex dark energy potential.
• To derive an upper bound on the universe's future lifetime based on the constraint that observers must be smaller than the universe and that our ordered observations are typical.
• To explore the implications of these bounds for the string landscape, particularly the existence and longevity of metastable vacua suitable for observers.
• To assess whether a cosmological constant with a lifetime exceeding ~10^60 years is consistent with our non-vacuum-fluctuation observations.
• To examine whether the observed dark energy is near a positive local minimum or if the universe is already sliding toward collapse.

Proposed method

• Uses a spatially flat Friedmann-Robertson-Walker (FRW) model with a scalar field φ and potential V(φ), incorporating dust and scalar field energy densities.
• Applies the equations of motion for H(t), φ(t), and v(t) = -dφ/dt, and eliminates time to derive first-order differential equations in terms of φ.
• Derives a second-order differential equation for K = (1/2)v² in terms of φ, enabling numerical or analytical solution for the evolution of the scalar field.
• Imposes boundary conditions at the present epoch (Ω_m0 ≈ 0.3, w₀ ≈ -1) to determine initial field values φ_i that reproduce current observations.
• Uses the ratio R = t_future / t_past to estimate the future lifetime relative to the past age of the universe.
• Applies the observer selection principle: if the universe were to expand to a volume exceeding e^{10^50}, vacuum fluctuations would produce too many observers, contradicting our ordered observations.

Experimental results

Research questions

• RQ1 What is the minimum possible future lifetime of the universe if the dark energy potential is non-convex and current observations are accurate?
• RQ2 What upper bound on the future lifetime of the universe can be derived from the assumption that observers are smaller than the universe and that our observations are typical?
• RQ3 How long can a universe with a positive cosmological constant (Λ > 0) last before vacuum fluctuations overwhelm ordered observations?
• RQ4 Are there significant long-lived positive metastable vacua in the string landscape that could support observers for longer than ~10^60 years?
• RQ5 Does the observed value of w(t) > -1 suggest that our universe is already sliding toward a Big Crunch rather than being in a stable de Sitter phase?

Key findings

• The future lifetime of the universe is bounded from below by 26 billion years, derived from current observations of dark energy and the assumption of a non-convex potential.
• If the universe undergoes power-law expansion, the upper bound on its future lifetime is approximately e^{10^50} years, based on observer selection constraints.
• For exponential expansion at the current rate (Λ > 0), the upper bound is ~10^60 years, as volumes larger than e^{10^50} would produce too many vacuum-fluctuation observers.
• The observed dark energy is unlikely to be a true cosmological constant unless it decays within ~10^60 years, as longer-lived de Sitter phases would be inconsistent with our ordered observations.
• The string landscape or stringscape should not contain significant numbers of long-lived positive metastable vacua with lifetimes exceeding ~10^60 years, as such vacua would dominate the observer count.
• The universe may already be sliding toward a Big Crunch if w(t) > -1, suggesting that the current dark energy is not in a stable minimum but in a transient, non-convex potential.