Papers › Linear matter density perturbations in the $Λ_{\rm s}$CDM model: Examining growth...
Linear matter density perturbations in the $Λ_{\rm s}$CDM model: Examining growth dynamics and addressing the S₈ tension
Özgür Akarsu, Arman Çam, Evangelos A. Paraskevas, Leandros Perivolaropoulos
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We investigate linear matter density perturbations in the ΛₛCDM, in which the Λ is replaced by late-time (z∼2) mirror AdS-dS transition, resulting in distinct growth dynamics. We use two complementary approaches: (i) determining the initial density contrast and its evolution rate for a given collapse scale factor, (ii) computing the collapse scale factor for a specified initial density contrast and evolution rate. We derive analytical solutions for the growth rate f=Ωₘ^γ and growth index γ in both models. Prior to the transition, the AdS-like Λ reduces cosmic friction, causing linear matter density perturbations to grow more rapidly than in ΛCDM; this effect is most pronounced just before the transition, with a growth rate around 15% higher than ΛCDM around z∼2. After the transition, ΛₛCDM behaves similarly to ΛCDM but features a larger cosmological constant, leading to higher H(z) and greater cosmic friction that more effectively suppresses growth. Before the transition, γ remains below both the ΛCDM and EdS values (γ≈6/11); during the transition, it increases rapidly and then grows gradually, paralleling ΛCDM while remaining slightly higher in the post-transition era-though overall, it stays near γ∼0.55. Using the Planck best-fit values, Ωₘ₀=0.28 for ΛₛCDM and Ωₘ₀=0.32 for ΛCDM, we find f=0.49 and f=0.53, respectively. ΛₛCDM predicts a value of f=0.48, recently obtained from LSS data when γ is treated as a free parameter in ΛCDM. This suggests that ΛₛCDM may resolve the structure growth anomaly, without deviating from γ∼0.55.
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