Inverse-Power-Law Scalar-Field Cosmology in (n+2) Dimensions: Slow- Roll Evolution and de Sitter-Like Asymptotics

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DEMIREL E. C. G., İHSAN Y.

Journal of advanced research in natural and applied sciences (Online), cilt.12, sa.3, ss.389-397, 2026 (TRDizin)

Özet

Abstract − This study investigates a homogeneous canonical scalar field with an inverse-power-law potential in an (𝑛 + 2)-dimensional spatially flat Friedmann-Robertson-Walker/Friedmann- Lemaître-Robertson-Walker (FRW/FLRW) spacetime. The approximately 5% baryonicmatter, 25% dark-matter, and 70% dark-energy fractions are used only as present-day observational motivation and are not imposed as fixed weights in the scalar-field dynamics. Using the metric signature (+, −, . . . , −), the scalar-field definition and the higher-dimensional Friedmann, acceleration, Klein-Gordon, and conservation equations are formulated consistently with the gravitational coupling 𝐺ₙ₊₂. For 𝐾 > 0, 𝛼 > 0, 𝜙 > 0, and integer 𝑛 ≥ 2, the scalar-fielddominated late-time regime is analyzed under the slow-roll approximation. The solution obeys an asymptotic power-law scaling with exponent 2/(𝛼 + 4). Substitution back into the field equations shows that the kinetic-to-potential-energy ratio, the second slow-roll ratio, and the Hubble slow-roll parameter all tend to zero. Consequently, the scalar-field equation-of-state parameter approaches -1 and the dimension-dependent acceleration condition is satisfied asymptotically. The resulting expansion is de Sitter-like in its equation-of-state and slow-roll behavior, although 𝐻 remains time dependent and the solution is not an exact de Sitter fixed point. The analysis is restricted to homogeneous background evolution; observational parameter fitting, perturbations, stability, and structure formation are left for future work.