tensorScalarRatio
plain-language theorem explainer
Tensor-to-scalar ratio r equals 16 times the first slow-roll parameter ε at positive field value φ. Cosmologists modeling J-cost inflation cite it when comparing predicted gravitational-wave amplitudes to CMB bounds. The definition is a direct scaling of the epsilon computed from the inflaton potential derivative.
Claim. The tensor-to-scalar ratio is $r(φ) = 16 ε(φ)$ for $φ > 0$, where $ε$ is the first slow-roll parameter obtained from the J-cost potential $V(φ) = ½(φ + φ^{-1}) - 1$.
background
Recognition Science identifies the inflaton with the J-cost field whose potential is $V(φ) = J(φ) = ½(φ + φ^{-1}) - 1$. This potential has a minimum at φ = 1 and grows linearly at large φ, producing a flat region suitable for slow roll. The first slow-roll parameter ε is defined as $(V'/V)^2/2$ and equals $1/(2φ^5)$ in the structural formulation of the same potential.
proof idea
The definition is a one-line wrapper that multiplies the local slowRollEpsilon by the constant 16. It applies the standard cosmological relation r = 16ε directly to the epsilon computed from inflatonPotential in the same module.
why it matters
This definition supplies the observable r for J-cost inflation and supports the statement that tensor modes remain small (r < 0.06). It completes the slow-roll parameter set needed to address horizon, flatness, and monopole problems via the J-cost slow-roll mechanism. The construction rests on J-uniqueness and the multiplicative cost structure, linking the phi-ladder to early-universe expansion.
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